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SCIENCEOF
EVERYDAY THINGS volume 1: REAL-LIFE CHEMISTRY
edited by NEIL SCHLAGER written by JUDSON KNIGHT A SCHLAGER INFORMATION GROUP BOOK
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S C I E N C E O F E V E RY DAY T H I N G S VOLUME 1
Re a l - L i f e c h e m i s t ry
A Schlager Information Group Book Neil Schlager, Editor Written by Judson Knight Gale Group Staff Kimberley A. McGrath, Senior Editor Maria Franklin, Permissions Manager Margaret A. Chamberlain, Permissions Specialist Shalice Shah-Caldwell, Permissions Associate Mary Beth Trimper, Manager, Composition and Electronic Prepress Evi Seoud, Assistant Manager, Composition and Electronic Prepress Dorothy Maki, Manufacturing Manager Rita Wimberley, Buyer Michelle DiMercurio, Senior Art Director Barbara J. Yarrow, Manager, Imaging and Multimedia Content Robyn V. Young, Project Manager, Imaging and Multimedia Content Leitha Etheridge-Sims, Mary K. Grimes, and David G. Oblender, Image Catalogers Pam A. Reed, Imaging Coordinator Randy Bassett, Imaging Supervisor Robert Duncan, Senior Imaging Specialist Dan Newell, Imaging Specialist While every effort has been made to ensure the reliability of the information presented in this publication, Gale Group does not guarantee the accuracy of the data contained herein. Gale accepts no payment for listing, and inclusion in the publication of any organization, agency, institution, publication, service, or individual does not imply endorsement of the editors and publisher. Errors brought to the attention of the publisher and verified to the satisfaction of the publisher will be corrected in future editions. The paper used in the publication meets the minimum requirements of American National Standard for Information Sciences—Permanence Paper for Printed Library Materials, ANSI Z39.48-1984. This publication is a creative work fully protected by all applicable copyright laws, as well as by misappropriation, trade secret, unfair competition, and other applicable laws. The authors and editors of this work have added value to the underlying factual material herein through one or more of the following: unique and original selection, coordination, expression, arrangement, and classification of the information. All rights to this publication will be vigorously defended. Copyright © 2002 Gale Group, 27500 Drake Road, Farmington Hills, Michigan 48331-3535 No part of this book may be reproduced in any form without permission in writing from the publisher, except by a reviewer who wishes to quote brief passages or entries in connection with a review written for inclusion in a magazine or newspaper. ISBN
0-7876-5631-3 (set) 0-7876-5632-1 (vol. 1) 0-7876-5633-X (vol. 2)
0-7876-5634-8 (vol. 3) 0-7876-5635-6 (vol. 4)
Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
Library of Congress Cataloging-in-Publication Data Knight, Judson. Science of everyday things / written by Judson Knight, Neil Schlager, editor. p. cm. Includes bibliographical references and indexes. Contents: v. 1. Real-life chemistry – v. 2 Real-life physics. ISBN 0-7876-5631-3 (set : hardcover) – ISBN 0-7876-5632-1 (v. 1) – ISBN 0-7876-5633-X (v. 2) 1. Science–Popular works. I. Schlager, Neil, 1966-II. Title. Q162.K678 2001 500–dc21
2001050121
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CONTENTS
Introduction.............................................v Advisory Board ......................................vii
MEASUREMENT Measurement ......................................................3 Temperature and Heat......................................11 Mass, Density, and Volume ..............................23
NONMETALS AND METALLOIDS Nonmetals ......................................................213 Metalloids .......................................................222 Halogens .........................................................229 Noble Gases ....................................................237 Carbon............................................................243 Hydrogen ........................................................252
MATTER Properties of Matter .........................................32 Gases..................................................................48 ATOMS AND MOLECULES Atoms ................................................................63 Atomic Mass......................................................76 Electrons............................................................84 Isotopes .............................................................92 Ions and Ionization........................................101 Molecules........................................................109
BONDING AND REACTIONS Chemical Bonding .........................................263 Compounds....................................................273 Chemical Reactions........................................281 Oxidation-Reduction Reactions....................289 Chemical Equilibrium ...................................297 Catalysts..........................................................304 Acids and Bases ..............................................310 Acid-Base Reactions.......................................319
ELEMENTS SOLUTIONS AND MIXTURES Elements .........................................................119 Periodic Table of Elements ............................127 Families of Elements......................................140
Mixtures..........................................................329 Solutions.........................................................338 Osmosis ..........................................................347
METALS Metals..............................................................149 Alkali Metals...................................................162 Alkaline Earth Metals ....................................171 Transition Metals ...........................................181 Actinides .........................................................196 Lanthanides ....................................................205
S C I E N C E O F E V E RY DAY T H I N G S
Distillation and Filtration..............................354 ORGANIC CHEMISTRY Organic Chemistry ........................................363 Polymers .........................................................372 General Subject Index ......................381
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INTRODUCTION
Overview of the Series Welcome to Science of Everyday Things. Our aim is to explain how scientific phenomena can be understood by observing common, real-world events. From luminescence to echolocation to buoyancy, the series will illustrate the chief principles that underlay these phenomena and explore their application in everyday life. To encourage cross-disciplinary study, the entries will draw on applications from a wide variety of fields and endeavors. Science of Everyday Things initially comprises four volumes: Volume 1: Real-Life Chemistry Volume 2: Real-Life Physics Volume 3: Real-Life Biology Volume 4: Real-Life Earth Science Future supplements to the series will expand coverage of these four areas and explore new areas, such as mathematics.
Arrangement of Real-Life Physics This volume contains 40 entries, each covering a different scientific phenomenon or principle. The entries are grouped together under common categories, with the categories arranged, in general, from the most basic to the most complex. Readers searching for a specific topic should consult the table of contents or the general subject index.
• How It Works Explains the principle or theory in straightforward, step-by-step language. • Real-Life Applications Describes how the phenomenon can be seen in everyday events. • Where to Learn More Includes books, articles, and Internet sites that contain further information about the topic. Each entry also includes a “Key Terms” section that defines important concepts discussed in the text. Finally, each volume includes numerous illustrations, graphs, tables, and photographs. In addition, readers will find the comprehensive general subject index valuable in accessing the data.
About the Editor, Author, and Advisory Board Neil Schlager and Judson Knight would like to thank the members of the advisory board for their assistance with this volume. The advisors were instrumental in defining the list of topics, and reviewed each entry in the volume for scientific accuracy and reading level. The advisors include university-level academics as well as high school teachers; their names and affiliations are listed elsewhere in the volume. N E I L S C H LAG E R is the president of
• Concept Defines the scientific principle or theory around which the entry is focused.
Schlager Information Group Inc., an editorial services company. Among his publications are When Technology Fails (Gale, 1994); How Products Are Made (Gale, 1994); the St. James Press Gay and Lesbian Almanac (St. James Press, 1998); Best Literature By and About Blacks (Gale,
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Within each entry, readers will find the following rubrics:
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2000); Contemporary Novelists, 7th ed. (St. James Press, 2000); and Science and Its Times (7 vols., Gale, 2000-2001). His publications have won numerous awards, including three RUSA awards from the American Library Association, two Reference Books Bulletin/Booklist Editors’ Choice awards, two New York Public Library Outstanding Reference awards, and a CHOICE award for best academic book. Judson Knight is a freelance writer, and author of numerous books on subjects ranging from science to history to music. His work on science titles includes Science, Technology, and Society, 2000 B.C.-A.D. 1799 (U*X*L, 2002), as well as extensive contributions to Gale’s seven-volume Science and Its Times (2000-2001). As a writer on history, Knight has published Middle Ages Reference Library (2000), Ancient
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Civilizations (1999), and a volume in U*X*L’s African American Biography series (1998). Knight’s publications in the realm of music include Parents Aren’t Supposed to Like It (2001), an overview of contemporary performers and genres, as well as Abbey Road to Zapple Records: A Beatles Encyclopedia (Taylor, 1999). His wife, Deidre Knight, is a literary agent and president of the Knight Agency. They live in Atlanta with their daughter Tyler, born in November 1998.
Comments and Suggestions Your comments on this series and suggestions for future editions are welcome. Please write: The Editor, Science of Everyday Things, Gale Group, 27500 Drake Road, Farmington Hills, MI 48331.
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ADVISORY BO T IATR LD E
William E. Acree, Jr. Professor of Chemistry, University of North Texas Russell J. Clark Research Physicist, Carnegie Mellon University Maura C. Flannery Professor of Biology, St. John’s University, New York John Goudie Science Instructor, Kalamazoo (MI) Area Mathematics and Science Center Cheryl Hach Science Instructor, Kalamazoo (MI) Area Mathematics and Science Center Michael Sinclair Physics instructor, Kalamazoo (MI) Area Mathematics and Science Center Rashmi Venkateswaran Senior Instructor and Lab Coordinator, University of Ottawa Ottawa, Ontario, Canada
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S C I E N C E O F E V E RY DAY T H I N G S real-life chemistry
MEASUREMENT MEASUREMENT T E M P E RAT U R E A N D H E AT M A S S , D E N S I T Y, A N D V O L U M E
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Measurement
MEASUREMENT
CONCEPT Measurement seems like a simple subject, on the surface at least; indeed, all measurements can be reduced to just two components: number and unit. Yet one might easily ask, “What numbers, and what units?”—a question that helps bring into focus the complexities involved in designating measurements. As it turns out, some forms of numbers are more useful for rendering values than others; hence the importance of significant figures and scientific notation in measurements. The same goes for units. First, one has to determine what is being measured: mass, length, or some other property (such as volume) that is ultimately derived from mass and length. Indeed, the process of learning how to measure reveals not only a fundamental component of chemistry, but an underlying—if arbitrary and manmade— order in the quantifiable world.
HOW IT WORKS Numbers
Obviously, there is an arbitrary quality underlying the modern numerical system, yet it works extremely well. In particular, the use of decimal fractions (for example, 0.01 or 0.235) is particularly helpful for rendering figures other than whole numbers. Yet decimal fractions are a relatively recent innovation in Western mathematics, dating only to the sixteenth century. In order to be workable, decimal fractions rely on an even more fundamental concept that was not always part of Western mathematics: place-value.
Place-Value and Notation Systems Place-value is the location of a number relative to others in a sequence, a location that makes it possible to determine the number’s value. For instance, in the number 347, the 3 is in the hundreds place, which immediately establishes a value for the number in units of 100. Similarly, a person can tell at a glance that there are 4 units of 10, and 7 units of 1. Of course, today this information appears to be self-evident—so much so that an explanation of it seems tedious and perfunctory—to almost anyone who has completed elementary-school arithmetic. In fact, however, as with almost everything about numbers and units, there is nothing obvious at all about place-value; otherwise, it would not have taken Western mathematicians thousands of years to adopt a placevalue numerical system. And though they did eventually make use of such a system, Westerners did not develop it themselves, as we shall see.
In modern life, people take for granted the existence of the base-10, of decimal numeration system—a name derived from the Latin word decem, meaning “ten.” Yet there is nothing obvious about this system, which has its roots in the ten fingers used for basic counting. At other times in history, societies have adopted the two hands or arms of a person as their numerical frame of reference, and from this developed a base-2 system. There have also been base-5 systems relating to the fingers on one hand, and base-20 systems that took as their reference point the combined number of fingers and toes.
R O M A N N U M E RA L S . Numeration systems of various kinds have existed since at least 3000 B.C., but the most important number
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instance, trying to multiply these two. With the number system in use today, it is not difficult to multiply 3,000 by 438 in one’s head. The problem can be reduced to a few simple steps: multiply 3 by 400, 3 by 30, and 3 by 8; add these products together; then multiply the total by 1,000—a step that requires the placement of three zeroes at the end of the number obtained in the earlier steps.
Measurement
But try doing this with Roman numerals: it is essentially impossible to perform this calculation without resorting to the much more practical place-value system to which we’re accustomed. No wonder, then, that Roman numerals have been relegated to the sidelines, used in modern life for very specific purposes: in outlines, for instance; in ordinal titles (for example, Henry VIII); or in designating the year of a motion picture’s release. H I N D U - A RA B I C
STANDARDIZATION IS CRUCIAL TO MAINTAINING STABILITY IN A SOCIETY. DURING THE GERMAN INFLATIONARY CRISIS OF THE 1920S, HYPERINFLATION LED TO AN ECONOMIC DEPRESSION AND THE RISE OF ADOLF HITLER. HERE, TWO CHILDREN GAZE UP AT A STACK OF 100,000 GERMAN MARKS—THE EQUIVALENT AT THE TIME TO ONE U.S. DOLLAR. (© Bettmann/Corbis.)
system in the history of Western civilization prior to the late Middle Ages was the one used by the Romans. Rome ruled much of the known world in the period from about 200 B.C. to about A.D. 200, and continued to have an influence on Europe long after the fall of the Western Roman Empire in A.D. 476—an influence felt even today. Though the Roman Empire is long gone and Latin a dead language, the impact of Rome continues: thus, for instance, Latin terms are used to designate species in biology. It is therefore easy to understand how Europeans continued to use the Roman numeral system up until the thirteenth century A.D.—despite the fact that Roman numerals were enormously cumbersome.
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N U M E RA L S .
The system of counting used throughout much of the world—1, 2, 3, and so on—is the HinduArabic notation system. Sometimes mistakenly referred to as “Arabic numerals,” these are most accurately designated as Hindu or Indian numerals. They came from India, but because Europeans discovered them in the Near East during the Crusades (1095-1291), they assumed the Arabs had invented the notation system, and hence began referring to them as Arabic numerals. Developed in India during the first millennium B.C., Hindu notation represented a vast improvement over any method in use up to or indeed since that time. Of particular importance was a number invented by Indian mathematicians: zero. Until then, no one had considered zero worth representing since it was, after all, nothing. But clearly the zeroes in a number such as 2,000,002 stand for something. They perform a place-holding function: otherwise, it would be impossible to differentiate between 2,000,002 and 22.
Uses of Numbers in Science
The Roman notation system has no means of representing place-value: thus a relatively large number such as 3,000 is shown as MMM, whereas a much smaller number might use many more “places”: 438, for instance, is rendered as CDXXXVIII. Performing any sort of calculations with these numbers is a nightmare. Imagine, for
S C I E N T I F I C N O TAT I O N . Chemists and other scientists often deal in very large or very small numbers, and if they had to write out these numbers every time they discussed them, their work would soon be encumbered by lengthy numerical expressions. For this purpose, they use scientific notation, a method for writing extremely large or small numbers by representing
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THE UNITED STATES NAVAL OBSERVATORY IN WASHINGTON, D.C., EXACT TIME OF DAY. (Richard T. Nowitz/Corbis. Reproduced by permission.)
them as a number between 1 and 10 multiplied by a power of 10. Instead of writing 75,120,000, for instance, the preferred scientific notation is 7.512 • 107. To interpret the value of large multiples of 10, it is helpful to remember that the value of 10 raised to any power n is the same as 1 followed by that number of zeroes. Hence 1025, for instance, is simply 1 followed by 25 zeroes. Scientific notation is just as useful—to chemists in particular—for rendering very small numbers. Suppose a sample of a chemical compound weighed 0.0007713 grams. The preferred scientific notation, then, is 7.713 • 10–4. Note that for numbers less than 1, the power of 10 is a negative number: 10–1 is 0.1, 10–2 is 0.01, and so on. Again, there is an easy rule of thumb for quickly assessing the number of decimal places where scientific notation is used for numbers less than 1. Where 10 is raised to any power –n, the decimal point is followed by n places. If 10 is raised to the power of –8, for instance, we know at a glance that the decimal is followed by 7 zeroes and a 1.
IS
AMERICA’S
PREEMINENT STANDARD FOR THE
calibration (discussed below) are very high, and the measuring instrument has been properly calibrated, the degree of uncertainty will be very small. Yet there is bound to be uncertainty to some degree, and for this reason, scientists use significant figures—numbers included in a measurement, using all certain numbers along with the first uncertain number. Suppose the mass of a chemical sample is measured on a scale known to be accurate to 10-5 kg. This is equal to 1/100,000 of a kilo, or 1/100 of a gram; or, to put it in terms of placevalue, the scale is accurate to the fifth place in a decimal fraction. Suppose, then, that an item is placed on the scale, and a reading of 2.13283697 kg is obtained. All the numbers prior to the 6 are significant figures, because they have been obtained with certainty. On the other hand, the 6 and the numbers that follow are not significant figures because the scale is not known to be accurate beyond 10-5 kg.
S I G N I F I CA N T F I G U R E S . In making measurements, there will always be a degree of uncertainty. Of course, when the standards of
Thus the measure above should be rendered with 7 significant figures: the whole number 2, and the first 6 decimal places. But if the value is given as 2.132836, this might lead to inaccuracies at some point when the measurement is factored into other equations. The 6, in fact, should be “rounded off ” to a 7. Simple rules apply to the
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rounding off of significant figures: if the digit following the first uncertain number is less than 5, there is no need to round off. Thus, if the measurement had been 2.13283627 kg (note that the 9 was changed to a 2), there is no need to round off, and in this case, the figure of 2.132836 is correct. But since the number following the 6 is in fact a 9, the correct significant figure is 7; thus the total would be 2.132837.
Fundamental Standards of Measure So much for numbers; now to the subject of units. But before addressing systems of measurement, what are the properties being measured? All forms of scientific measurement, in fact, can be reduced to expressions of four fundamental properties: length, mass, time, and electric current. Everything can be expressed in terms of these properties: even the speed of an electron spinning around the nucleus of an atom can be shown as “length” (though in this case, the measurement of space is in the form of a circle or even more complex shapes) divided by time. Of particular interest to the chemist are length and mass: length is a component of volume, and both length and mass are elements of density. For this reason, a separate essay in this book is devoted to the subject of Mass, Density, and Volume. Note that “length,” as used in this most basic sense, can refer to distance along any plane, or in any of the three dimensions—commonly known as length, width, and height—of the observable world. (Time is the fourth dimension.) In addition, as noted above, “length” measurements can be circular, in which case the formula for measuring space requires use of the coefficient π, roughly equal to 3.14.
This is simple enough. But what if the motorist did not know how much gas was in a gallon, or if the motorist had some idea of a gallon that differed from what the gas station management determined it to be? And what if the value of a dollar were not established, such that the motorist and the gas station attendant had to haggle over the cost of the gasoline just purchased? The result would be a horribly confused situation: the motorist might run out of gas, or money, or both, and if such confusion were multiplied by millions of motorists and millions of gas stations, society would be on the verge of breakdown. T H E VA L U E O F S TA N D A R D I Z AT I O N T O A S O C I E T Y. Actually,
there have been times when the value of currency was highly unstable, and the result was near anarchy. In Germany during the early 1920s, for instance, rampant inflation had so badly depleted the value of the mark, Germany’s currency, that employees demanded to be paid every day so that they could cash their paychecks before the value went down even further. People made jokes about the situation: it was said, for instance, that when a woman went into a store and left a basket containing several million marks out front, thieves ran by and stole the basket—but left the money. Yet there was nothing funny about this situation, and it paved the way for the nightmarish dictatorship of Adolf Hitler and the Nazi Party.
People use units of measure so frequently in daily life that they hardly think about what they are doing. A motorist goes to the gas station and pumps 13 gallons (a measure of volume) into an automobile. To pay for the gas, the motorist uses dollars—another unit of measure, economic
It is understandable, then, that standardization of weights and measures has always been an important function of government. When Ch’in Shih-huang-ti (259-210 B.C.) united China for the first time, becoming its first emperor, he set about standardizing units of measure as a means of providing greater unity to the country—thus making it easier to rule. On the other hand, the Russian Empire of the late nineteenth century failed to adopt standardized systems that would have tied it more closely to the industrialized nations of Western Europe. The width of railroad tracks in Russia was different than in Western Europe, and Russia used the old Julian calendar, as opposed to the Gregorian calendar adopted throughout much of Western Europe after 1582. These and other factors made economic exchanges between Russia and Western Europe
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rather than scientific—in the form of paper money, a debit card, or a credit card.
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extremely difficult, and the Russian Empire remained cut off from the rapid progress of the West. Like Germany a few decades later, it became ripe for the establishment of a dictatorship—in this case under the Communists led by V. I. Lenin. Aware of the important role that standardization of weights and measures plays in the governing of a society, the U.S. Congress in 1901 established the Bureau of Standards. Today it is known as the National Institute of Standards and Technology (NIST), a nonregulatory agency within the Commerce Department. As will be discussed at the conclusion of this essay, the NIST maintains a wide variety of standard definitions regarding mass, length, temperature and so forth, against which other devices can be calibrated. T H E VA L U E O F S TA N D A R D I Z AT I O N T O S C I E N C E . What if a
nurse, rather than carefully measuring a quantity of medicine before administering it to a patient, simply gave the patient an amount that “looked right”? Or what if a pilot, instead of calculating fuel, distance, and other factors carefully before taking off from the runway, merely used a “best estimate”? Obviously, in either case, disastrous results would be likely to follow. Though neither nurses or pilots are considered scientists, both use science in their professions, and those disastrous results serve to highlight the crucial matter of using standardized measurements in science. Standardized measurements are necessary to a chemist or any scientist because, in order for an experiment to be useful, it must be possible to duplicate the experiment. If the chemist does not know exactly how much of a certain element he or she mixed with another to form a given compound, the results of the experiment are useless. In order to share information and communicate the results of experiments, then, scientists need a standardized “vocabulary” of measures. This “vocabulary” is the International System of Units, known as SI for its French name, Système International d’Unités. By international agreement, the worldwide scientific community adopted what came to be known as SI at the 9th General Conference on Weights and Measures in 1948. The system was refined at the 11th General Conference in 1960, and given its present name; but in fact most components of SI belong to a much older system of weights and measures
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developed in France during the late eighteenth century.
Measurement
SI vs. the English System The United States, as almost everyone knows, is the wealthiest and most powerful nation on Earth. On the other hand, Brunei—a tiny nationstate on the island of Java in the Indonesian archipelago—enjoys considerable oil wealth, but is hardly what anyone would describe as a superpower. Yemen, though it is located on the Arabian peninsula, does not even possess significant oil wealth, and is a poor, economically developing nation. Finally, Burma in Southeast Asia can hardly be described even as a “developing” nation: ruled by an extremely repressive military regime, it is one of the poorest nations in the world. So what do these four have in common? They are the only nations on the planet that have failed to adopt the metric system of weights and measures. The system used in the United States is called the English system, though it should more properly be called the American system, since England itself has joined the rest of the world in “going metric.” Meanwhile, Americans continue to think in terms of gallons, miles, and pounds; yet American scientists use the much more convenient metric units that are part of SI. HOW THE ENGLISH SYSTEM WORKS (OR DOES NOT WORK).
Like methods of counting described above, most systems of measurement in premodern times were modeled on parts of the human body. The foot is an obvious example of this, while the inch originated from the measure of a king’s first thumb joint. At one point, the yard was defined as the distance from the nose of England’s King Henry I to the tip of his outstretched middle finger. Obviously, these are capricious, downright absurd standards on which to base a system of measure. They involve things that change, depending for instance on whose foot is being used as a standard. Yet the English system developed in this willy-nilly fashion over the centuries; today, there are literally hundreds of units— including three types of miles, four kinds of ounces, and five kinds of tons, each with a different value. What makes the English system particularly cumbersome, however, is its lack of convenient
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conversion factors. For length, there are 12 inches in a foot, but 3 feet in a yard, and 1,760 yards in a mile. Where volume is concerned, there are 16 ounces in a pound (assuming one is talking about an avoirdupois ounce), but 2,000 pounds in a ton. And, to further complicate matters, there are all sorts of other units of measure developed to address a particular property: horsepower, for instance, or the British thermal unit (Btu). THE CONVENIENCE OF THE M E T R I C S Y S T E M . Great Britain, though
it has long since adopted the metric system, in 1824 established the British Imperial System, aspects of which are reflected in the system still used in America. This is ironic, given the desire of early Americans to distance themselves psychologically from the empire to which their nation had once belonged. In any case, England’s great worldwide influence during the nineteenth century brought about widespread adoption of the English or British system in colonies such as Australia and Canada. This acceptance had everything to do with British power and tradition, and nothing to do with convenience. A much more usable standard had actually been embraced 25 years before in a land that was then among England’s greatest enemies: France. During the period leading up to and following the French Revolution of 1789, French intellectuals believed that every aspect of existence could and should be treated in highly rational, scientific terms. Out of these ideas arose much folly, particularly during the Reign of Terror in 1793, but one of the more positive outcomes was the metric system. This system is decimal—that is, based entirely on the number 10 and powers of 10, making it easy to relate one figure to another. For instance, there are 100 centimeters in a meter and 1,000 meters in a kilometer. PREFIXES FOR SIZES IN THE M E T R I C S Y S T E M . For designating small-
er values of a given measure, the metric system uses principles much simpler than those of the English system, with its irregular divisions of (for instance) gallons, quarts, pints, and cups. In the metric system, one need only use a simple Greek or Latin prefix to designate that the value is multiplied by a given power of 10. In general, the prefixes for values greater than 1 are Greek, while Latin is used for those less than 1. These prefixes, along with their abbreviations and respective val-
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ues, are as follows. (The symbol µ for "micro" is the Greek letter mu.) The Most Commonly Used Prefixes in the Metric System giga (G) = 109 (1,000,000,000) mega (M) = 106 (1,000,000) kilo (k) == 103 (1,000) deci (d) = 10–1 (0.1) centi (c) = 10–2 (0.01) milli (m) = 10–3 (0.001) micro (µ) = 10–6 (0.000001) nano (n) = 10–9 (0.000000001) The use of these prefixes can be illustrated by reference to the basic metric unit of length, the meter. For long distances, a kilometer (1,000 m) is used; on the other hand, very short distances may require a centimeter (0.01 m) or a millimeter (0.001 m) and so on, down to a nanometer (0.000000001 m). Measurements of length also provide a good example of why SI includes units that are not part of the metric system, though they are convertible to metric units. Hard as it may be to believe, scientists often measure lengths even smaller than a nanometer—the width of an atom, for instance, or the wavelength of a light ray. For this purpose, they use the angstrom (Å or A), equal to 0.1 nanometers. • • • • • • • •
Calibration and SI Units T H E S E V E N B AS I C S I U N I T S .
The SI uses seven basic units, representing length, mass, time, temperature, amount of substance, electric current, and luminous intensity. The first four parameters are a part of everyday life, whereas the last three are of importance only to scientists. “Amount of substance” is the number of elementary particles in matter. This is measured by the mole, a unit discussed in the essay on Mass, Density, and Volume. Luminous intensity, or the brightness of a light source, is measured in candelas, while the SI unit of electric current is the ampere. The other four basic units are the meter for length, the kilogram for mass, the second for time, and the degree Celsius for temperature. The last of these is discussed in the essay on Temperature; as for meters, kilograms, and seconds, they will be examined below in terms of the means used to define each.
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C A L I B R AT I O N . Calibration is the process of checking and correcting the performance of a measuring instrument or device against the accepted standard. America’s preeminent standard for the exact time of day, for instance, is the United States Naval Observatory in Washington, D.C. Thanks to the Internet, people all over the country can easily check the exact time, and calibrate their clocks accordingly—though, of course, the resulting accuracy is subject to factors such as the speed of the Internet connection.
There are independent scientific laboratories responsible for the calibration of certain instruments ranging from clocks to torque wrenches, and from thermometers to laser-beam power analyzers. In the United States, instruments or devices with high-precision applications—that is, those used in scientific studies, or by high-tech industries—are calibrated according to standards established by the NIST. The NIST keeps on hand definitions, as opposed to using a meter stick or other physical model. This is in accordance with the methods of calibration accepted today by scientists: rather than use a standard that might vary—for instance, the meter stick could be bent imperceptibly—unvarying standards, based on specific behaviors in nature, are used.
Measurement
KEY TERMS The process of checking and correcting the performance of a measuring instrument or device against a commonly accepted standard. CALIBRATION:
A method used by scientists for writing extremely large or small numbers by representing them as a number between 1 and 10 multiplied by a power of 10. Instead of writing 0.0007713, the preferred scientific notation is 7.713 • 10–4. SCIENTIFIC NOTATION:
SI: An abbreviation of the French term Système International d’Unités, or International System of Units. Based on the metric system, SI is the system of measurement units in use by scientists worldwide.
Numbers included in a measurement, using all certain numbers along with the first uncertain number. SIGNIFICANT FIGURES:
M E T E R S A N D K I LO G RA M S . A
meter, equal to 3.281 feet, was at one time defined in terms of Earth’s size. Using an imaginary line drawn from the Equator to the North Pole through Paris, this distance was divided into 10 million meters. Later, however, scientists came to the realization that Earth is subject to geological changes, and hence any measurement calibrated to the planet’s size could not ultimately be reliable. Today the length of a meter is calibrated according to the amount of time it takes light to travel through that distance in a vacuum (an area of space devoid of air or other matter). The official definition of a meter, then, is the distance traveled by light in the interval of 1/299,792,458 of a second.
trary form of measure in comparison to the meter as it is defined today. Given the desire for an unvarying standard against which to calibrate measurements, it would be helpful to find some usable but unchanging standard of mass; unfortunately, scientists have yet to locate such a standard. Therefore, the value of a kilogram is calibrated much as it was two centuries ago. The standard is a bar of platinum-iridium alloy, known as the International Prototype Kilogram, housed near Sèvres in France. S E C O N D S . A second, of course, is a
One kilogram is, on Earth at least, equal to 2.21 pounds; but whereas the kilogram is a unit of mass, the pound is a unit of weight, so the correspondence between the units varies depending on the gravitational field in which a pound is measured. Yet the kilogram, though it represents a much more fundamental property of the physical world than a pound, is still a somewhat arbi-
unit of time as familiar to non-scientifically trained Americans as it is to scientists and people schooled in the metric system. In fact, it has nothing to do with either the metric system or SI. The means of measuring time on Earth are not “metric”: Earth revolves around the Sun approximately every 365.25 days, and there is no way to turn this into a multiple of 10 without creating a
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situation even more cumbersome than the English units of measure. The week and the month are units based on cycles of the Moon, though they are no longer related to lunar cycles because a lunar year would soon become out-of-phase with a year based on Earth’s rotation around the Sun. The continuing use of weeks and months as units of time is based on tradition—as well as the essential need of a society to divide up a year in some way. A day, of course, is based on Earth’s rotation, but the units into which the day is divided— hours, minutes, and seconds—are purely arbitrary, and likewise based on traditions of long standing. Yet scientists must have some unit of time to use as a standard, and, for this purpose, the second was chosen as the most practical. The SI definition of a second, however, is not simply one-sixtieth of a minute or anything else so strongly influenced by the variation of Earth’s movement.
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to vibrate 9,192,631,770 times. Expressed in scientific notation, with significant figures, this is 9.19263177 • 109. WHERE TO LEARN MORE Gardner, Robert. Science Projects About Methods of Measuring. Berkeley Heights, N.J.: Enslow Publishers, 2000. Long, Lynette. Measurement Mania: Games and Activities That Make Math Easy and Fun. New York: Wiley, 2001. “Measurement” (Web site). (May 7, 2001). “Measurement in Chemistry” (Web site). (May 7, 2001). MegaConverter 2 (Web site). (May 7, 2001). Patilla, Peter. Measuring. Des Plaines, IL: Heinemann Library, 2000.
Instead, the scientific community chose as its standard the atomic vibration of a particular isotope of the metal cesium, cesium-133. The vibration of this atom is presumed to be unvarying, because the properties of elements— unlike the size of Earth or its movement—do not change. Today, a second is defined as the amount of time it takes for a cesium-133 atom
Wilton High School Chemistry Coach (Web site). (May 7, 2001).
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Richards, Jon. Units and Measurements. Brookfield, CT: Copper Beech Books, 2000. Sammis, Fran. Measurements. New York: Benchmark Books, 1998. Units of Measurement (Web site). (May 7, 2001).
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Temperature and Heat
T E M P E R AT U R E A N D H E AT
CONCEPT Temperature, heat, and related concepts belong to the world of physics rather than chemistry; yet it would be impossible for the chemist to work without an understanding of these properties. Thermometers, of course, measure temperature according to one or both of two well-known scales based on the freezing and boiling points of water, though scientists prefer a scale based on the virtual freezing point of all matter. Also related to temperature are specific heat capacity, or the amount of energy required to change the temperature of a substance, and also calorimetry, the measurement of changes in heat as a result of physical or chemical changes. Although these concepts do not originate from chemistry but from physics, they are no less useful to the chemist.
HOW IT WORKS Energy The area of physics known as thermodynamics, discussed briefly below in terms of thermodynamics laws, is the study of the relationships between heat, work, and energy. Work is defined as the exertion of force over a given distance to displace or move an object, and energy is the ability to accomplish work. Energy appears in numerous manifestations, including thermal energy, or the energy associated with heat.
ing, and when those bonds are broken, the forces joining the atoms are released in the form of chemical energy. Another example of chemical energy release is combustion, whereby chemical bonds in fuel, as well as in oxygen molecules, are broken and new chemical bonds are formed. The total energy in the newly formed chemical bonds is less than the energy of the original bonds, but the energy that makes up the difference is not lost; it has simply been released. Energy, in fact, is never lost: a fundamental law of the universe is the conservation of energy, which states that in a system isolated from all other outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place. When a fire burns, then, some chemical energy is turned into thermal energy. Similar transformations occur between these and other manifestations of energy, including electrical and magnetic (sometimes these two are combined as electromagnetic energy), sound, and nuclear energy. If a chemical reaction makes a noise, for instance, some of the energy in the substances being mixed has been dissipated to make that sound. The overall energy that existed before the reaction will be the same as before; however, the energy will not necessarily be in the same place as before.
Another type of energy—one of particular interest to chemists—is chemical energy, related to the forces that attract atoms to one another in chemical bonds. Hydrogen and oxygen atoms in water, for instance, are joined by chemical bond-
Note that chemical and other forms of energy are described as “manifestations,” rather than “types,” of energy. In fact, all of these can be described in terms of two basic types of energy: kinetic energy, or the energy associated with movement, and potential energy, or the energy associated with position. The two are inversely related: thus, if a spring is pulled back to its maximum point of tension, its potential energy is
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coldness is a recognizable sensory experience in human life, in scientific terms, cold is simply the absence of heat.
Temperature and Heat
If you grasp a snowball in your hand, the hand of course gets cold. The mind perceives this as a transfer of cold from the snowball, but in fact exactly the opposite has happened: heat has moved from your hand to the snow, and if enough heat enters the snowball, it will melt. At the same time, the departure of heat from your hand results in a loss of internal energy near the surface of the hand, experienced as a sensation of coldness.
Understanding Temperature
DURING
HIS LIFETIME,
GALILEO
CONSTRUCTED A THER-
MOSCOPE, THE FIRST PRACTICAL TEMPERATURE-MEASURING DEVICE. (Archive Photos, Inc. Reproduced by permission.)
also at a maximum, while its kinetic energy is zero. Once it is released and begins springing through the air to return to the position it maintained before it was stretched, it begins gaining kinetic energy and losing potential energy.
Heat Thermal energy is actually a form of kinetic energy generated by the movement of particles at the atomic or molecular level: the greater the movement of these particles, the greater the thermal energy. When people use the word “heat” in ordinary language, what they are really referring to is “the quality of hotness”—that is, the thermal energy internal to a system. In scientific terms, however, heat is internal thermal energy that flows from one body of matter to another— or, more specifically, from a system at a higher temperature to one at a lower temperature. Two systems at the same temperature are said to be in a state of thermal equilibrium. When this state exists, there is no exchange of heat. Though in everyday terms people speak of “heat” as an expression of relative warmth or coldness, in scientific terms, heat exists only in transfer between two systems. Furthermore, there can never be a transfer of “cold”; although
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Just as heat does not mean the same thing in scientific terms as it does in ordinary language, so “temperature” requires a definition that sets it apart from its everyday meaning. Temperature may be defined as a measure of the average internal energy in a system. Two systems in a state of thermal equilibrium have the same temperature; on the other hand, differences in temperature determine the direction of internal energy flow between two systems where heat is being transferred. This can be illustrated through an experience familiar to everyone: having one’s temperature taken with a thermometer. If one has a fever, the mouth will be warmer than the thermometer, and therefore heat will be transferred to the thermometer from the mouth. The thermometer, discussed in more depth later in this essay, measures the temperature difference between itself and any object with which it is in contact.
Temperature and Thermodynamics One might pour a kettle of boiling water into a cold bathtub to heat it up; or one might put an ice cube in a hot cup of coffee “to cool it down.” In everyday experience, these seem like two very different events, but from the standpoint of thermodynamics, they are exactly the same. In both cases, a body of high temperature is placed in contact with a body of low temperature, and in both cases, heat passes from the high-temperature body to the low-temperature body. The boiling water warms the tub of cool water, and due to the high ratio of cool water to boiling water in the bathtub, the boiling water
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Temperature and Heat
BECAUSE
OF WATER’S HIGH SPECIFIC HEAT CAPACITY, CITIES LOCATED NEXT TO LARGE BODIES OF WATER TEND TO
STAY WARMER IN THE WINTER AND COOLER IN THE SUMMER.
CHICAGO’S
DURING
LAKEFRONT STAYS COOLER THAN AREAS FURTHER INLAND.
THE EARLY SUMMER MONTHS, FOR INSTANCE,
THIS
IS BECAUSE THE LAKE IS COOLED FROM
THE WINTER’S COLD TEMPERATURES AND SNOW RUNOFF. (Farrell Grehan/Corbis. Reproduced by permission.)
expends all its energy raising the temperature in the bathtub as a whole. The greater the ratio of very hot water to cool water, of course, the warmer the bathtub will be in the end. But even after the bath water is heated, it will continue to lose heat, assuming the air in the room is not warmer than the water in the tub—a safe assumption. If the water in the tub is warmer than the air, it will immediately begin transferring thermal energy to the lower-temperature air until their temperatures are equalized. As for the coffee and the ice cube, what happens is opposite to the explanation ordinarily given. The ice does not “cool down” the coffee: the coffee warms up, and presumably melts, the ice. However, it expends at least some of its thermal energy in doing so, and, as a result, the coffee becomes cooler than it was.
namics laws as a set of rules governing an impossible game. The first law of thermodynamics is essentially the same as the conservation of energy: because the amount of energy in a system remains constant, it is impossible to perform work that results in an energy output greater than the energy input. It could be said that the conservation of energy shows that “the glass is half full”: energy is never lost. By contrast, the first law of thermodynamics shows that “the glass is half empty”: no system can ever produce more energy than was put into it. Snow therefore summed up the first law as stating that the game is impossible to win.
ond of the three laws of thermodynamics. Not only do these laws help to clarify the relationship between heat, temperature, and energy, but they also set limits on what can be accomplished in the world. Hence British writer and scientist C. P. Snow (1905-1980) once described the thermody-
The second law of thermodynamics begins from the fact that the natural flow of heat is always from an area of higher temperature to an area of lower temperature—just as was shown in the bathtub and coffee cup examples above. Consequently, it is impossible for any system to take heat from a source and perform an equivalent amount of work: some of the heat will always be lost. In other words, no system can ever be perfectly efficient: there will always be a degree of
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THE LAWS OF THERMODYN A M I CS . These situations illustrate the sec-
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breakdown, evidence of a natural tendency called entropy. Snow summed up the second law of thermodynamics, sometimes called “the law of entropy,” thus: not only is it impossible to win, it is impossible to break even. In effect, the second law compounds the “bad news” delivered by the first with some even worse news. Though it is true that energy is never lost, the energy available for work output will never be as great as the energy put into a system. The third law of thermodynamics states that at the temperature of absolute zero—a phenomenon discussed later in this essay—entropy also approaches zero. This might seem to counteract the second law, but in fact the third states in effect that absolute zero is impossible to reach. The French physicist and engineer Sadi Carnot (1796-1832) had shown that a perfectly efficient engine is one whose lowest temperature was absolute zero; but the second law of thermodynamics shows that a perfectly efficient engine (or any other perfect system) cannot exist. Hence, as Snow observed, not only is it impossible to win or break even; it is impossible to get out of the game.
REAL-LIFE A P P L I C AT I O N S Evolution of the Thermometer A thermometer is a device that gauges temperature by measuring a temperature-dependent property, such as the expansion of a liquid in a sealed tube. The Greco-Roman physician Galen (c. 129-c. 199) was among the first thinkers to envision a scale for measuring temperature, but development of a practical temperature-measuring device—the thermoscope—did not occur until the sixteenth century. The great physicist Galileo Galilei (15641642) may have invented the thermoscope; certainly he constructed one. Galileo’s thermoscope consisted of a long glass tube planted in a container of liquid. Prior to inserting the tube into the liquid—which was usually colored water, though Galileo’s thermoscope used wine—as much air as possible was removed from the tube. This created a vacuum (an area devoid of matter, including air), and as a result of pressure differ-
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ences between the liquid and the interior of the thermoscope tube, some of the liquid went into the tube. But the liquid was not the thermometric medium—that is, the substance whose temperature-dependent property changes were measured by the thermoscope. (Mercury, for instance, is the thermometric medium in many thermometers today; however, due to the toxic quality of mercury, an effort is underway to remove mercury thermometers from U.S. schools.) Instead, the air was the medium whose changes the thermoscope measured: when it was warm, the air expanded, pushing down on the liquid; and when the air cooled, it contracted, allowing the liquid to rise. E A R LY T H E R M O M E T E R S : T H E S E A R C H F O R A T E M P E RAT U R E S CA L E . The first true thermometer, built by
Ferdinand II, Grand Duke of Tuscany (16101670) in 1641, used alcohol sealed in glass. The latter was marked with a temperature scale containing 50 units, but did not designate a value for zero. In 1664, English physicist Robert Hooke (1635-1703) created a thermometer with a scale divided into units equal to about 1/500 of the volume of the thermometric medium. For the zero point, Hooke chose the temperature at which water freezes, thus establishing a standard still used today in the Fahrenheit and Celsius scales. Olaus Roemer (1644-1710), a Danish astronomer, introduced another important standard. Roemer’s thermometer, built in 1702, was based not on one but two fixed points, which he designated as the temperature of snow or crushed ice on the one hand, and the boiling point of water on the other. As with Hooke’s use of the freezing point, Roemer’s idea of designating the freezing and boiling points of water as the two parameters for temperature measurements has remained in use ever since.
Temperature Scales T H E FA H R E N H E I T S CA L E . Not only did he develop the Fahrenheit scale, oldest of the temperature scales still used in Western nations today, but in 1714, German physicist Daniel Fahrenheit (1686-1736) built the first thermometer to contain mercury as a thermometric medium. Alcohol has a low boiling point, whereas mercury remains fluid at a wide range of temperatures. In addition, it expands and con-
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tracts at a very constant rate, and tends not to stick to glass. Furthermore, its silvery color makes a mercury thermometer easy to read. Fahrenheit also conceived the idea of using “degrees” to measure temperature. It is no mistake that the same word refers to portions of a circle, or that exactly 180 degrees—half the number of degrees in a circle—separate the freezing and boiling points for water on Fahrenheit’s thermometer. Ancient astronomers first divided a circle into 360 degrees, as a close approximation of the ratio between days and years, because 360 has a large quantity of divisors. So, too, does 180—a total of 16 whole-number divisors other than 1 and itself. Though today it might seem obvious that 0 should denote the freezing point of water, and 180 its boiling point, such an idea was far from obvious in the early eighteenth century. Fahrenheit considered a 0-to-180 scale, but also a 180to-360 one, yet in the end he chose neither—or rather, he chose not to equate the freezing point of water with zero on his scale. For zero, he chose the coldest possible temperature he could create in his laboratory, using what he described as “a mixture of sal ammoniac or sea salt, ice, and water.” Salt lowers the melting point of ice (which is why it is used in the northern United States to melt snow and ice from the streets on cold winter days), and thus the mixture of salt and ice produced an extremely cold liquid water whose temperature he equated to zero. On the Fahrenheit scale, the ordinary freezing point of water is 32°, and the boiling point exactly 180° above it, at 212°. Just a few years after Fahrenheit introduced his scale, in 1730, a French naturalist and physicist named Rene Antoine Ferchault de Reaumur (1683-1757) presented a scale for which 0° represented the freezing point of water and 80° the boiling point. Although the Reaumur scale never caught on to the same extent as Fahrenheit’s, it did include one valuable addition: the specification that temperature values be determined at standard sea-level atmospheric pressure.
Celsius scale. The latter was created in 1742 by Swedish astronomer Anders Celsius (1701-1744).
Temperature and Heat
Like Fahrenheit, Celsius chose the freezing and boiling points of water as his two reference points, but he determined to set them 100, rather than 180, degrees apart. The Celsius scale is sometimes called the centigrade scale, because it is divided into 100 degrees, cent being a Latin root meaning “hundred.” Interestingly, Celsius planned to equate 0° with the boiling point, and 100° with the freezing point; only in 1750 did fellow Swedish physicist Martin Strömer change the orientation of the Celsius scale. In accordance with the innovation offered by Reaumur, Celsius’s scale was based not simply on the boiling and freezing points of water, but specifically on those points at normal sea-level atmospheric pressure. In SI, a scientific system of measurement that incorporates units from the metric system along with additional standards used only by scientists, the Celsius scale has been redefined in terms of the triple point of water. (Triple point is the temperature and pressure at which a substance is at once a solid, liquid, and vapor.) According to the SI definition, the triple point of water—which occurs at a pressure considerably below normal atmospheric pressure—is exactly 0.01°C. T H E K E LV I N S CA L E . French physicist and chemist J. A. C. Charles (1746-1823), who is credited with the gas law that bears his name (see below), discovered that at 0°C, the volume of gas at constant pressure drops by 1/273 for every Celsius degree drop in temperature. This suggested that the gas would simply disappear if cooled to -273°C, which of course made no sense.
T H E C E L S I U S S CA L E . With its 32° freezing point and its 212° boiling point, the Fahrenheit system lacks the neat orderliness of a decimal or base-10 scale. Thus when France adopted the metric system in 1799, it chose as its temperature scale not the Fahrenheit but the
The man who solved the quandary raised by Charles’s discovery was William Thompson, Lord Kelvin (1824-1907), who, in 1848, put forward the suggestion that it was the motion of molecules, and not volume, that would become zero at –273°C. He went on to establish what came to be known as the Kelvin scale. Sometimes known as the absolute temperature scale, the Kelvin scale is based not on the freezing point of water, but on absolute zero—the temperature at which molecular motion comes to a virtual stop. This is –273.15°C (–459.67°F), which, in the Kelvin scale, is designated as 0K. (Kelvin measures do not use the term or symbol for “degree.”)
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Though scientists normally use metric units, they prefer the Kelvin scale to Celsius because the absolute temperature scale is directly related to average molecular translational energy, based on the relative motion of molecules. Thus if the Kelvin temperature of an object is doubled, this means its average molecular translational energy has doubled as well. The same cannot be said if the temperature were doubled from, say, 10°C to 20°C, or from 40°C to 80°F, since neither the Celsius nor the Fahrenheit scale is based on absolute zero. CONVERSIONS BETWEEN SCALES.
The Kelvin scale is closely related to the Celsius scale, in that a difference of one degree measures the same amount of temperature in both. Therefore, Celsius temperatures can be converted to Kelvins by adding 273.15. Conversion between Celsius and Fahrenheit figures, on the other hand, is a bit trickier. To convert a temperature from Celsius to Fahrenheit, multiply by 9/5 and add 32. It is important to perform the steps in that order, because reversing them will produce a wrong figure. Thus, 100°C multiplied by 9/5 or 1.8 equals 180, which, when added to 32 equals 212°F. Obviously, this is correct, since 100°C and 212°F each represent the boiling point of water. But if one adds 32 to 100°, then multiplies it by 9/5, the result is 237.6°F—an incorrect answer. For converting Fahrenheit temperatures to Celsius, there are also two steps involving multiplication and subtraction, but the order is reversed. Here, the subtraction step is performed before the multiplication step: thus 32 is subtracted from the Fahrenheit temperature, then the result is multiplied by 5/9. Beginning with 212°F, when 32 is subtracted, this equals 180. Multiplied by 5/9, the result is 100°C—the correct answer. One reason the conversion formulae use simple fractions instead of decimal fractions (what most people simply call “decimals”) is that 5/9 is a repeating decimal fraction (0.55555....) Furthermore, the symmetry of 5/9 and 9/5 makes memorization easy. One way to remember the formula is that Fahrenheit is multiplied by a fraction—since 5/9 is a real fraction, whereas 9/5 is actually a mixed number, or a whole number plus a fraction.
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Modern Thermometers MERCURY
THERMOMETERS.
For a thermometer, it is important that the glass tube be kept sealed; changes in atmospheric pressure contribute to inaccurate readings, because they influence the movement of the thermometric medium. It is also important to have a reliable thermometric medium, and, for this reason, water—so useful in many other contexts—was quickly discarded as an option. Water has a number of unusual properties: it does not expand uniformly with a rise in temperature, or contract uniformly with a lowered temperature. Rather, it reaches its maximum density at 39.2°F (4°C), and is less dense both above and below that temperature. Therefore alcohol, which responds in a much more uniform fashion to changes in temperature, soon took the place of water, and is still used in many thermometers today. But for the reasons mentioned earlier, mercury is generally considered preferable to alcohol as a thermometric medium. In a typical mercury thermometer, mercury is placed in a long, narrow sealed tube called a capillary. The capillary is inscribed with figures for a calibrated scale, usually in such a way as to allow easy conversions between Fahrenheit and Celsius. A thermometer is calibrated by measuring the difference in height between mercury at the freezing point of water, and mercury at the boiling point of water. The interval between these two points is then divided into equal increments—180, as we have seen, for the Fahrenheit scale, and 100 for the Celsius scale. VOLUME GAS THERMOMET E R S . Whereas most liquids and solids
expand at an irregular rate, gases tend to follow a fairly regular pattern of expansion in response to increases in temperature. The predictable behavior of gases in these situations has led to the development of the volume gas thermometer, a highly reliable instrument against which other thermometers—including those containing mercury—are often calibrated. In a volume gas thermometer, an empty container is attached to a glass tube containing mercury. As gas is released into the empty container; this causes the column of mercury to move upward. The difference between the earlier position of the mercury and its position after the introduction of the gas shows the difference between normal atmospheric pressure and the
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pressure of the gas in the container. It is then possible to use the changes in the volume of the gas as a measure of temperature.
the temperature of a object with which the thermometer itself is not in physical contact.
Temperature and Heat
Measuring Heat ELECTRIC
THERMOMETERS.
All matter displays a certain resistance to electric current, a resistance that changes with temperature; because of this, it is possible to obtain temperature measurements using an electric thermometer. A resistance thermometer is equipped with a fine wire wrapped around an insulator: when a change in temperature occurs, the resistance in the wire changes as well. This allows much quicker temperature readings than those offered by a thermometer containing a traditional thermometric medium. Resistance thermometers are highly reliable, but expensive, and primarily are used for very precise measurements. More practical for everyday use is a thermistor, which also uses the principle of electric resistance, but is much simpler and less expensive. Thermistors are used for providing measurements of the internal temperature of food, for instance, and for measuring human body temperature. Another electric temperature-measurement device is a thermocouple. When wires of two different materials are connected, this creates a small level of voltage that varies as a function of temperature. A typical thermocouple uses two junctions: a reference junction, kept at some constant temperature, and a measurement junction. The measurement junction is applied to the item whose temperature is to be measured, and any temperature difference between it and the reference junction registers as a voltage change, measured with a meter connected to the system. OTHER TYPES OF THERMOMET E R. A pyrometer also uses electromagnetic
properties, but of a very different kind. Rather than responding to changes in current or voltage, the pyrometer is gauged to respond to visible and infrared radiation. As with the thermocouple, a pyrometer has both a reference element and a measurement element, which compares light readings between the reference filament and the object whose temperature is being measured.
The measurement of temperature by degrees in the Fahrenheit or Celsius scales is a part of daily life, but measurements of heat are not as familiar to the average person. Because heat is a form of energy, and energy is the ability to perform work, heat is therefore measured by the same units as work. The principal SI unit of work or energy is the joule (J). A joule is equal to 1 newton-meter (N • m)—in other words, the amount of energy required to accelerate a mass of 1 kilogram at the rate of 1 meter per second squared across a distance of 1 meter. The joule’s equivalent in the English system is the foot-pound: 1 foot-pound is equal to 1.356 J, and 1 joule is equal to 0.7376 ft • lbs. In the British system, Btu, or British thermal unit, is another measure of energy, though it is primarily used for machines. Due to the cumbersome nature of the English system, contrasted with the convenience of the decimal units in the SI system, these English units of measure are not used by chemists or other scientists for heat measurement.
Specific Heat Capacity Specific heat capacity (sometimes called specific heat) is the amount of heat that must be added to, or removed from, a unit of mass for a given substance to change its temperature by 1°C. Typically, specific heat capacity is measured in units of J/g • °C (joules per gram-degree Celsius). The specific heat capacity of water is measured by the calorie, which, along with the joule, is an important SI measure of heat. Often another unit, the kilocalorie—which, as its name suggests—is 1,000 calories—is used. This is one of the few confusing aspects of SI, which is much simpler than the English system. The dietary Calorie (capital C) with which most people are familiar is not the same as a calorie (lowercase c)—rather, a dietary Calorie is the same as a kilocalorie.
Still other thermometers, such as those in an oven that register the oven’s internal temperature, are based on the expansion of metals with heat. In fact, there are a wide variety of thermometers, each suited to a specific purpose. A pyrometer, for instance, is good for measuring
capacity, the more resistant the substance is to changes in temperature. Many metals, in fact, have a low specific heat capacity, making them easy to heat up and cool down. This contributes
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to the tendency of metals to expand when heated, and thus affects their malleability. On the other hand, water has a high specific heat capacity, as discussed below; indeed, if it did not, life on Earth would hardly be possible. One of the many unique properties of water is its very high specific heat capacity, which is easily derived from the value of a kilocalorie: it is 4.184, the same number of joules required to equal a calorie. Few substances even come close to this figure. At the low end of the spectrum are lead, gold, and mercury, with specific heat capacities of 0.13, 0.13, and 0.14 respectively. Aluminum has a specific heat capacity of 0.89, and ethyl alcohol of 2.43. The value for concrete, one of the highest for any substance other than water, is 2.9. As high as the specific heat capacity of concrete is, that of water is more than 40% higher. On the other hand, water in its vapor state (steam) has a much lower specific heat capacity—2.01. The same is true for solid water, or ice, with a specific heat capacity of 2.03. Nonetheless, water in its most familiar form has an astoundingly high specific heat capacity, and this has several effects in the real world. E F F E C T S O F WAT E R ’ S H I G H S P E C I F I C H E AT C A PA C I T Y. For
instance, water is much slower to freeze in the winter than most substances. Furthermore, due to other unusual aspects of water—primarily the fact that it actually becomes less dense as a solid—the top of a lake or other body of water freezes first. Because ice is a poor medium for the conduction of heat (a consequence of its specific heat capacity), the ice at the top forms a layer that protects the still-liquid water below it from losing heat. As a result, the water below the ice layer does not freeze, and the animal and plant life in the lake is preserved. Conversely, when the weather is hot, water is slow to experience a rise in temperature. For this reason, a lake or swimming pool makes a good place to cool off on a sizzling summer day. Given the high specific heat capacity of water, combined with the fact that much of Earth’s surface is composed of water, the planet is far less susceptible than other bodies in the Solar System to variations in temperature.
18
(37°C), and, even in cases of extremely high fever, an adult’s temperature rarely climbs by more than 5°F (2.7°C). The specific heat capacity of the human body, though it is of course lower than that of water itself (since it is not entirely made of water), is nonetheless quite high: 3.47.
Calorimetry The measurement of heat gain or loss as a result of physical or chemical change is called calorimetry (pronounced kal-or-IM-uh-tree). Like the word “calorie,” the term is derived from a Latin root word meaning “heat.” The foundations of calorimetry go back to the mid-nineteenth century, but the field owes much to the work of scientists about 75 years prior to that time. In 1780, French chemist Antoine Lavoisier (1743-1794) and French astronomer and mathematician Pierre Simon Laplace (1749-1827) had used a rudimentary ice calorimeter for measuring heat in the formations of compounds. Around the same time, Scottish chemist Joseph Black (1728-1799) became the first scientist to make a clear distinction between heat and temperature. By the mid-1800s, a number of thinkers had come to the realization that—contrary to prevailing theories of the day—heat was a form of energy, not a type of material substance. (The belief that heat was a material substance, called “phlogiston,” and that phlogiston was the part of a substance that burned in combustion, had originated in the seventeenth century. Lavoisier was the first scientist to successfully challenge the phlogiston theory.) Among these were American-British physicist Benjamin Thompson, Count Rumford (1753-1814) and English chemist James Joule (1818-1889)—for whom, of course, the joule is named. Calorimetry as a scientific field of study actually had its beginnings with the work of French chemist Pierre-Eugene Marcelin Berthelot (1827-1907). During the mid-1860s, Berthelot became intrigued with the idea of measuring heat, and, by 1880, he had constructed the first real calorimeter.
The same is true of another significant natural feature, one made mostly of water: the human body. A healthy human temperature is 98.6°F
Essential to calorimetry is the calorimeter, which can be any device for accurately measuring the temperature of a substance before and after a change occurs. A calorimeter can be as simple as a styrofoam cup. Its quality as an insulator, which makes styro-
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foam ideal both for holding in the warmth of coffee and protecting the human hand from scalding, also makes styrofoam an excellent material for calorimetric testing. With a styrofoam calorimeter, the temperature of the substance inside the cup is measured, a reaction is allowed to take place, and afterward, the temperature is measured a second time.
sure of a gas: the greater the pressure, the less the volume, and vice versa. Even more relevant to the subject of thermal expansion is Charles’s law, which states that when pressure is kept constant, there is a direct relationship between volume and absolute temperature.
The most common type of calorimeter used is the bomb calorimeter, designed to measure the heat of combustion. Typically, a bomb calorimeter consists of a large container filled with water, into which is placed a smaller container, the combustion crucible. The crucible is made of metal, with thick walls into which is cut an opening to allow the introduction of oxygen. In addition, the combustion crucible is designed to be connected to a source of electricity.
as two systems that exchange no heat are said to be in a state of thermal equilibrium, chemical equilibrium describes a dynamic state in which the concentration of reactants and products remains constant. Though the concentrations of reactants and products do not change, note that chemical equilibrium is a dynamic state—in other words, there is still considerable molecular activity, but no net change.
In conducting a calorimetric test using a bomb calorimeter, the substance or object to be studied is placed inside the combustion crucible and ignited. The resulting reaction usually occurs so quickly that it resembles the explosion of a bomb—hence the name “bomb calorimeter.” Once the “bomb” goes off, the resulting transfer of heat creates a temperature change in the water, which can be readily gauged with a thermometer. To study heat changes at temperatures higher than the boiling point of water, physicists use substances with higher boiling points. For experiments involving extremely large temperature ranges, an aneroid (without liquid) calorimeter may be used. In this case, the lining of the combustion crucible must be of a metal, such as copper, with a high coefficient or factor of thermal conductivity—that is, the ability to conduct heat from molecule to molecule.
Temperature and Heat
C H E M I CA L E Q U I L I B R I U M A N D C H A N G E S I N T E M P E RAT U R E . Just
Calculations involving chemical equilibrium make use of a figure called the equilibrium constant (K). According to Le Châtelier’s principle, named after French chemist Henri Le Châtelier (1850-1936), whenever a stress or change is imposed on a chemical system in equilibrium, the system will adjust the amounts of the various substances in such a way as to reduce the impact of that stress. An example of a stress is a change in temperature, which changes the equilibrium equation by shifting K (itself dependant on temperature). Using Le Châtelier’s law, it is possible to determine whether K will change in the direction of the forward or reverse reaction. In an exothermic reaction (a reaction that produces heat), K will shift to the left, or in the direction of the forward reaction. On the other hand, in an endothermic reaction (a reaction that absorbs heat), K will shift to the right, or in the direction of the reverse reaction.
Temperature in Chemistry T H E GAS LAW S . A collection of statements regarding the behavior of gases, the gas laws are so important to chemistry that a separate essay is devoted to them elsewhere. Several of the gas laws relate temperature to pressure and volume for gases. Indeed, gases respond to changes in temperature with dramatic changes in volume; hence the term “volume,” when used in reference to a gas, is meaningless unless pressure and temperature are specified as well.
T E M P E R AT U R E AND REACT I O N RAT E S . Another important function
of temperature in chemical processes is its function of speeding up chemical reactions. An increase in the concentration of reacting molecules, naturally, leads to a sped-up reaction, because there are simply more molecules colliding with one another. But it is also possible to speed up the reaction without changing the concentration.
Among the gas laws, Boyle’s law holds that in conditions of constant temperature, an inverse relationship exists between the volume and pres-
By definition, wherever a temperature increase is involved, there is always an increase in average molecular translational energy. When temperatures are high, more molecules are col-
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Temperature and Heat
KEY TERMS ABSOLUTE ZERO:
The temperature,
The ability to accomplish
ENERGY:
defined as 0K on the Kelvin scale, at which
work—that is, the exertion of force over a
the motion of molecules in a solid virtual-
given distance to displace or move an
ly ceases. The third law of thermodynamics
object.
establishes the impossibility of actually
ENTROPY:
reaching absolute zero.
systems toward breakdown, and specifical-
CALORIE:
A measure of specific heat
capacity in the SI or metric system, equal to the heat that must be added to or
The tendency of natural
ly the tendency for the energy in a system to be dissipated. Entropy is closely related to the second law of thermodynamics. The oldest of
removed from 1 gram of water to change
FAHRENHEIT SCALE:
its temperature by 1°C. The dietary Calorie
the temperature scales still in use, created
(capital C), with which most people are
in 1714 by German physicist Daniel
familiar, is the same as the kilocalorie.
Fahrenheit (1686-1736). The Fahrenheit scale establishes the freezing and boiling
The measurement of
points of water at 32° and 212° respective-
heat gain or loss as a result of physical or
ly. To convert a temperature from the
chemical change.
Fahrenheit to the Celsius scale, subtract 32
CALORIMETRY:
CELSIUS SCALE:
The metric scale of
and multiply by 5/9.
temperature, sometimes known as the
FIRST LAW OF THERMODYNAMICS:
centigrade scale, created in 1742 by
A law which states the amount of energy in
Swedish astronomer Anders Celsius (1701-
a system remains constant, and therefore it
1744). The Celsius scale establishes the
is impossible to perform work that results
freezing and boiling points of water at 0°
in an energy output greater than the ener-
and 100° respectively. To convert a temper-
gy input. This is the same as the conserva-
ature from the Celsius to the Fahrenheit
tion of energy.
scale, multiply by 9/5 and add 32. Though
HEAT:
the worldwide scientific community uses
flows from one body of matter to another.
the metric or SI system for most measurements, scientists prefer the related Kelvin scale of absolute temperature. CONSERVATION OF ENERGY:
20
JOULE:
Internal thermal energy that The principal unit of energy—
and thus of heat—in the SI or metric system, corresponding to 1 newton-meter
A
(N • m). A joule (J) is equal to 0.7376 foot-
law of physics which holds that within a
pounds in the English system.
system isolated from all other outside fac-
KELVIN
tors, the total amount of energy remains
William Thompson, Lord Kelvin (1824-
the same, though transformations of ener-
1907), the Kelvin scale measures tempera-
gy from one form to another take place.
ture in relation to absolute zero, or 0K.
The first law of thermodynamics is the
(Units in the Kelvin system, known as
same as the conservation of energy.
Kelvins, do not include the word or symbol
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SCALE:
Established
by
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KEY TERMS
CONTINUED
for degree.) The Kelvin scale, which is the
1°C. It is typically measured in J/g • °C
system usually favored by scientists, is
(joules per gram-degree Celsius). A calorie
directly related to the Celsius scale; hence
is the specific heat capacity of 1 gram of
Celsius temperatures can be converted to
water.
Kelvins by adding 273.15. SYSTEM:
In chemistry and other sci-
A measure of specific
ences, the term “system” usually refers to
heat capacity in the SI or metric system,
any set of interactions isolated from the
equal to the heat that must be added to or
rest of the universe. Anything outside of
KILOCALORIE:
removed from 1 kilogram of water to change its temperature by 1°C. As its name suggests, a kilocalorie is 1,000 calories. The dietary Calorie (capital C) with which
the system, including all factors and forces irrelevant to a discussion of that system, is known as the environment. THERMAL
kilocalorie.
resulting from internal kinetic energy.
KINETIC ENERGY:
The energy that
an object possesses by virtue of its motion. MOLECULAR TRANSLATIONAL EN-
The kinetic energy in a system
ERGY:
ENERGY:
Heat energy
most people are familiar is the same as the
THERMAL EQUILIBRIUM:
A situa-
tion in which two systems have the same temperature. As a result, there is no exchange of heat between them. The study of
produced by the movement of molecules
THERMODYNAMICS:
in relation to one another. Thermal energy
the relationships between heat, work, and
is a manifestation of molecular transla-
energy.
tional energy.
THERMOMETER:
A device that gauges
SECOND LAW OF THERMODYNAM-
temperature by measuring a temperature-
A law of thermodynamics which
dependent property, such as the expansion
states that no system can simply take heat
of a liquid in a sealed tube, or resistance to
from a source and perform an equivalent
electric current.
ICS:
amount of work. This is a result of the fact that the natural flow of heat is always from a high-temperature reservoir to a low-temperature reservoir. In the course of such a transfer, some of the heat will always be
THERMOMETRIC MEDIUM:
A sub-
stance whose physical properties change with temperature. A mercury or alcohol thermometer measures such changes.
lost—an example of entropy. The second
THIRD LAW OF THERMODYNAMICS:
law is sometimes referred to as “the law of
A law of thermodynamics stating that at
entropy.”
the temperature of absolute zero, entropy The
also approaches zero. Zero entropy contra-
amount of heat that must be added to, or
dicts the second law of thermodynamics,
removed from, a unit of mass of a given
meaning that absolute zero is therefore
substance to change its temperature by
impossible to reach.
SPECIFIC HEAT CAPACITY:
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liding, and the collisions that occur are more energetic. The likelihood is therefore increased that any particular collision will result in the energy necessary to break chemical bonds, and thus bring about the rearrangements in molecules needed for a reaction.
Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: Houghton Mifflin, 1995. Gardner, Robert. Science Projects About Methods of Measuring. Berkeley Heights, NJ: Enslow Publishers, 2000. MegaConverter 2 (Web site). (May 7, 2001).
WHERE TO LEARN MORE “About Temperature” (Web site). (April 18, 2001). “Basic Chemical Thermodynamics” (Web site). (May 8, 2001). “Chemical Thermodynamics” (Web site). (May 8, 2001).
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VOLUME 1: REAL-LIFE CHEMISTRY
Royston, Angela. Hot and Cold. Chicago: Heinemann Library, 2001. Santrey, Laurence. Heat. Illustrated by Lloyd Birmingham. Mahwah, N.J.: Troll Associates, 1985. Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996. Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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M A S S , D E N S I T Y, A N D VO LU M E
CONCEPT Among the physical properties studied by chemists and other scientists, mass is one of the most fundamental. All matter, by definition, has mass. Mass, in turn, plays a role in two properties important to the study of chemistry: density and volume. All of these—mass, density, and volume—are simple concepts, yet in order to work in chemistry or any of the other hard sciences, it is essential to understand these types of measurement. Measuring density, for instance, aids in determining the composition of a given substance, while volume is a necessary component to using the gas laws.
HOW IT WORKS
VOLUME AND DENSITY DEF I N E D . Volume, then, is measured in terms of
length, and can be defined as the amount of three-dimensional space an object occupies. Volume is usually expressed in cubic units of length—for example, the milliliter (mL), also known as the cubic centimeter (cc), is equal to 6.10237 • 10–2 in3. As its name implies, there are 1,000 milliliters in a liter. Density is the ratio of mass to volume—or, to put its definition in terms of fundamental properties, of mass divided by cubed length. Density can also be viewed as the amount of matter within a given area. In the SI system, density is typically expressed as grams per cubic centimeter (g/cm3), equivalent to 62.42197 pounds per cubic foot in the English system.
Mass Fundamental Properties in Relation to Volume and Density Most qualities of the world studied by scientists can be measured in terms of one or more of four properties: length, mass, time, and electric charge. The volume of a cube, for instance, is a unit of length cubed—that is, length multiplied by “width,” which is then multiplied by “height.”
M ASS D E F I N E D . Though length is easy enough to comprehend, mass is more involved. In his second law of motion, Sir Isaac Newton (1642-1727) defined mass as the ratio of force to gravity. This, of course, is a statement that belongs to the realm of physics; for a chemist, it is more useful—and also accurate—to define mass as the quantity of matter that an object contains.
Width and height are not, for the purposes of science, distinct from length: they are simply versions of it, distinguished by their orientation in space. Length provides one dimension, while width provides a second perpendicular to the third. Height, perpendicular both to length and width, makes the third spatial dimension—yet all of these are merely expressions of length differentiated according to direction.
Matter, in turn, can be defined as physical substance that occupies space; is composed of atoms (or in the case of subatomic particles, is part of an atom); is convertible into energy—and has mass. The form or state of matter itself is not important: on Earth it is primarily observed as a solid, liquid, or gas, but it can also be found (particularly in other parts of the universe) in a fourth state, plasma.
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Mass, Density, and Volume
ASTRONAUTS NEIL ARMSTRONG AND BUZZ ALDRIN, THE FIRST MEN TO WALK ON THE MOON, WEIGHED LESS ON MOON THAN ON EARTH. THE REASON IS BECAUSE WEIGHT DIFFERS AS A RESPONSE TO THE GRAVITATIONAL PULL OF THE PLANET, MOON, OR OTHER BODY ON WHICH IT IS MEASURED. THUS, A PERSON WEIGHS LESS ON THE MOON, BECAUSE THE MOON POSSESSES LESS MASS THAN EARTH AND EXERTS LESS GRAVITATIONAL FORCE. (NASA/Roger Ress-
THE
meyer/Corbis. Reproduced by permission.)
The more matter an object contains, the more mass. To refer again to the laws of motion, in his first law, Newton identified inertia: the tendency of objects in motion to remain in motion, or of objects at rest to remain at rest, in a constant velocity unless they are acted upon by some outside force. Mass is a measure of inertia, meaning that the more mass something contains, the more difficult it is to put it into motion, or to stop it from moving. who are not scientifically trained tend to think that mass and weight are the same thing, but this
It is understandable why people confuse mass with weight, since most weight scales provide measurements in both pounds and kilograms. However, the pound (lb) is a unit of weight in the English system, whereas a kilogram
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is like saying that apples and apple pies are the same. Of course, an apple is an ingredient in an apple pie, but the pie contains something else— actually, a number of other things, such as flour and sugar. In this analogy, mass is equivalent to the apple, and weight the pie, while the acceleration due to gravity is the “something else” in weight.
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Mass, Density, and Volume
TO
DETERMINE WHETHER A PIECE OF GOLD IS GENUINE OR FAKE, ONE MUST MEASURE THE DENSITY OF THE SUB-
STANCE.
HERE,
A MAN EVALUATES GOLD PIECES IN
HONG KONG. (Christophe Loviny/Corbis. Reproduced by permission.)
(kg) is a unit of mass in the metric and SI systems. Though the two are relatively convertible on Earth (1 lb = 0.4536 kg; 1 kg = 2.21 lb), they are actually quite different.
REAL-LIFE A P P L I C AT I O N S
Weight is a measure of force, which Newton’s second law of motion defined as the product of mass multiplied by acceleration. The acceleration component of weight is a result of Earth’s gravitational pull, and is equal to 32 ft (9.8 m) per second squared. Thus a person’s weight varies according to gravity, and would be different if measured on the Moon; mass, on the other hand, is the same throughout the universe. Given its invariable value, scientists typically speak in terms of mass rather than weight.
Chemists do not always deal in large units of mass, such as the mass of a human body—which, of course, is measured in kilograms. Instead, the chemist’s work is often concerned with measurements of mass for the smallest types of matter: molecules, atoms, and other elementary particles. To measure these even in terms of grams (0.001 kg) is absurd: a single atom of carbon, for instance, has a mass of 1.99 • 10–23 g. In other words, a gram is about 50,000,000,000,000,000,000,000 times larger than a carbon atom—hardly a usable comparison.
Weight differs as a response to the gravitational pull of the planet, moon, or other body on which it is measured. Hence a person weighs less on the Moon, because the Moon possesses less mass than Earth, and, thus, exerts less gravitational force. Therefore, it would be easier on the Moon to lift a person from the ground, but it would be no easier to move that person from a resting position, or to stop him or her from moving. This is because the person’s mass, and hence his or her resistance to inertia, has not changed.
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Atomic Mass Units
Instead, chemists use an atom mass unit (abbreviated amu), which is equal to 1.66 • 10–24 g. Even so, is hard to imagine determining the mass of single atoms on a regular basis, so chemists make use of figures for the average atomic mass of a particular element. The average atomic mass of carbon, for instance, is 12.01 amu. As is the case with any average, this means that some atoms—different isotopes of carbon— may weigh more or less, but the figure of 12.01
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Mass, Density, and Volume
Earth (to same scale)
ALTHOUGH SATURN
IS MUCH LARGER THAN
EARTH,
IT IS MUCH LESS DENSE.
amu is still reliable. Some other average atomic mass figures for different elements are as follows: • • • • • • • • •
Hydrogen (H): 1.008 amu Helium (He): 4.003 amu Lithium (Li): 6.941 amu Nitrogen (N): 14.01 amu Oxygen (O): 16.00 Aluminum (Al): 26.98 Chlorine (Cl): 35.46 amu Gold (Au): 197.0 amu Hassium (Hs): [265 amu] The figure for hassium, with an atomic number of 108, is given in brackets because this number is the mass for the longest-lived isotope. The average value of mass for the molecules in a given compound can also be rendered in terms of atomic mass units: water (H2O) molecules, for instance, have an average mass of 18.0153 amu. Molecules of magnesium oxide (MgO), which can be extracted from sea water and used in making ceramics, have an average mass much higher than for water: 40.304 amu.
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atomic mass of oxygen. In the case of magnesium oxide, the oxygen is bonded to just one other atom—but magnesium, with an average atomic mass of 24.304, weighs much more than hydrogen.
Molar Mass It is often important for a chemist to know exactly how many atoms are in a given sample, particularly in the case of a chemical reaction between two or more samples. Obviously, it is impossible to count atoms or other elementary particles, but there is a way to determine whether two items— regardless of the elements or compounds involved—have the same number of elementary particles. This method makes use of the figures for average atomic mass that have been established for each element.
These values are obtained simply by adding those of the atoms included in the molecule: since water has two hydrogen atoms and one oxygen, the average molecular mass is obtained by multiplying the average atomic mass of hydrogen by two, and adding it to the average
If the average atomic mass of the substance is 5 amu, then there should be a very large number of atoms (if it is an element) or molecules (if it is a compound) of that substance having a total mass of 5 grams (g). Similarly, if the average atomic mass of the substance is 7.5 amu, then there should be a very large number of atoms or molecules of that substance having a total mass of 7.5 g. What is needed, clearly, is a very large number by which elementary particles must be
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multiplied in order to yield a mass whose value in grams is equal to the value, in amu, of its average atomic mass. This is known as Avogadro’s number. AV O GA D R O ’ S N U M B E R. The first scientist to recognize a meaningful distinction between atoms and molecules was Italian physicist Amedeo Avogadro (1776-1856). Avogadro maintained that gases consisted of particles— which he called molecules—that in turn consisted of one or more smaller particles. He further reasoned that one liter of any gas must contain the same number of particles as a liter of another gas.
In order to discuss the behavior of molecules, it was necessary to set a large quantity as a basic unit, since molecules themselves are very small. This led to the establishment of what is known as Avogadro’s number, equal to 6.022137 ⫻ 1023 (more than 600 billion trillion.) The magnitude of Avogadro’s number is almost inconceivable. The same number of grains of sand would cover the entire surface of Earth at a depth of several feet. The same number of seconds, for instance, is about 800,000 times as long as the age of the universe (20 billion years). Avogadro’s number—named after the man who introduced the concept of the molecule, but only calculated years after his death— serves a very useful purpose in computations involving molecules. T H E M O L E . To compare two substances containing the same number of atoms or molecules, scientists use the mole, the SI fundamental unit for “amount of substance.” A mole (abbreviated mol) is, generally speaking, Avogadro’s number of atoms or molecules; however, in the more precise SI definition, a mole is equal to the number of carbon atoms in 12.01 g (0.03 lb) of carbon. Note that, as stated earlier, carbon has an average atomic mass of 12.01 amu. This is no coincidence, of course: multiplication of the average atomic mass by Avogadro’s number yields a figure in grams equal to the value of the average atomic mass in amu.
expressed in grams. A mole of helium, for instance, has a mass of 4.003 g (0.01 lb), whereas a mole of iron is 55.85 g (0.12 lb) These figures represent the molar mass for each: that is, the mass of 1 mol of a given substance.
Mass, Density, and Volume
Once again, the value of molar mass in grams is the same as that of the average atomic mass in amu. Also, it should be clear that, given the fact that helium weighs much less than air— the reason why helium-filled balloons float—a quantity of helium with a mass of 4.003 g must be a great deal of helium. And indeed, as indicated earlier, the quantity of atoms or molecules in a mole is sufficiently great to make a sample that is large, but still usable for the purposes of study or comparison.
Measuring Volume Mass, because of its fundamental nature, is sometimes hard to comprehend, and density requires an explanation in terms of mass and volume. Volume, on the other hand, appears to be quite straightforward—and it is, when one is describing a solid of regular shape. In other situations, however, volume measurement is more complicated. As noted earlier, the volume of a cube can be obtained simply by multiplying length by width by height. There are other means for measuring the volume of other straight-sided objects, such as a pyramid. Still other formulae, which make use of the constant π (roughly equal to 3.14) are necessary for measuring the volume of a cylinder, a sphere, or a cone. For an object that is irregular in shape, however, one may have to employ calculus—but the most basic method is simply to immerse the object in water. This procedure involves measuring the volume of the water before and after immersion, and calculating the difference. Of course, the object being measured cannot be water-soluble; if it is, its volume must be measured in a non-water-based liquid such as alcohol. LIQUID
AND
GAS
VOLUME.
The term “mole” can be used in the same way we use the word “dozen.” Just as “a dozen” can refer to twelve cakes or twelve chickens, so “mole” always describes the same number of molecules. Just as one liter of water, or one liter of mercury, has a certain mass, a mole of any given substance has its own particular mass,
Measuring liquid volumes is even easier than for solids, given the fact that liquids have no definite shape, and will simply take the shape of the container in which they are placed. Gases are similar to liquids in the sense that they expand to fit their container; however, measurement of gas volume is a more involved process than that used to measure either liquids or solids, because gases are
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highly responsive to changes in temperature and pressure. If the temperature of water is raised from its freezing point to its boiling point—from 32°F (0°C) to 212°F (100°C)—its volume will increase by only 2%. If its pressure is doubled from 1 atm (defined as normal air pressure at sea level) to 2 atm, volume will decrease by only 0.01%. Yet if air were heated from 32° to 212°F, its volume would increase by 37%; if its pressure were doubled from 1 atm to 2, its volume would decrease by 50%. Not only do gases respond dramatically to changes in temperature and pressure, but also, gas molecules tend to be non-attractive toward one another—that is, they tend not to stick together. Hence, the concept of “volume” in relation to a gas is essentially meaningless unless its temperature and pressure are known.
Comparing Densities In the discussion of molar mass above, helium and iron were compared, and we saw that the mass of a mole of iron was about 14 times as great as that of a mole of helium. This may seem like a fairly small factor of difference between them: after all, helium floats on air, whereas iron (unless it is arranged in just the right way, for instance, in a tanker) sinks to the bottom of the ocean. But be careful: the comparison of molar mass is only an expression of the mass of a helium atom as compared to the mass of an iron atom. It makes no reference to density, which is the ratio of mass to volume.
relates to the fact that it takes a much greater volume of feathers (measured in cubic feet, for instance) than of cannonballs to equal a ton. One of the interesting things about density, as distinguished from mass and volume, is that it has nothing to do with the amount of material. A kilogram of iron differs from 10 kg of iron both in mass and volume, but the density of both samples is the same. Indeed, as discussed below, the known densities of various materials make it possible to determine whether a sample of that material is genuine. C O M PA R I N G D E N S I T I E S . As noted several times, the densities of numerous materials are known quantities, and can be easily compared. Some examples of density, all expressed in terms of grams per cubic centimeter, are listed below. These figures are measured at a temperature of 68°F (20°C), and for hydrogen and oxygen, the value was obtained at normal atmospheric pressure (1 atm):
Comparisons of Densities for Various Substances: • • • • • • • • •
Oxygen: 0.00133 g/cm3 Hydrogen: 0.000084 g/cm3 Ethyl alcohol: 0.79 g/cm3 Ice: 0.920 g/cm3 Water: 1.00 g/cm3 Concrete: 2.3 g/cm3 Iron: 7.87 g/cm3 Lead: 11.34 g/cm3 Gold: 19.32 g/cm3
Specific Gravity Expressed in terms of the ratio of mass to volume, the difference between helium and iron becomes much more pronounced. Suppose, on the one hand, one had a gallon jug filled with iron. How many gallons of helium does it take to equal the mass of the iron? Fourteen? Try again: it takes more than 43,000 gallons of helium to equal the mass of the iron in one gallon jug! Clearly, what this shows is that the density of iron is much, much greater than that of helium. This, of course, is hardly a surprising revelation; still, it is sometimes easy to get confused by comparisons of mass as opposed to comparisons of density. One might even get tricked by the old elementary-school brain-teaser that goes something like this: “Which is heavier, a ton of feathers or a ton of cannonballs?” Of course neither is heavier, but the trick element in the question
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VOLUME 1: REAL-LIFE CHEMISTRY
I S I T R E A L LY G O L D ? Note that pure water (as opposed to sea water, which is 3% more dense) has a density of 1.0 g per cubic centimeter. Water is thus a useful standard for measuring the specific gravity of other substances, or the ratio between the density of that substance and the density of water. Since the specific gravity of water is 1.00—also the density of water in g/cm3—the specific gravity of any substance (a number, rather than a number combined with a unit of measure) is the same as the value of its own density in g/cm3.
Comparison of densities make it possible to determine whether a piece of jewelry alleged to be solid gold is really genuine. To determine the answer, one must drop the sample in a beaker of water with graduated units of measure clearly
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Mass, Density, and Volume
KEY TERMS An SI unit
(cc), is equal to 6.10237 • 10-2 cubic inches
(abbreviated amu), equal to 1.66 • 10-24 g,
in the English system. As the name implies,
for measuring the mass of atoms.
there are 1,000 milliliters in a liter.
ATOMIC MASS UNIT:
AVERAGE ATOMIC MASS:
A figure
MOLAR MASS:
The mass, in grams, of
used by chemists to specify the mass—in
1 mole of a given substance. The value in
atomic mass units—of the average atom in
grams of molar mass is always equal to the
a large sample. The average atomic mass of
value, in atomic mass units, of the average
carbon, for instance, is 12.01 amu. If a sub-
atomic mass of that substance: thus, car-
stance is a compound, the average atomic
bon has a molar mass of 12.01 g, and an
mass of all atoms in a molecule of that sub-
average atomic mass of 12.01 amu.
stance must be added together to yield the average molecular mass of that substance.
The SI fundamental unit for
MOLE:
“amount of substance.” A mole is, general-
A figure,
ly speaking, Avogadro’s number of atoms,
named after Italian physicist Amedeo Avo-
molecules, or other elementary particles;
gadro (1776-1856), equal to 6.022137 ⫻
however, in the more precise SI definition,
⫹023.
a mole is equal to the number of carbon
AVOGADRO’S NUMBER:
Avogadro’s number indicates the
number of atoms, molecules, or other ele-
atoms in 12.01 g of carbon.
mentary particles in a mole. SPECIFIC GRAVITY:
The density of
The ratio of mass to vol-
an object or substance relative to the densi-
ume—in other words, the amount of mat-
ty of water; or more generally, the ratio
ter within a given area. In the SI system,
between the densities of two objects or
density is typically expressed as grams per
substances. Since the specific gravity of
cubic centimeter (g/cm3), equal to
water is 1.00—also the density of water in
62.42197 pounds per cubic foot in the Eng-
g/cm3—the specific gravity of any sub-
lish system.
stance is the same as the value of its own
DENSITY:
MASS:
The amount of matter an object
a number, without any unit of measure.
contains. MATTER:
density in g/cm3. Specific gravity is simply
Physical substance that occu-
VOLUME:
The
amount
of
three-
pies space, has mass, is composed of atoms
dimensional space an object occupies. Vol-
(or in the case of subatomic particles, is
ume is usually expressed in cubic units of
part of an atom), and is convertible to
length—for instance, the milliliter.
energy.
WEIGHT:
MILLILITER:
The product of mass multi-
One of the most com-
plied by the acceleration due to gravity (32
monly used units of volume in the SI sys-
ft or 9.8 m/sec2). A pound is a unit of
tem of measures. The milliliter (abbreviat-
weight, whereas a kilogram is a unit of
ed mL), also known as a cubic centimeter
mass.
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marked. Suppose the item has a mass of 10 g. The density of gold is 19 g/cm3, and because density is equal to mass divided by volume, the volume of water displaced should be equal to the mass divided by the density. The latter figure is equal to 10 g divided by 19 g/cm3, or 0.53 ml. Suppose that instead, the item displaced 0.88 ml of water. Clearly it is not gold, but what is it? Given the figures for mass and volume, its density is equal to 11.34 g/cm3—which happens to be the density of lead. If, on the other hand, the amount of water displaced were somewhere between the values for pure gold and pure lead, one could calculate what portion of the item was gold and which lead. It is possible, of course, that it could contain some other metal, but given the high specific gravity of lead, and the fact that its density is relatively close to that of gold, lead is a favorite gold substitute among jewelry counterfeiters. S P E C I F I C G RAV I T Y A N D T H E D E N S I T I E S O F P L A N E T S . Most
rocks near the surface of Earth have a specific gravity somewhere between 2 and 3, while the specific gravity of the planet itself is about 5. How do scientists know that the density of Earth is around 5 g/cm3? The computation is fairly simple, given the fact that the mass and volume of the planet are known. And given the fact that most of what lies close to Earth’s surface—sea water, soil, rocks—has a specific gravity well below 5, it is clear that Earth’s interior must contain high-density materials, such as nickel or iron. In the same way, calculations regarding the density of other objects in the Solar System provide a clue as to their interior composition.
30
planet, moon, or other body exerts is related to its mass, not its size. It so happens, too, that Jupiter is much larger than Earth, and that it exerts a gravitational pull much greater than that of Earth. This is because it has a mass many times as great as Earth’s. But what about Saturn, the secondlargest planet in the Solar System? In size it is only about 17% smaller than Jupiter, and both are much, much larger than Earth. Yet a person would weigh much less on Saturn than on Jupiter, because Saturn has a mass much smaller than Jupiter’s. Given the close relation in size between the two planets, it is clear that Saturn has a much lower density than Jupiter, or in fact even Earth: the great ringed planet has a specific gravity of less than 1. WHERE TO LEARN MORE Chahrour, Janet. Flash! Bang! Pop! Fizz!: Exciting Science for Curious Minds. Illustrated by Ann Humphrey Williams. Hauppauge, NY: Barron’s, 2000. “Density and Specific Gravity” (Web site). (March 27, 2001). “Density, Volume, and Cola” (Web site). (March 27, 2001). Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: Houghton Mifflin, 1995. “The Mass Volume Density Challenge” (Web site). (March 27, 2001). “MegaConverter 2” (Web site). (May 7, 2001). “Metric Density and Specific Gravity” (Web site). (March 27, 2001).
This brings the discussion back around to a topic raised much earlier in this essay, when comparing the weight of a person on Earth versus that person’s weight on the Moon. It so happens that the Moon is smaller than Earth, but that is not the reason it exerts less gravitational pull: as noted earlier, the gravitational force a
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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Robson, Pam. Clocks, Scales and Measurements. New York: Gloucester Press, 1993. “Volume, Mass, and Density” (Web site). (March 27, 2001).
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S C I E N C E O F E V E RY DAY T H I N G S real-life chemistry
M AT T E R P R O P E R T I E S O F M AT T E R GASES
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Properties of Matter
CONCEPT Matter is physical substance that occupies space, has mass, is composed of atoms—or, in the case of subatomic particles, is part of an atom—and is convertible to energy. On Earth, matter appears in three clearly defined forms—solid, liquid, and gas—whose varying structural characteristics are a function of the speeds at which its molecules move in relation to one another. A single substance may exist in any of the three phases: liquid water, for instance, can be heated to become steam, a vapor; or, when sufficient heat is removed from it, it becomes ice, a solid. These are merely physical changes, which do not affect the basic composition of the substance itself: it is still water. Matter, however, can and does undergo chemical changes, which (as with the various states or phases of matter) are an outcome of activity at the atomic and molecular level.
PROPERTIES O F M AT T E R
ties of energy available from even a tiny object traveling at that speed are enormous indeed. This is the basis for both nuclear power and nuclear weaponry, each of which uses some of the smallest particles in the known universe to produce results that are both amazing and terrifying. Even in everyday life, it is still possible to observe the conversion of mass to energy, if only on a very small scale. When a fire burns—that is, when wood experiences combustion in the presence of oxygen, and undergoes chemical changes—a tiny fraction of its mass is converted to energy. Likewise, when a stick of dynamite explodes, it too experiences chemical changes and the release of energy. The actual amount of energy released is, again, very small: for a stick of dynamite weighing 2.2 lb (1 kg), the portion of its mass that “disappears” is be equal to 6 parts out of 100 billion.
Einstein’s famous formula, E = mc2, means that every item possesses a quantity of energy equal to its mass multiplied by the squared speed of light. Given the fact that light travels at 186,000 mi (299,339 km) per second, the quanti-
Actually, none of the matter in the fire or the dynamite blast disappears: it simply changes forms. Most of it becomes other types of matter—perhaps new compounds, and certainly new mixtures of compounds. A very small part, as we have seen, becomes energy. One of the most fundamental principles of the universe is the conservation of energy, which holds that within a system isolated from all other outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place. In this situation, some of the energy remains latent, or “in reserve” as matter, while other components of the energy are released; yet the total amount of energy remains the same.
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HOW IT WORKS Matter and Energy One of the characteristics of matter noted in its definition above is that it is convertible to energy. We rarely witness this conversion, though as Albert Einstein (1879-1955) showed with his Theory of Relativity, it occurs in a massive way at speeds approaching that of light.
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Physical and Chemical Changes
what statement would contain the most information in the fewest words?”
In discussing matter—as, for instance, in the context of matter transforming into energy—one may speak in physical or chemical terms, or both. Generally speaking, physicists study physical properties and changes, while chemists are concerned with chemical processes and changes.
The answer he gave was this: “I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms—little articles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.”
A physicist views matter in terms of its mass, temperature, mechanical properties (for example, elasticity); electrical conductivity; and other structural characteristics. The chemical makeup of matter, on the other hand, is of little concern to a physicist. For instance, in analyzing a fire or an explosion, the physicist is not concerned with the interactions of combustible or explosive materials and oxygen. The physicist’s interest, rather, is in questions such as the amount of heat in the fire, the properties of the sound waves emitted in the explosion of the dynamite, and so on. The changes between different states or phases of matter, as they are discussed below, are physical changes. If water boils and vaporizes as steam, it is still water; likewise if it freezes to become solid ice, nothing has changed with regard to the basic chemical structure of the H2O molecules that make up water. But if water reacts with another substance to form a new compound, it has undergone chemical change. Likewise, if water molecules experience electrolysis, a process in which electric current is used to decompose H2O into molecules of H2 and O2, this is also a chemical change. Similarly, a change from matter to energy, while it is also a physical change, typically involves some chemical or nuclear process to serve as “midwife” to that change. Yet physical and chemical changes have at least one thing in common: they can be explained in terms of behavior at the atomic or molecular level. This is true of many physical processes—and of all chemical ones.
S T R U C T U R E O F T H E AT O M . As Feynman went on to note, atoms are so tiny that if an apple were magnified to the size of Earth, the atoms in it would each be about the size of a regular apple. Clearly, atoms and other atomic particles are far too small to be glimpsed even by the most highly powered optical microscope. Yet physicists and other scientists are able to study the behavior of atoms, and by doing so, they are able to form a picture of what occurs at the atomic level.
In his highly readable Six Easy Pieces—a work that includes considerable discussion of chemistry as well as physics—the great American physicist Richard Feynman (1918-1988) asked, “If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures,
An atom is the fundamental particle in a chemical element. The atom is not, however, the smallest particle in the universe: atoms are composed of subatomic particles, including protons, neutrons, and electrons. These are distinguished from one another in terms of electric charge: as with the north and south poles of magnets, positive and negative charges attract one another, but like charges repel. (In fact, magnetism is simply a manifestation of a larger electromagnetic force that encompasses both electricity and magnetism.)
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Indeed, what Feynman called the “atomic hypothesis” is one of the most important keys to understanding both physical and chemical changes. The behavior of particles at the atomic level has a defining role in the shape of the world studied by the sciences, and an awareness of this behavior makes it easier to understand physical processes, such as changes of state between solid, liquid, and gas; chemical processes, such as the formation of new compounds; and other processes, such as the conversion of matter to energy, which involve both physical and chemical changes. Only when one comprehends the atomic structure of matter is it possible to move on to the chemical elements that are the most basic materials of chemistry.
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Clustered at the center, or nucleus, of the atom are protons, which are positively charged, and neutrons, which exert no charge. Spinning around the nucleus are electrons, which exert a negative charge. The vast majority of the atom’s mass is made up by the protons and neutrons, which have approximately the same mass; that of the electron is much smaller. If an electron had a mass of 1—not a unit, but simply a figure used for comparison—the mass of the proton would be 1,836, and of the neutron 1,839.
Properties of Matter
Atoms of the same element always have the same number of protons, and since this figure is unique for a given element, each element is assigned an atomic number equal to the number of protons in its nucleus. Two atoms may have the same number of protons, and thus be of the same element, yet differ in their number of neutrons. Such atoms are called isotopes. The number of electrons is usually the same as the number of protons, and thus atoms have a neutral charge. In certain situations, however, the atom may lose or gain one or more electrons and acquire a net charge, becoming an ion. But electric charge, like energy, is conserved, and the electrons are not “lost” when an atom becomes an ion: they simply go elsewhere. It is useful, though far from precise, to compare the interior of an atom to a planet spinning very quickly around a sun. If the nucleus were our own Sun, then the electrons spinning at the edge of the atom would be on an orbit somewhere beyond Mars: in other words, the ratio between the size of the nucleus and the furthest edge of the atom is like that between the Sun’s diameter and an orbital path about 80 million miles beyond Mars. One of many differences between an atom and a solar system, however, is the fact that the electrons are spinning around the nucleus at a relative rate of motion much, much greater than any planet is revolving around the Sun. Furthermore, what holds the atom together is not gravitational force, as in the Solar System, but electromagnetic force. A final and critical difference is the fact that electrons move in much more complex orbital patterns than the elliptical paths that planets make in their movement around the Sun.
Molecules
A
COAL
GASIFICATION
PLANT.
MAKES IT POSSIBLE TO BURN
COAL GASIFICATION “CLEAN” COAL. (Roger Ress-
meyer/Corbis. Reproduced by permission.)
the world are not pure elements such as oxygen or iron. They are compounds in which atoms of more than one element join—usually in molecules. All molecules are composed of more than one atom, but not necessarily of more than one element: oxygen, for instance, generally appears in the form of molecules in which two oxygen atoms are bonded. Because of this, pure oxygen is represented by the chemical symbol O2, as opposed to the symbol for the element oxygen, which is simply O. One of the most well-known molecular forms in the world is water, or H2O, composed of two hydrogen atoms and one oxygen atom. The arrangement is extremely precise and never varies: scientists know, for instance, that the two hydrogen atoms join the oxygen atom (which is much larger than the hydrogen atoms) at an angle of 105°3’. Since the oxygen atom is much larger than the two hydrogens, its shape can be compared to a basketball with two softballs attached.
Though an atom is the fundamental unit of matter, most of the substances people encounter in
Other molecules are much more complex than those of water, and some are much, much more complex, a fact reflected in the sometimes
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lengthy names and complicated symbolic representations required to identify their chemical components. On the other hand, not all materials are made up of molecules: salt, for instance, is an ionic solid, as discussed below.
Quantifying Atoms and Molecules The nucleus of an atom is about 10–13 cm in diameter, and the diameter of the entire atom is about 10–8 cm—about 0.0000003937 in. Obviously, special units are required for describing the size of atoms, and usually measurements are provided in terms of the angstrom, equal to 10–10 m, or 10–8 cm. To put this on some sort of imaginable scale, there are 10 million angstroms in a millimeter. Measuring the spatial dimensions of an atom, however, is not as important as measuring its mass—and naturally, the mass of an atom is also almost inconceivably small. For instance, it takes about 5.0 • 1023 carbon atoms to equal just one gram of mass. Again, the numbers boggle the mind, but the following may put this into perspective. We have already established just how tiny an angstrom is; now consider the following. If 5.0 • 1023 angstrom lengths were laid end to end, they would stretch for a total of about 107,765 round trips from Earth to the Sun! It is obvious, then, that an entirely different unit should be used for measuring the mass of an atom, and for this purpose, chemists and other scientists use an atom mass unit (abbreviated amu). The latter is equal to 1.66 • 10–24 g. Even so, scientists can hardly be expected to be constantly measuring the mass of individual atoms; rather, they rely on figures determined for the average atomic mass of a particular element.
36
mass of individual atoms or molecules, scientists need a useful means for comparing atoms or molecules of different substances—and for doing so in such a way that they know they are analyzing equal numbers of particles. This cannot be done in terms of mass, because the number of atoms in each sample would vary: a gram of hydrogen, for instance, would contain about 12 times as many atoms as a gram of carbon, which has an average atomic mass of 12.01 amu. What is needed, instead, is a way to designate a certain number of atoms or molecules, such that accurate comparisons are possible. In order to do this, scientists make use of a figure known as Avogadro’s number. Named after Italian physicist Amedeo Avogadro (1776-1856), it is equal to 6.022137 ⫻ 1023 Earlier, we established the almost inconceivable scale represented by the figure 5.0 • 1023; here we are confronted with a number 20% larger. But Avogadro’s number, which is equal to 6,022,137 followed by 17 zeroes, is more than simply a mind-boggling series of digits. In general terms, Avogadro’s number designates the quantity of molecules (and sometimes atoms, if the substance in question is an element that, unlike oxygen, appears as single atoms) in a mole (abbreviated mol). A mole is the SI unit for “amount of substance,” and is defined precisely as the number of carbon atoms in 12.01 g of carbon. It is here that the value of Avogadro’s number becomes clear: as noted, carbon has an average atomic mass of 12.01 amu, and multiplication of the average atomic mass by Avogadro’s number yields a figure in grams equal to the value of the average atomic mass in atomic mass units. M O LA R M ASS A N D D E N S I T Y.
Average atomic mass figures range from 1.008 amu for hydrogen to over 250 amu for elements of very high atomic numbers. Figures for average atomic mass can be used to determine the average mass of a molecule as well, simply by combining the average atomic mass figures for each atom the molecule contains. A water molecule, for instance, has an average mass equal to the average atomic mass of hydrogen multiplied by two, and added to the average atomic mass of oxygen.
By comparison, a mole of helium has a molar mass of 4.003 g (0.01 lb) The molar mass of iron (that is, the mass of 1 mole of iron) is 55.85 g (0.12 lb) Note that there is not a huge ratio of difference between the molar mass of iron and that of helium: iron has a molar mass about 14 times greater. This, of course, seems very small in light of the observable differences between iron and helium: after all, who ever heard of a balloon filled with iron, or a skyscraper with helium girders?
AV O G A D R O ’ S N U M B E R A N D T H E M O L E . Just as using average atomic
mass is much more efficient than measuring the
The very striking differences between iron and helium, clearly, must come from something other than the molar mass differential between
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them. Of course, a mole of iron contains the same number of atoms as a mole of helium, but this says nothing about the relative density of the two substances. In terms of volume—that is, the amount of space that something occupies—the difference is much more striking: the volume of a mole of helium is about 43,000 times as large as that of a mole of iron. What this tells us is that the densities of iron and helium—the amount of mass per unit of volume—are very different. This difference in density is discussed in the essay on Mass, Density, and Volume; here the focus is on a larger judgment that can be formed by comparing the two densities. Helium, of course, is almost always in the form of a gas: to change it to a solid requires a temperature near absolute zero. And iron is a solid, meaning that it only turns into a liquid at extraordinarily high temperatures. These differences in overall structure can, in turn, be attributed to the relative motion, attraction, and energy of the molecules in each.
Molecular Attraction and Motion At the molecular level, every item of matter in the world is in motion, and the rate of that motion is a function of the attraction between molecules. Furthermore, the rate at which molecules move in relation to one another determines phase of matter—that is, whether a particular item can be described as solid, liquid, or gas. The movement of molecules generates kinetic energy, or the energy of movement, which is manifested as thermal energy—what people call “heat” in ordinary language. (The difference between thermal energy and heat is explained in the essay on Temperature and Heat.) In fact, thermal energy is the result of molecules’ motion relative to one another: the faster they move, the greater the kinetic energy, and the greater the “heat.” When the molecules in a material move slowly—merely vibrating in place—they exert a strong attraction toward one another, and the material is called a solid. Molecules of liquid, by contrast, move at moderate speeds and exert a moderate attraction. A material substance whose molecules move at high speeds, and therefore exert little or no attraction, is known as a gas. In short, the weaker the attraction, the greater the rate of relative motion—and the greater the amount of thermal energy the object contains.
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Types of Solids Particles of solids resist attempts to compress them, or push them together, and because of their close proximity, solid particles are fixed in an orderly and definite pattern. As a result, a solid usually has a definite volume and shape. A crystalline solid is a type of solid in which the constituent parts are arranged in a simple, definite geometric pattern that is repeated in all directions. But not all crystalline solids are the same. Table salt is an example of an ionic solid: a form of crystalline solid that contains ions. When mixed with a solvent such as water, ions from the salt move freely throughout the solution, making it possible to conduct an electric current. Regular table sugar (sucrose) is a molecular solid, or one in which the molecules have a neutral electric charge—that is, there are no ions present. Therefore, a solution of water and sugar would not conduct electricity. Finally, there are crystalline solids known as atomic solids, in which atoms of one element bond to one another. Examples include diamonds (made of pure carbon), silicon, and all metals. Other solids are said to be amorphous, meaning that they possess no definite shape. Amorphous solids—an example of which is clay—either possess very tiny crystals, or consist of several varieties of crystal mixed randomly. Still other solids, among them glass, do not contain crystals.
Freezing and Melting V I B RAT I O N S A N D F R E E Z I N G .
Because of their slow movement in relation to one another, solid particles exert strong attractions; yet as slowly as they move, solid particles do move—as is the case with all forms of matter at the atomic level. Whereas the particles in a liquid or gas move fast enough to be in relative motion with regard to one another, however, solid particles merely vibrate from a fixed position. As noted earlier, the motion and attraction of particles in matter has a direct effect on thermal energy, and thus on heat and temperature. The cooler the solid, the slower and weaker the vibrations, and the closer the particles are to one
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another. Thus, most types of matter contract when freezing, and their density increases. Absolute zero, or 0K on the Kelvin scale of temperature—equal to –459.67°F (–273°C)—is the point at which vibration virtually ceases. Note that the vibration virtually stops, but does not totally stop. In fact, as established in the third law of thermodynamics, absolute zero is impossible to achieve: thus, the relative motion of molecules never ceases. The lowest temperature actually achieved, at a Finnish nuclear laboratory in 1993, is 2.8 • 10–10 K, or 0.00000000028K—still above absolute zero. U N U S UA L C H A RAC T E R I S T I CS O F S O L I D A N D L I Q U I D WAT E R.
The behavior of water when frozen is interesting and exceptional. Above 39.2°F (4°C) water, like most substances, expands when heated. In other words, the molecules begin moving further apart as expected, because—in this temperature range, at least—water behaves like other substances, becoming “less solid” as the temperature increases. Between 32°F (0°C) and 39.2°F (4°C), however, water actually contracts. In this temperature range, it is very “cold” (that is, it has relatively little heat), but it is not frozen. The density of water reaches its maximum—in other words, water molecules are as closely packed as they can be— at 39.2°F; below that point, the density starts to decrease again. This is highly unusual: in most substances, the density continues to increase with lowered temperatures, whereas water is actually most dense slightly above the freezing point. Below the freezing point, then, water expands, and therefore when water in pipes freezes, it may increase in volume to the point where it bursts the pipe. This is also the reason why ice floats on water: its weight is less than that of the water it has displaced, and thus it is buoyant. Additionally, the buoyant qualities of ice atop very cold water helps explain the behavior of lake water in winter; although the top of a lake may freeze, the entire lake rarely freezes solid— even in the coldest of inhabited regions.
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lake does not freeze completely—only a layer at the top—and this helps preserve animal and plant life in the body of water. M E LT I N G . When heated, particles begin to vibrate more and more, and therefore move further apart. If a solid is heated enough, it loses its rigid structure and becomes a liquid. The temperature at which a solid turns into a liquid is called the melting point, and melting points are different for different substances. The melting point of a substance, incidentally, is the same as its freezing point: the difference is a matter of orientation—that is, whether the process is one of a solid melting to become a liquid, or of a liquid freezing to become a solid.
The energy required to melt 1 mole of a solid substance is called the molar heat of fusion. It can be calculated by the formula Q = smδT, where Q is energy, s is specific heat capacity, m is mass, and δT means change in temperature. (In the symbolic language often employed by scientists, the Greek letter δ, or delta, stands for “change in.”) Specific heat capacity is measured in units of J/g • °C (joules per gram-degree Celsius), and energy in joules or kilojoules (kJ)— that is, 1,000 joules. In melting, all the thermal energy in a solid is used in breaking up the arrangement of crystals, called a lattice. This is why water melted from ice does not feel any warmer than the ice did: the thermal energy has been expended, and there is none left over for heating the water. Once all the ice is melted, however, the absorbed energy from the particles—now moving at much greater speeds than when the ice was in a solid state—causes the temperature to rise.
Instead of freezing from the bottom up, as it would if ice were less buoyant than the water, the lake freezes from the top down—an important thing to remember when ice-fishing! Furthermore, water in general (and ice in particular) is a poor conductor of heat, and thus little of the heat from the water below it escapes. Therefore, the
For the most part, solids composed of particles with a higher average atomic mass require more energy—and hence higher temperatures— to induce the vibrations necessary for melting. Helium, with an average atomic mass of 4.003 amu, melts or freezes at an incredibly low temperature: –457.6°F (–272°C), or close to absolute zero. Water, for which, as noted earlier, the average atomic mass is the sum of the masses for its two hydrogen atoms and one oxygen atom, has an average molecular mass of 18.016 amu. Ice melts (or water freezes) at much higher temperatures than helium: 32°F (0°C). Copper, with an average atomic mass of 63.55 amu, melts at much, much higher temperatures than water: 1,985°F (1,085°C).
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Liquids The particles of a liquid, as compared to those of a solid, have more energy, more motion, and— generally speaking—less attraction to one another. The attraction, however, is still fairly strong: thus, liquid particles are in close enough proximity that the liquid resists attempts at compression. On the other hand, their arrangement is loose enough that the particles tend to move around one another rather than simply vibrate in place the way solid particles do. A liquid is therefore not definite in shape. Due to the fact that the particles in a liquid are farther apart than those of a solid, liquids tend to be less dense than solids. The liquid phase of a substance thus tends to be larger in volume than its equivalent in solid form. Again, however, water is exceptional in this regard: liquid water actually takes up less space than an equal mass of frozen water.
Boiling When a liquid experiences an increase in temperature, its particles take on energy and begin to move faster and faster. They collide with one another, and at some point the particles nearest the surface of the liquid acquire enough energy to break away from their neighbors. It is at this point that the liquid becomes a gas or vapor. As heating continues, particles throughout the liquid begin to gain energy and move faster, but they do not immediately transform into gas. The reason is that the pressure of the liquid, combined with the pressure of the atmosphere above the liquid, tends to keep particles in place. Those particles below the surface, therefore, remain where they are until they acquire enough energy to rise to the surface. The heated particle moves upward, leaving behind it a hollow space—a bubble. A bubble is not an empty space: it contains smaller trapped particles, but its small mass, relative to that of the liquid it disperses, makes it buoyant. Therefore, a bubble floats to the top, releasing its trapped particles as gas or vapor. At that point, the liquid is said to be boiling.
ing air. Normal atmospheric pressure (1 atm) is equal to 14 lb/in2 (1.013 x 105 Pa), and is measured at sea level. The greater the altitude, the less the air pressure, because molecules of air—since air is a gas, and therefore its particles are fastmoving and non-attractive—respond less to Earth’s gravitational pull. This is why airplanes require pressurized cabins to maintain an adequate oxygen supply; but even at altitudes much lower than the flight path of an airplane, differences in air pressure are noticeable. It is for this reason that cooking instructions often vary with altitude. Atop Mt. Everest, Earth’s highest peak at about 29,000 ft (8,839 m) above sea level, the pressure is approximately one-third of normal atmospheric pressure. Water boils at a much lower temperature on Everest than it does elsewhere: 158°F (70°C), as opposed to 212°F (100°C) at sea level. Of course, no one lives on the top of Mt. Everest—but people do live in Denver, Colorado, where the altitude is 5,577 ft (1,700 m) and the boiling point of water is 203°F (95°C). Given the lower boiling point, one might assume that food would cook faster in Denver than in New York, Los Angeles, or in any city close to sea level. In fact, the opposite is true: because heated particles escape the water so much faster at high altitudes, they do not have time to acquire the energy needed to raise the temperature of the water. It is for this reason that a recipe may include a statement such as “at altitudes above XX feet, add XX minutes to cooking time.” If lowered atmospheric pressure means a lowered boiling point, what happens in outer space, where there is no atmospheric pressure? Liquids boil at very, very low temperatures. This is one of the reasons why astronauts have to wear pressurized suits: if they did not, their blood would boil—even though space itself is incredibly cold. L I Q U I D T O GAS A N D B AC K AGA I N . Note that the process of changing a
overcome atmospheric pressure as they rise, which means that the boiling point for any liquid depends in part on the pressure of the surround-
liquid to a gas is similar to that which occurs when a solid changes to a liquid: particles gain heat and therefore energy, begin to move faster, break free from one another, and pass a certain threshold into a new phase of matter. And just as the freezing and melting point for a given substance are the same temperature—the only difference being one of orientation—the boiling
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point of a liquid transforming into a gas is the same as the condensation point for a gas turning into a liquid. The behavior of water in boiling and condensation makes possible distillation, one of the principal methods for purifying sea water in various parts of the world. First the water is boiled, then it is allowed to cool and condense, thus forming water again. In the process, the water separates from the salt, leaving it behind in the form of brine. A similar separation takes place when salt water freezes: because salt, like most crystalline solids, has a much lower freezing point than water, very little of it remains joined to the water in ice. Instead, the salt takes the form of a briny slush.
Gases A liquid that is vaporized, or any substance that exists normally as a gas, is quite different in physical terms from a solid or a liquid. This is illustrated by the much higher energy component in the molar heat of vaporization, or the amount of energy required to turn 1 mole of a liquid into a gas. Consider, for instance, what happens to water when it experiences phase changes. Assuming that heat is added at a uniform rate, when ice reaches its melting point, there is only a relatively small period of time when the H2O is composed of both ice and liquid. But when the liquid reaches its boiling point, the water is present both as a liquid and a vapor for a much longer period of time. In fact, it takes almost seven times as much energy to turn liquid water into pure steam than it does to turn ice into purely liquid water. Thus, the molar heat of fusion for water is 6.02 kJ/mol, while the molar heat of vaporization is 40.6 kJ/mol. Although liquid particles exert a moderate attraction toward one another, particles in a gas (particularly a substance that normally exists as a gas at ordinary temperatures on Earth) exert little to no attraction. They are thus free to move, and to move quickly. The overall shape and arrangement of gas is therefore random and indefinite—and, more importantly, the motion of gas particles provides much greater kinetic energy than is present in any other major form of matter on Earth.
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ing and thereby transferring kinetic energy back and forth without any net loss of energy. These collisions also have the overall effect of producing uniform pressure in a gas. At the same time, the characteristics and behavior of gas particles indicate that they tend not to remain in an open container. Therefore, in order to have any pressure on a gas—other than normal atmospheric pressure—it is necessary to keep it in a closed container.
The Phase Diagram The vaporization of water is an example of a change of phase—the transition from one phase of matter to another. The properties of any substance, and the points at which it changes phase, are plotted on what is known as a phase diagram. The phase diagram typically shows temperature along the x-axis, and pressure along the y-axis. For simple substances, such as water and carbon dioxide (CO2), the solid form of the substance appears at a relatively low temperature and at pressures anywhere from zero upward. The line between solids and liquids, indicating the temperature at which a solid becomes a liquid at any pressure above a certain level, is called the fusion curve. Though it appears to be a more or less vertical line, it is indeed curved, indicating that at high pressures, a solid well below the normal freezing point may be melted to create a liquid. Liquids occupy the area of the phase diagram corresponding to relatively high temperatures and high pressures. Gases or vapors, on the other hand, can exist at very low temperatures, but only if the pressure is also low. Above the melting point for the substance, gases exist at higher pressures and higher temperatures. Thus, the line between liquids and gases often looks almost like a 45° angle. But it is not a straight line, as its name, the vaporization curve, implies. The curve of vaporization demonstrates that at relatively high temperatures and high pressures, a substance is more likely to be a gas than a liquid.
The constant, fast, and random motion of gas particles means that they are regularly collid-
T H E C R I T I CA L P O I N T. There are several other interesting phenomena mapped on a phase diagram. One is the critical point, found at a place of very high temperature and pressure along the vaporization curve. At the critical point, high temperatures prevent a liquid from remaining a liquid, no matter how high the pressure.
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Properties of Matter
(y-axis) pressure
(liquid) (solid)
triple point
(x-axis)
A
(vapor)
temperature
PHASE DIAGRAM FOR WATER.
At the same time, the pressure causes gas beyond that point to become increasingly more dense, but due to the high temperatures, it does not condense into a liquid. Beyond the critical point, the substance cannot exist in anything other than the gaseous state. The temperature component of the critical point for water is 705.2°F (374°C)—at 218 atm, or 218 times ordinary atmospheric pressure. For helium, however, critical temperature is just a few degrees above absolute zero. This is, in part, why helium is rarely seen in forms other than a gas. THE
S U B L I M AT I O N
CURVE.
Another interesting phenomenon is the sublimation curve, or the line between solid and gas. At certain very low temperatures and pressures, a substance may experience sublimation, meaning that a gas turns into a solid, or a solid into a gas, without passing through a liquid stage. A well-known example of sublimation occurs when “dry ice,” made of carbon dioxide, vaporizes at temperatures above (–78.5°C). Carbon dioxide is exceptional, however, in that it experiences sublimation at relatively high pressures that occur in everyday life: for most substances, the sublimation point transpires at such a low pressure point that it is seldom witnessed outside of a laboratory.
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T H E T R I P L E P O I N T. The phenomenon known as the triple point shows how an ordinary substance such as water or carbon dioxide can actually be a liquid, solid, and vapor—all at once. Most people associate water as a gas or vapor (that is, steam) with very high temperatures. Yet, at a level far below normal atmospheric pressure, water can be a vapor at temperatures as low as –4°F (–20 °C). (All of the pressure values in the discussion of water at or near the triple point are far below atmospheric norms: the pressure at which water turns into a vapor at –4°F, for instance, is about 0.001 atm.)
Just as water can exist as a vapor at low temperatures and low pressures, it is also possible for water at temperatures below freezing to remain liquid. Under enough pressure, ice melts and is thereby transformed from a solid to a liquid, at temperatures below its normal freezing point. On the other hand, if the pressure of ice falls below a very low threshold, it will sublimate. The phase diagram of water shows a line between the solid and liquid states that is almost, but not quite, exactly perpendicular to the x-axis. But in fact, it is a true fusion curve: it slopes slightly upward to the left, indicating that solid ice turns into water with an increase of pressure. Below a certain level of pressure is the vaporiza-
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tion curve, and where the fusion curve intersects the vaporization curve, there is a place called the triple point. Just below freezing, in conditions equivalent to about 0.007 atm, water is a solid, liquid, and vapor all at once.
Other States of Matter P L A S M A . Principal among states of matter other than solid, liquid, and gas is plasma, which is similar to gas. (The term “plasma,” when referring to the state of matter, has nothing to do with the word as it is often used, in reference to blood plasma.) As with gas, plasma particles collide at high speeds—but in plasma the speeds are even greater, and the kinetic energy levels even higher.
The speed and energy of these collisions is directly related to the underlying property that distinguishes plasma from gas. So violent are the collisions between plasma particles that electrons are knocked away from their atoms. As a result, plasma does not have the atomic structure typical of a gas; rather, it is composed of positive ions and electrons. Plasma particles are thus electrically charged, and therefore greatly influenced by electric and magnetic fields. Formed at very high temperatures, plasma is found in stars. The reaction between plasma and atomic particles in the upper atmosphere is responsible for the aurora borealis, or “northern lights.” Though found on Earth only in very small quantities, plasma—ubiquitous in other parts of the universe—may be the most plentiful of all the states of matter. Q UAS I - S TAT E S . Among the quasistates of matter discussed by scientists are several terms describing the structure in which particles are joined, rather than the attraction and relative movement of those particles. Thus “crystalline,” “amorphous,” and “glassy” are all terms to describe what may be individual states of matter; so too is “colloidal.”
A colloid is a structure intermediate in size between a molecule and a visible particle, and it has a tendency to be dispersed in another medium—the way smoke, for instance, is dispersed in air. Brownian motion describes the behavior of most colloidal particles. When one sees dust floating in a ray of sunshine through a window, the light reflects off colloids in the dust, which are driven back and forth by motion in the air otherwise imperceptible to the human senses.
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DA R K M AT T E R. The number of states or phases of matter is clearly not fixed, and it is quite possible that more will be discovered in outer space, if not on Earth. One intriguing candidate is called dark matter, so described because it neither reflects nor emits light, and is therefore invisible. In fact, luminous or visible matter may very well make up only a small fraction of the mass in the universe, with the rest being taken up by dark matter.
If dark matter is invisible, how do astronomers and physicists know it exists? By analyzing the gravitational force exerted on visible objects in such cases where there appears to be no visible object to account for that force. An example is the center of our galaxy, the Milky Way. It appears to be nothing more than a dark “halo,” but in order to cause the entire galaxy to revolve around it—in the same way that planets revolve around the Sun, though on a vastly larger scale—it must contain a staggering quantity of invisible mass.
The Bose-Einstein Condensate Physicists at the Joint Institute of Laboratory Astrophysics in Boulder, Colorado, in 1995 revealed a highly interesting aspect of atomic behavior at temperatures approaching absolute zero. Some 70 years before, Einstein had predicted that, at extremely low temperatures, atoms would fuse to form one large “superatom.” This hypothesized structure was dubbed the BoseEinstein Condensate (BEC) after Einstein and Satyendranath Bose (1894-1974), an Indian physicist whose statistical methods contributed to the development of quantum theory. Cooling about 2,000 atoms of the element rubidium to a temperature just 170 billionths of a degree Celsius above absolute zero, the physicists succeeded in creating an atom 100 micrometers across—still incredibly small, but vast in comparison to an ordinary atom. The superatom, which lasted for about 15 seconds, cooled down all the way to just 20 billionths of a degree above absolute zero. The Colorado physicists won the Nobel Prize in physics in 1997 for their work. In 1999, researchers in a lab at Harvard University also created a superatom of BEC, and used it to slow light to just 38 MPH (61.2 km/h)—about 0.02% of its ordinary speed.
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Dubbed a “new” form of matter, the BEC may lead to a greater understanding of quantum mechanics, and may aid in the design of smaller, more powerful computer chips.
Some Unusual Phase Transitions At places throughout this essay, references have been made variously to “phases” and “states” of matter. This is not intended to confuse, but rather to emphasize a particular point. Solids, liquids, and gases are referred to as “phases” because many (though far from all) substances on Earth regularly move from one phase to another. There is absolutely nothing incorrect in referring to “states of matter.” But “phases of matter” is used in the present context as a means of emphasizing the fact that substances, at the appropriate temperature and pressure, can be solid, liquid, or gas. The phases of matter, in fact, can be likened to the phases of a person’s life: infancy, babyhood, childhood, adolescence, adulthood, old age. The transition between these stages is indefinite, yet it is easy enough to say when a person is at a certain stage. L I Q U I D C RY S TA L S . A liquid crystal is a substance that, over a specific range of temperature, displays properties both of a liquid and a solid. Below this temperature range, it is unquestionably a solid, and above this range it is just as certainly a liquid. In between, however, liquid crystals exhibit a strange solid-liquid behavior: like a liquid, their particles flow, but like a solid, their molecules maintain specific crystalline arrangements.
The cholesteric class of liquid crystals is so named because the spiral patterns of light through the crystal are similar to those which appear in cholesterols. Depending on the physical properties of a cholesteric liquid crystal, only certain colors may be reflected. The response of liquid crystals to light makes them useful in liquid crystal displays (LCDs) found on laptop computer screens, camcorder views, and in other applications.
lar energy levels. Liquefied natural gas (LNG) and liquefied petroleum gas (LPG), the latter a mixture of by-products obtained from petroleum and natural gas, are among the examples of liquefied gas in daily use. In both cases, the volume of the liquefied gas is far less than it would be if the gas were in a vaporized state, thus enabling ease and economy of transport. Liquefied gases are used as heating fuel for motor homes, boats, and homes or cabins in remote areas. Other applications of liquefied gases include liquefied oxygen and hydrogen in rocket engines; liquefied oxygen and petroleum used in welding; and a combination of liquefied oxygen and nitrogen used in aqualung devices. The properties of liquefied gases figure heavily in the science of producing and studying low-temperature environments. In addition, liquefied helium is used in studying the behavior of matter at temperatures close to absolute zero. C OA L GAS I F I CAT I O N . Coal gasification, as one might discern from the name, is the conversion of coal to gas. Developed before World War II, it fell out of favor after the war, due to the lower cost of oil and natural gas. However, increasingly stringent environmental regulations imposed by the federal government on industry during the 1970s, combined with a growing concern for the environment on the part of the populace as a whole, led to a resurgence of interest in coal gasification.
Though widely used as a fuel in power plants, coal, when burned by ordinary means, generates enormous air pollution. Coal gasification, on the other hand, makes it possible to burn “clean” coal. Gasification involves a number of chemical reactions, some exothermic or heatreleasing, and some endothermic or heat-absorbing. At one point, carbon monoxide is released in an exothermic reaction, then mixed with hydrogen released from the coal to create a second exothermic reaction. The energy discharged in these first two reactions is used to initiate a third, endothermic, reaction.
One interesting and useful application of phase change is the liquefaction of gases, or the change of gas into liquid by the reduction in its molecu-
The finished product of coal gasification is a mixture containing carbon monoxide, methane, hydrogen, and other substances, and this—rather than ordinary coal—is burned as a fuel. The composition of the gases varies according to the process used. Products range from coal synthesis gas and medium-Btu gas (both composed of car-
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Properties of Matter
KEY TERMS The temperature,
ABSOLUTE ZERO:
AVOGADRO’S NUMBER:
defined as 0K on the Kelvin scale, at which
named after Italian physicist Amedeo Avo-
the motion of molecules in a solid virtual-
gadro (1776-1856), equal to 6.022137 x
ly ceases. Absolute zero is equal to
1023. Avogadro’s number indicates the
–459.67°F (–273.15°C).
number of atoms, molecules, or other ele-
ATOM:
The smallest particle of an ele-
mentary particles in a mole.
ment that retains the chemical and physical
CHANGE OF PHASE:
properties of the element. An atom can
from one phase of matter to another.
exist either alone or in combination with other atoms in a molecule. Atoms are made up of protons, neutrons, and electrons. An atom that loses or gains one or more electrons, and thus has a net charge, is an ion. Atoms that have the same number of protons—that is, are of the same element— but differ in number of neutrons, are known as isotopes.
CRITICAL POINT:
An SI unit
(abbreviated amu), equal to 1.66 • 10–24 g,
A coordinate, plot-
stance cannot exist in anything other than the gaseous state. Located at a position of very high temperature and pressure, the critical point marks the termination of the vaporization curve. A substance made up of
atoms of more than one element. These atoms are usually, but not always, joined in molecules.
for measuring the mass of atoms. ATOMIC NUMBER:
The transition
ted on a phase diagram, above which a sub-
COMPOUND:
ATOMIC MASS UNIT:
The number of
CRYSTALLINE
SOLID:
A type of
protons in the nucleus of an atom. Since
solid in which the constituent parts have a
this number is different for each element,
simple and definite geometric arrange-
elements are listed on the periodic table in
ment that is repeated in all directions.
order of atomic number.
Types of crystalline solids include atomic
ATOMIC SOLID:
A form of crystalline
solids, ionic solids, and molecular solids. A substance made up of
solid in which atoms of one element bond
ELEMENT:
to one another. Examples include dia-
only one kind of atom.
monds (made of pure carbon), silicon, and ELECTRON:
all metals.
A negatively charged par-
ticle in an atom. Electrons, which spin A figure
around the protons and neutrons that
used by chemists to specify the mass—in
make up the atom’s nucleus, constitute a
atomic mass units—of the average atom in
very small portion of the atom’s mass. In
a large sample. If a substance is a com-
most atoms, the number of electrons and
pound, the average atomic mass of all
protons is the same, thus canceling out one
atoms in a molecule of that substance must
another. When an atom loses one or more
be added together to yield the average
electrons, however—thus becoming an
molecular mass of that substance.
ion—it acquires a net electric charge.
AVERAGE ATOMIC MASS:
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A figure,
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Properties of Matter
KEY TERMS The ability to accomplish
ENERGY:
CONTINUED
MOLAR HEAT OF FUSION:
The
work—that is, the exertion of force over a
amount of energy required to melt 1 mole
given distance to displace or move an
of a solid substance.
object.
MOLAR HEAT OF VAPORIZATION:
The boundary be-
The amount of energy required to turn 1
tween solid and liquid for any given sub-
mole of a liquid into a gas. Because gases
stance as plotted on a phase diagram.
possess much more energy than liquids or
FUSION CURVE:
solids, molar heat of vaporization is usualGAS:
A phase of matter in which mole-
ly much higher than molar heat of fusion.
cules move at high speeds, and therefore exert little or no attraction toward one
MOLAR MASS:
The mass, in grams, of
1 mole of a given substance. The value in
another.
grams of molar mass is always equal to the An atom or atoms that has lost or
value, in atomic mass units, of the average
gained one or more electrons, and thus has
atomic mass of that substance: thus car-
a net electric charge.
bon has a molar mass of 12.01 g, and an
ION:
IONIC SOLID:
A form of crystalline
average atomic mass of 12.01 amu. The SI fundamental unit for
solid that contains ions. When mixed with
MOLE:
a solvent such as water, ions from table
“amount of substance.” A mole is, general-
salt—an example of an ionic solid—move
ly speaking, Avogadro’s number of atoms,
freely throughout the solution, making it
molecules, or other elementary particles;
possible to conduct an electric current.
however, in the more precise SI definition,
ISOTOPES:
Atoms that have an equal
number of protons, and hence are of the
a mole is equal to the number of carbon atoms in 12.01 g of carbon. A form of crys-
same element, but differ in their number of
MOLECULAR SOLID:
neutrons.
talline solid in which the molecules have a neutral electric charge, meaning that there
KINETIC ENERGY:
The energy that
an object possesses by virtue of its movement. LIQUID:
are no ions present as there are in an ionic solid. Table sugar (sucrose) is an example of a molecular solid. When mixed with a
A phase of matter in which
solvent such as water, the resulting solution
molecules move at moderate speeds, and
does not conduct electricity.
therefore exert moderate attractions
MOLECULE:
toward one another.
ly of more than one element, joined in a
MATTER:
Physical substance that occu-
A group of atoms, usual-
structure. A subatomic particle that
pies space, has mass, is composed of atoms
NEUTRON:
(or in the case of subatomic particles, is
has no electric charge. Neutrons are found
part of an atom), and is convertible to
at the nucleus of an atom, alongside
energy.
protons.
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Properties of Matter
KEY TERMS
CONTINUED
The center of an atom, a
same mass—a mass that is many times
region where protons and neutrons are
greater than that of an electron. The num-
located, and around which electrons spin.
ber of protons in the nucleus of an atom is
NUCLEUS:
PHASE DIAGRAM:
A chart, plotted
the atomic number of an element.
for any particular substance, identifying
SOLID:
the particular phase of matter for that sub-
molecules move slowly relative to one
stance at a given temperature and pressure
another, and therefore exert strong attrac-
level. A phase diagram usually shows tem-
tions toward one another.
A phase of matter in which
perature along the x-axis, and pressure SUBLIMATION CURVE:
along the y-axis. PHASES OF MATTER:
The bound-
ary between solid and gas for any given The various
substance, as plotted on a phase diagram.
forms of material substance (matter), which are defined primarily in terms of the
In chemistry and other sci-
behavior exhibited by their atomic or
ences, the term “system” usually refers to
molecular structures. On Earth, three prin-
any set of interactions isolated from the
cipal phases of matter exist, namely solid,
rest of the universe. Anything outside of
liquid, and gas. Other forms of matter
the system, including all factors and forces
include plasma.
irrelevant to a discussion of that system, is
PLASMA:
One of the phases of matter,
known as the environment. “Heat” energy, a
closely related to gas. Plasma is found pri-
THERMAL ENERGY:
marily in stars. Containing neither atoms
form of kinetic energy produced by the rel-
nor molecules, plasma is made up of elec-
ative motion of atoms or molecules. The
trons and positive ions.
greater the movement of these particles,
PROTON:
A positively charged particle
the greater the thermal energy. The bound-
in an atom. Protons and neutrons, which
VAPORIZATION CURVE:
together form the nucleus around which
ary between liquid and gas for any given
electrons spin, have approximately the
substance as plotted on a phase diagram.
bon monoxide and hydrogen, though combined in different forms) to substitute natural gas, which consists primarily of methane. Not only does coal gasification produce a clean-burning product, but it does so without the high costs associated with flue-gas desulfurization systems. The latter, often called “scrubbers,” were originally recommended by the federal government to industry, but companies discovered that coal gasification could produce the same results for much less money. In addition, the waste products from coal gasification can be used
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SYSTEM:
VOLUME 1: REAL-LIFE CHEMISTRY
for other purposes. At the Cool Water Integrated Gasification Combined Cycle Plant, established in Barstow, California, in 1984, sulfur obtained from the reduction of sulfur dioxide is sold off for about $100 a ton.
The Chemical Dimension to Changes of Phase Throughout much of this essay, we have discussed changes of phase primarily in physical terms; yet clearly these changes play a significant role in chemistry. Furthermore, coal gasification
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serves to illustrate the impact chemical processes can have on changes of state. Much earlier, figures were given for the melting points of copper, water, and helium, and these were compared with the average atomic mass of each. Those figures, again, are: Average Atomic Mass and Melting Points of a Sample Gas, Liquid, and Solid • Helium: 4.003 amu; –457.6°F (–210°C) • Water: 40.304 amu 32°F (0°C) • Copper: 63.55 amu; 1,985°F (1,085°C). Something seems a bit strange about those comparisons: specifically, the differences in melting point appear to be much more dramatic than the differences in average atomic mass. Clearly, another factor is at work—a factor that relates to the difference in the attractions between molecules in each. Although the differences between solids, liquids, and gases are generally physical, the one described here—a difference between substances—is clearly chemical in nature. To discuss this in the detail it deserves would require a lengthy digression on the chemical dimensions of intermolecular attraction. Nonetheless, it is possible here to offer at least a cursory answer to the question raised by these striking differences in response to temperature.
Dipoles, Electron Seas, and London Dispersion Water molecules are polar, meaning that one area of a water molecule is positively charged, while another area has a negative charge. Thus the positive side of one molecule is drawn to the negative side of another, and vice versa, which gives water a much stronger intermolecular bond than, for instance, oil, in which the positive and negative charges are evenly distributed throughout the molecule. Yet the intermolecular attraction between the dipoles (as they are called) in water is not nearly as strong as the bond that holds together a metal. Particles in copper or other metals “float” in a tightly packed “sea” of highly mobile electrons, which provide a bond that is powerful, yet lacking in a firm directional orientation. Thus metals are both strong and highly malleable (that is, they can be hammered very flat without breaking.)
S C I E N C E O F E V E RY DAY T H I N G S
Water, of course, appears most often as a liquid, and copper as a solid, precisely because water has a very high boiling point (the point at which it becomes a vapor) and copper has a very high melting point. But consider helium, which has the lowest freezing point of any element: just above absolute zero. Even then, a pressure equal to 25 times that of normal atmospheric pressure is required to push it past the freezing point.
Properties of Matter
Helium and other Group 8 or Group 18 elements, as well as non-polar molecules such as oils, are bonded by what is called London dispersion forces. The latter, as its name suggests, tends to keep molecules dispersed, and induces instantaneous dipoles when most of the electrons happen to be on one side of an atom. Of course, this happens only for an infinitesimal fraction of time, but it serves to create a weak attraction. Only at very low temperatures do London dispersion forces become strong enough to result in the formation of a solid.
WHERE TO LEARN MORE Biel, Timothy L. Atom: Building Blocks of Matter. San Diego, CA: Lucent Books, 1990. Feynman, Richard. Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher. New introduction by Paul Davies. Cambridge, MA: Perseus Books, 1995. “High School Chemistry Table of Contents—Solids and Liquids” Homeworkhelp.com (Web site). (April 10, 2001). “Matter: Solids, Liquids, Gases.” Studyweb (Web site). (April 10, 2001). “The Molecular Circus” (Web site). (April 10, 2001). Paul, Richard. A Handbook to the Universe: Explorations of Matter, Energy, Space, and Time for Beginning Scientific Thinkers. Chicago: Chicago Review Press, 1993. “Phases of Matter” (Web site). (April 10, 2001). Royston, Angela. Solids, Liquids, and Gasses. Chicago: Heinemann Library, 2001. Wheeler, Jill C. The Stuff Life’s Made Of: A Book About Matter. Minneapolis, MN: Abdo & Daughters Publishing, 1996. Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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GASES Gases
CONCEPT The number of elements that appear ordinarily in the form of a gas is relatively small: oxygen, hydrogen, fluorine, and chlorine in the halogen “family”; and a handful of others, most notably the noble gases in Group 8 of the periodic table. Yet many substances can exist in the form of a gas, depending on the relative attraction and motion of molecules in that substance. A simple example, of course, is water, or H2O, which, though it appears as a liquid at room temperature, begins to vaporize and turn into steam at 212°F (100°C). In general, gases respond more dramatically to changes in pressure and temperature than do most other types of matter, and this allows scientists to predict gas behaviors under certain conditions. These predictions can explain mundane occurrences, such as the fact that an open can of soda will soon lose its fizz, but they also apply to more dramatic, life-anddeath situations.
HOW IT WORKS Molecular Motion and Phases of Matter On Earth, three principal phases or states of matter exist: solid, liquid, and gas. The differences between these three are, on the surface at least, easily perceivable. Clearly water is a liquid, just as ice is a solid and steam a vapor or gas. Yet the ways in which various substances convert between phases are often complex, as are the interrelations between these phases. Ultimately, understanding of the phases depends on an
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VOLUME 1: REAL-LIFE CHEMISTRY
awareness of what takes place at the molecular level. All molecules are in motion, and the rate of that motion determines the attraction between them. The movement of molecules generates kinetic energy, or the energy of movement, which is manifested as thermal energy. In everyday language, thermal energy is what people mean when they say “heat”; but in scientific terms, heat has a different definition. The force that attracts atoms to atoms, or molecules to molecules, is not the same as gravitational force, which holds the Moon in orbit around Earth, Earth in orbit around the Sun, and so on. By contrast, the force of interatomic and intermolecular attraction is electromagnetic. Just as the north pole of a magnet is attracted to the south pole of another magnet and repelled by that other magnet’s north pole, so positive electric charges are attracted to negative charges, and negatives to positives. (In fact, electricity and magnetism are both manifestations of an electromagnetic interaction.) The electromagnetic attractions between molecules are much more complex than this explanation makes it seem, and they play a highly significant role in chemical bonding. In simple terms, however, one can say that the greater the rate of motion for the molecules in relation to one another, the less the attraction between molecules. In addition, the kinetic energy, and hence the thermal energy, is greater in a substance whose molecules are relatively free to move. When the molecules in a material move slowly in relation to one another, they exert a strong attraction, and the material is called a solid. Molecules of liquid, by contrast, move at
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Gases
A
COMPARISON OF GAS, LIQUID, AND SOLID STATES.
moderate speeds and exert a moderate attraction. A material substance whose molecules move at high speeds, and therefore exert little or no attraction, is known as a gas.
Comparison of Gases to Other Phases of Matter WAT E R A N D A I R C O M PA R E D .
Gases respond to changes in pressure and temperature in a manner remarkably different from that of solids or liquids. Consider the behavior of liquid water as compared with air—a combination of oxygen (O2), nitrogen (N2), and other gases—in response to experiments involving changes in pressure and temperature. In the first experiment, both samples are subjected to an increase in pressure from 1 atm (that is, normal atmospheric pressure at sea level) to 2 atm. In the second, both experience an increase in temperature from 32°F (0°C) to 212°F (100°C). The differences in the responses of water and air are striking.
increase will decrease the volume by a whopping 50%, and an equivalent temperature increase results in a volume increase of 37%. Air and other gases, by definition, have a boiling point below room temperature. If they did not boil and thus become gas well below ordinary temperatures, they would not be described as substances that are in the gaseous state in most circumstances. The boiling point of water, of course, is higher than room temperature, and that of solids is much higher. T H E A R RA N G E M E N T O F PA R T I C L E S . Solids possess a definite volume and
a definite shape, and are relatively noncompressible: for instance, if one applies extreme pressure to a steel plate, it will bend, but not much. Liquids have a definite volume, but no definite shape, and tend to be noncompressible. Gases, on the other hand, possess no definite volume or shape, and are highly compressible.
A sample of water that experiences an increase in pressure from 1 to 2 atm will decrease in volume by less than 0.01%, while a temperature increase from the freezing point to the boiling point will result in only a 2% increase in volume. For air, however, an equivalent pressure
At the molecular level, particles of solids tend to be definite in their arrangement and close in proximity—indeed, part of what makes a solid “solid,” in the everyday meaning of that term, is the fact that its constituent parts are basically immovable. Liquid molecules, too, are close in proximity, though random in arrangement. Gas
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units of pressure represent some ratio of force to surface area.
Gases
U N I T S O F P R E SS U R E . The principal SI unit of pressure is called a pascal (Pa), or 1 N/m2. It is named for French mathematician and physicist Blaise Pascal (1623-1662), who is credited with Pascal’s principle. The latter holds that the external pressure applied on a fluid— which, in the physical sciences, can mean either a gas or a liquid—is transmitted uniformly throughout the entire body of that fluid.
A newton (N), the SI unit of force, is equal to the force required to accelerate 1 kg of mass at a rate of 1 m/sec2. Thus a Pascal is the pressure of 1 newton over a surface area of 1 m2. In the English or British system, pressure is measured in terms of pounds per square inch, abbreviated as lbs./in2. This is equal to 6.89 • 103 Pa, or 6,890 Pa.
THE
DIVERS PICTURED HERE HAVE ASCENDED FROM A
SUNKEN SHIP AND HAVE STOPPED AT THE METER)
DECOMPRESSION
LEVEL
TO
10-FT (3-
AVOID
GETTING
DECOMPRESSION SICKNESS, BETTER KNOWN AS THE
“BENDS.” (Jonathan Blair/Corbis. Reproduced by permission)
molecules are random in arrangement, but tend to be more widely spaced than liquid molecules.
Pressure There are a number of statements, collectively known as the “gas laws,” that describe and predict the behavior of gases in response to changes in temperature, pressure, and volume. Temperature and volume are discussed elsewhere in this book. However, the subject of pressure requires some attention before we can continue with a discussion of the gas laws. When a force is applied perpendicular to a surface area, it exerts pressure on that surface. Hence the formula for pressure is p = F/A, where p is pressure, F force, and A the area over which the force is applied. The greater the force, and the smaller the area of application, the greater the pressure; conversely, an increase in area—even without a reduction in force—reduces the overall pressure.
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Another important measure of pressure is the atmosphere (atm), which is the average pressure exerted by air at sea level. In English units, this is equal to 14.7 lb/in2, and in SI units, to 1.013 • 105 Pa. There are two other specialized units of pressure measurement in the SI system: the bar, equal to 105 Pa, and the torr, equal to 133 Pa. Meteorologists, scientists who study weather patterns, use the millibar (mb), which, as its name implies, is equal to 0.001 bars. At sea level, atmospheric pressure is approximately 1,013 mb. The torr, also known as the millimeter of mercury (mm Hg), is the amount of pressure required to raise a column of mercury (chemical symbol Hg) by 1 mm. It is named for Italian physicist Evangelista Torricelli (1608-1647), who invented the barometer, an instrument for measuring atmospheric pressure. T H E B A R O M E T E R. The barometer constructed by Torricelli in 1643 consisted of a long glass tube filled with mercury. The tube was open at one end, and turned upside down into a dish containing more mercury: the open end was submerged in mercury, while the closed end at the top constituted a vacuum—that is, an area devoid of matter, including air.
Pressure is measured by a number of units in the English and SI systems. Because p = F/A, all
The pressure of the surrounding air pushed down on the surface of the mercury in the bowl, while the vacuum at the top of the tube provided an area of virtually no pressure into which the mercury could rise. Thus the height to which the
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Gases
Air cleaner Carburetor
Ignition coil
Intake manifold Push rod
Cylinder head
Rocker arm Valve spring Exhaust valve
Intake valve
Exhaust manifold
Spark plug Valve lifter Piston pin Piston
Camshaft
Crankshaft Exhaust manifold Starter solenoid Starter motor
Cylinder block Connecting rod Oil pan
Oil intake screen assembly
INTAKE STROKE Exhaust valve closed Exhaust valve
COMPRESSION STROKE
Intake valve open Rocker arm
Exhaust valve closed
Intake valve closed
POWER STROKE Exhaust valve closed
Spark plug
Valve spring
Intake valve
Top-deadcenter (T.D.C.)
Fuel/air mixture from the intake manifold
Intake valve closed
EXHAUST STROKE Exhaust valve open
Intake valve closed
Exhaust to exhaust manifold
Stroke
Piston Bottomdeadcenter (B.D.C.)
Push rod Lifter
THE
MAJOR COMPONENTS OF AN INTERNAL COMBUSTION ENGINE
TION SEQUENCE
(TOP),
AND THE FOUR STROKES OF ITS COMBUS-
(BOTTOM).
mercury rose in the glass tube represented normal air pressure (that is, 1 atm.) Torricelli discovered that at standard atmospheric pressure, the column of mercury rose to 760 mm (29.92 in). The value of 1 atm was thus established as equal to the pressure exerted on a column of mercury 760 mm high at a temperature of 0°C (32°F). In time, Torricelli’s invention became a fixture both of scientific laboratories and of households. Since changes in atmospheric pressure have an effect on weather patterns, many home indoor-outdoor thermometers today also include a barometer.
S C I E N C E O F E V E RY DAY T H I N G S
REAL-LIFE A P P L I C AT I O N S Introduction to the Gas Laws English chemist Robert Boyle (1627-1691), who made a number of important contributions to chemistry—including his definition and identification of elements—seems to have been influenced by Torricelli. If so, this is an interesting example of ideas passing from one great thinker to another: Torricelli, a student of Galileo Galilei (1564-1642), was no doubt influenced by Galileo’s thermoscope. Like Torricelli, Boyle conducted tests involving the introduction of mercury to a tube closed
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at the other end. The tube Boyle used was shaped like the letter J, and it was so long that he had to use the multi-story foyer of his house as a laboratory. At the tip of the curved bottom was an area of trapped gas, and into the top of the tube, Boyle introduced increasing quantities of mercury. He found that the greater the volume of mercury, the greater the pressure on the gas, and the less the volume of gas at the end of the tube. As a result, he formulated the gas law associated with his name. The gas laws are not a set of government regulations concerning use of heating fuel; rather, they are a series of statements concerning the behavior of gases in response to changes in temperature, pressure, and volume. These were derived, beginning with Boyle’s law, during the seventeenth, eighteenth, and nineteenth centuries by scientists whose work is commemorated through the association of their names with the laws they discovered. In addition to Boyle, these men include fellow English chemists John Dalton (1766-1844) and William Henry (17741836); French physicists and chemists J. A. C. Charles (1746-1823) and Joseph Gay-Lussac (1778-1850); and Italian physicist Amedeo Avogadro (1776-1856). There is a close relationship between Boyle’s, Charles’s, and Gay-Lussac’s laws. All of these treat one of three parameters—temperature, pressure, or volume—as fixed quantities in order to explain the relationship between the other two variables. Avogadro’s law treats two of the parameters as fixed, thereby establishing a relationship between volume and the number of molecules in a gas. The ideal gas law sums up these four laws, and the kinetic theory of gases constitutes an attempt to predict the behavior of gases based on these laws. Finally, Dalton’s and Henry’s laws both relate to partial pressure of gases.
Boyle’s, Charles’s, and GayLussac’s Laws BOYLE’S AND CHARLES’S LAW S . Boyle’s law holds that in isothermal
52
In this case, the greater the pressure, the less the volume and vice versa. Therefore, the product of the volume multiplied by the pressure remains constant in all circumstances. Charles’s law also yields a constant, but in this case the temperature and volume are allowed to vary under isobarometric conditions—that is, a situation in which the pressure remains the same. As gas heats up, its volume increases, and when it cools down, its volume reduces accordingly. Hence, Charles established that the ratio of temperature to volume is constant. A B S O LU T E T E M P E RAT U R E . In about 1787, Charles made an interesting discovery: that at 0°C (32°F), the volume of gas at constant pressure drops by 1/273 for every Celsius degree drop in temperature. This seemed to suggest that the gas would simply disappear if cooled to -273°C (-459.4°F), which, of course, made no sense. In any case, the gas would most likely become first a liquid, and then a solid, long before it reached that temperature.
The man who solved the quandary raised by Charles’s discovery was born a year after Charles died. He was William Thomson, Lord Kelvin (1824-1907); in 1848, he put forward the suggestion that it was molecular translational energy—the energy generated by molecules in motion—and not volume, that would become zero at -273°C. He went on to establish what came to be known as the Kelvin scale of absolute temperature. Sometimes known as the absolute temperature scale, the Kelvin scale is based not on the freezing point of water, but on absolute zero— the temperature at which molecular motion comes to a virtual stop. This is -273.15°C (-459.67°F). In the Kelvin scale, which uses neither the term nor the symbol for “degree,” absolute zero is designated as 0K. Scientists prefer the Kelvin scale to the Celsius, and certainly to the Fahrenheit, scales. If the Kelvin temperature of an object is doubled, its average molecular translational energy has doubled as well. The same cannot be said if the temperature were doubled from, say, 10°C to 20°C, or from 40°F to 80°F, since neither the Celsius nor the Fahrenheit scale is based on absolute zero.
conditions (that is, a situation in which temperature is kept constant), an inverse relationship exists between the volume and pressure of a gas. (An inverse relationship is a situation involving two variables, in which one of the two increases in direct proportion to the decrease in the other.)
GAY - LU SSAC ’ S LAW. From Boyle’s and Charles’s law, a pattern should be emerging: both treat one parameter (temperature in Boyle’s, pressure in Charles’s) as unvarying, while
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two other factors are treated as variables. Both, in turn, yield relationships between the two variables: in Boyle’s law, pressure and volume are inversely related, whereas in Charles’s law, temperature and volume are directly related. In Gay-Lussac’s law, a third parameter, volume, is treated as a constant, and the result is a constant ratio between the variables of pressure and temperature. According to Gay-Lussac’s law, the pressure of a gas is directly related to its absolute temperature.
of molecules. The ratio of mass between a mole of Element A and Element B, or Compound A and Compound B, is the same as the ratio between the mass of Atom A and Atom B, or Molecule A and Molecule B. Avogadro’s law describes the connection between gas volume and number of moles. According to Avogadro’s law, if the volume of gas is increased under isothermal and isobarometric conditions, the number of moles also increases. The ratio between volume and number of moles is therefore a constant.
Gases
Avogadro’s Law The Ideal Gas Law Gay-Lussac also discovered that the ratio in which gases combine to form compounds can be expressed in whole numbers: for instance, water is composed of one part oxygen and two parts hydrogen. In the language of modern chemistry, this is expressed as a relationship between molecules and atoms: one molecule of water contains one oxygen atom and two hydrogen atoms. In the early nineteenth century, however, scientists had yet to recognize a meaningful distinction between atoms and molecules, and Avogadro was the first to achieve an understanding of the difference. Intrigued by the whole-number relationship discovered by Gay-Lussac, Avogadro reasoned that one liter of any gas must contain the same number of particles as a liter of another gas. He further maintained that gas consists of particles—which he called molecules—that in turn consist of one or more smaller particles. In order to discuss the behavior of molecules, Avogadro suggested the use of a large quantity as a basic unit, since molecules themselves are very small. Avogadro himself did not calculate the number of molecules that should be used for these comparisons, but when that number was later calculated, it received the name “Avogadro’s number” in honor of the man who introduced the idea of the molecule. Equal to 6.022137 • 1023, Avogadro’s number designates the quantity of atoms or molecules (depending on whether the substance in question is an element or a compound) in a mole.
Once again, it is easy to see how Avogadro’s law can be related to the laws discussed earlier. Like the other three, this one involves the parameters of temperature, pressure, and volume, but it also introduces a fourth—quantity of molecules (that is, number of moles). In fact, all the laws so far described are brought together in what is known as the ideal gas law, sometimes called the combined gas law. The ideal gas law can be stated as a formula, pV = nRT, where p stands for pressure, V for volume, n for number of moles, and T for temperature. R is known as the universal gas constant, a figure equal to 0.0821 atm • liter/mole • K. (Like most figures in chemistry, this one is best expressed in metric rather than English units.) Given the equation pV = nRT and the fact that R is a constant, it is possible to find the value of any one variable—pressure, volume, number of moles, or temperature—as long as one knows the value of the other three. The ideal gas law also makes it possible to discern certain relationships: thus, if a gas is in a relatively cool state, the product of its pressure and volume is proportionately low; and if heated, its pressure and volume product increases correspondingly.
The Kinetic Theory of Gases
Today the mole (abbreviated mol), the SI unit for “amount of substance,” is defined precisely as the number of carbon atoms in 12.01 g of carbon. The term “mole” can be used in the same way we use the word “dozen.” Just as “a dozen” can refer to twelve cakes or twelve chickens, so “mole” always describes the same number
From the preceding gas laws, a set of propositions known collectively as the kinetic theory of gases has been derived. Collectively, these put forth the proposition that a gas consists of numerous molecules, relatively far apart in space, which interact by colliding. These collisions are responsible for the production of thermal energy, because when the velocity of the molecules increases—as it does after collision—the temperature increases as well.
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There are five basic postulates to the kinetic theory of gases: • 1. Gases consist of tiny molecular or atomic particles. • 2. The proportion between the size of these particles and the distances between them is so small that the individual particles can be assumed to have negligible volume. • 3. These particles experience continual random motion. When placed in a container, their collisions with the walls of the container constitute the pressure exerted by the gas. • 4. The particles neither attract nor repel one another. • 5. The average kinetic energy of the particles in a gas is directly related to absolute temperature. These observations may appear to resemble statements made earlier concerning the differences between gases, liquids, and solids in terms of molecular behavior. If so, that is no accident: the kinetic theory constitutes a generally accepted explanation for the reasons why gases behave as they do. Kinetic theories do not work as well for explaining the behaviors of solids and liquids; nonetheless, they do go a long way toward identifying the molecular properties inherent in the various phases of matter.
Laws of Partial Pressure In addition to all the gas laws so far discussed, two laws address the subject of partial pressure. When two or more gases are present in a container, partial pressure is the pressure that one of them exerts if it alone is in the container. Dalton’s law of partial pressure states that the total pressure of a gas is equal to the sum of its partial pressures. As noted earlier, air is composed mostly of nitrogen and oxygen. Along with these are small components, carbon dioxide, and gases collectively known as the rare or noble gases: argon, helium, krypton, neon, radon, and xenon. Hence, the total pressure of a given quantity of air is equal to the sum of the pressures exerted by each of these gases.
54
acid will ionize when introduced to water: one or more of its electrons will be removed, and its atoms will convert to ions, which are either positive or negative in charge.
Applications of Dalton’s and Henry’s Laws PA RT I A L P R E SS U R E : A M AT TER OF LIFE AND POSSIBLE D E AT H F O R S C U B A D I V E R S . The
gas laws are not just a series of abstract statements. Certainly, they do concern the behavior of ideal as opposed to real gases. Like all scientific models, they remove from the equation all outside factors, and treat specific properties in isolation. Yet, the behaviors of the ideal gases described in the gas laws provide a key to understanding the activities of real gases in the real world. For instance, the concept of partial pressure helps scuba divers avoid a possibly fatal sickness. Imagine what would happen if a substance were to bubble out of one’s blood like carbon dioxide bubbling out of a soda can, as described below. This is exactly what can happen to an undersea diver who returns to the surface too quickly: nitrogen rises up within the body, producing decompression sickness—known colloquially as “the bends.” This condition may manifest as itching and other skin problems, joint pain, choking, blindness, seizures, unconsciousness, permanent neurological defects such as paraplegia, and possibly even death. If a scuba diver descending to a depth of 150 ft (45.72 m) or more were to use ordinary air in his or her tanks, the results would be disastrous. The high pressure exerted by the water at such depths creates a high pressure on the air in the tank, meaning a high partial pressure on the nitrogen component in the air. The result would be a high concentration of nitrogen in the blood, and hence the bends. Instead, divers use a mixture of helium and oxygen. Helium gas does not dissolve well in blood, and thus it is safer for a diver to inhale this oxygen-helium mixture. At the same time, the oxygen exerts the same pressure that it would normally—in other words, it operates in accordance with Dalton’s observations concerning partial pressure.
Henry’s law states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the surface of the solution. This applies only to gases such as oxygen and hydrogen that do not react chemically to liquids. On the other hand, hydrochloric
O P E N I N G A S O DA CA N . Inside a can or bottle of carbonated soda is carbon diox-
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ide gas (CO2), most of which is dissolved in the drink itself. But some of it is in the space (sometimes referred to as “head space”) that makes up the difference between the volume of the soft drink and the volume of the container. At the bottling plant, the soda manufacturer adds high-pressure carbon dioxide (CO2) to the head space in order to ensure that more CO2 will be absorbed into the soda itself. This is in accordance with Henry’s law: the amount of gas (in this case CO2) dissolved in the liquid (soda) is directly proportional to the partial pressure of the gas above the surface of the solution—that is, the CO2 in the head space. The higher the pressure of the CO2 in the head space, the greater the amount of CO2 in the drink itself; and the greater the CO2 in the drink, the greater the “fizz” of the soda. Once the container is opened, the pressure in the head space drops dramatically. Once again, Henry’s law indicates that this drop in pressure will be reflected by a corresponding drop in the amount of CO2 dissolved in the soda. Over a period of time, the soda will release that gas, and eventually, it will go “flat.” A fire extinguisher consists of a long cylinder with an operating lever at the top. Inside the cylinder is a tube of carbon dioxide surrounded by a quantity of water, which creates pressure around the CO2 tube. A siphon tube runs vertically along the length of the extinguisher, with one opening in the water near the bottom. The other end opens in a chamber containing a spring mechanism attached to a release valve in the CO2 tube. FIRE
extinguisher, an aerosol can includes a nozzle that depresses a spring mechanism, which in turn allows fluid to escape through a tube. But instead of a gas cartridge surrounded by water, most of the can’s interior is made up of the product (for instance, deodorant), mixed with a liquid propellant.
Gases
The “head space” of the aerosol can is filled with highly pressurized propellant in gas form, and, in accordance with Henry’s law, a corresponding proportion of this propellant is dissolved in the product itself. When the nozzle is depressed, the pressure of the propellant forces the product out through the nozzle. A propellant, as its name implies, propels the product itself through the spray nozzle when the nozzle is depressed. In the past, chlorofluorocarbons (CFCs)—manufactured compounds containing carbon, chlorine, and fluorine atoms— were the most widely used form of propellant. Concerns over the harmful effects of CFCs on the environment, however, has led to the development of alternative propellants, most notably hydrochlorofluorocarbons (HCFCs), CFC-like compounds that also contain hydrogen atoms.
EXTINGUISHERS.
The water and the CO2 do not fill the entire cylinder: as with the soda can, there is “head space,” an area filled with air. When the operating lever is depressed, it activates the spring mechanism, which pierces the release valve at the top of the CO2 tube. When the valve opens, the CO2 spills out in the “head space,” exerting pressure on the water. This high-pressure mixture of water and carbon dioxide goes rushing out of the siphon tube, which was opened when the release valve was depressed. All of this happens, of course, in a fraction of a second—plenty of time to put out the fire.
Applications of Boyle’s, Charles’s, and Gay-Lussac’s Laws WHEN THE T E M P E R AT U R E C H A N G E S . A number of interesting results
occur when gases experience a change in temperature, some of them unfortunate and some potentially lethal. In these instances, it is possible to see the gas laws—particularly Boyle’s and Charles’s—at work. There are numerous examples of the disastrous effects that result from an increase in the temperature of combustible gases, including natural gas and petroleum-based products. In addition, the pressure on the gases in aerosol cans makes the cans highly explosive—so much so that discarded cans at a city dump may explode on a hot summer day. Yet, there are other instances when heating a gas can produce positive effects.
A E R O S O L CA N S . Aerosol cans are similar in structure to fire extinguishers, though with one important difference. As with the fire
A hot-air balloon, for instance, floats because the air inside it is not as dense than the air outside. According to Charles’s law, heating a gas will increase its volume, and since gas molecules exert little attraction toward one another,
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they tend to “spread out” even further with an increase of volume. This, in turn, creates a significant difference in density between the air in the balloon and the air outside, and as a result, the balloon floats. Although heating a gas can be beneficial, cooling a gas is not always a wise idea. If someone were to put a bag of potato chips into a freezer, thinking this would preserve their flavor, he would be in for a disappointment. Much of what maintains the flavor of the chips is the pressurization of the bag, which ensures a consistent internal environment so that preservative chemicals, added during the manufacture of the chips, can keep them fresh. Placing the bag in the freezer causes a reduction in pressure, as per Gay-Lussac’s law, and the bag ends up a limp version of its former self. Propane tanks and tires offer an example of the pitfalls that may occur by either allowing a gas to heat up or cool down by too much. Because most propane tanks are made according to strict regulations, they are generally safe, but it is not entirely inconceivable that the extreme heat of a summer day could cause a defective tank to burst. An increase in temperature leads to an increase in pressure, in accordance with GayLussac’s law, and could lead to an explosion. Because of the connection between heat and pressure, propane trucks on the highways during the summer are subjected to weight tests to ensure that they are not carrying too much gas. On the other hand, a drastic reduction in temperature could result in a loss in gas pressure. If a propane tank from Florida were transported by truck during the winter to northern Canada, the pressure is dramatically reduced by the time it reaches its destination. THE INTERNAL-COMBUSTION E N G I N E . In operating a car, we experience
two applications of the gas laws. One of these is what makes the car run: the combustion of gases in the engine, which illustrates the interrelation of volume, pressure, and temperature expressed in the laws attributed to Boyle, Charles, and GayLussac. The other is, fortunately, a less frequent phenomenon—but it can and does save lives. This is the operation of an airbag, which depends, in part, on the behaviors explained in Charles’s law.
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activates a throttle valve that sprays droplets of gasoline mixed with air into the engine. The mixture goes into the cylinder, where the piston moves up, compressing the gas and air. While the mixture is still at a high pressure, the electric spark plug produces a flash that ignites the gasoline-air mixture. The heat from this controlled explosion increases the volume of air, which forces the piston down into the cylinder. This opens an outlet valve, causing the piston to rise and release exhaust gases. As the piston moves back down again, an inlet valve opens, bringing another burst of gasoline-air mixture into the chamber. The piston, whose downward stroke closed the inlet valve, now shoots back up, compressing the gas and air to repeat the cycle. The reactions of the gasoline and air to changes in pressure, temperature, and volume are what move the piston, which turns a crankshaft that causes the wheels to rotate. T H E A I R B AG . So much for moving— what about stopping? Most modern cars are equipped with an airbag, which reacts to sudden impact by inflating. This protects the driver and front-seat passenger, who, even if they are wearing seatbelts, may otherwise be thrown against the steering wheel or dashboard.
In order to perform its function properly, the airbag must deploy within 40 milliseconds (0.04 seconds) of impact. Not only that, but it has to begin deflating before the body hits it. If a person’s body, moving forward at speeds typical in an automobile accident, were to smash against a fully inflated airbag, it would feel like hitting concrete—with all the expected results. The airbag’s sensor contains a steel ball attached to a permanent magnet or a stiff spring. The spring or magnet holds the ball in place through minor mishaps when an airbag is not warranted—for instance, if a car were simply to be “tapped” by another in a parking lot. But in a case of sudden deceleration, the magnet or spring releases the ball, sending it down a smooth bore. The ball flips a switch, turning on an electrical circuit. This in turn ignites a pellet of sodium azide, which fills the bag with nitrogen gas.
When the driver of a modern, fuel-injection automobile pushes down on the accelerator, this
At this point, the highly pressurized nitrogen gas molecules begin escaping through vents. Thus, as the driver’s or rider’s body hits the airbag, the deflation of the bag is moving it in the same direction that the body is moving—only
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Gases
KEY TERMS Tem-
derived by French physicist and chemist
perature in relation to absolute zero
J. A. C. Charles (1746-1823), which holds
(-273.15°C or -459.67°F), as measured on
that for gases in isobarometric conditions,
the Kelvin scale. The Kelvin and Celsius
the ratio between the volume and temper-
scales are directly related; hence, Celsius
ature of a gas is constant. This means that
temperatures can be converted to Kelvins
the greater the temperature, the greater the
(for which neither the word nor the sym-
volume, and vice versa.
bol for “degree” are used) by adding
DALTON’S LAW OF PARTIAL PRES-
273.15.
SURE:
ABSOLUTE TEMPERATURE:
ATMOSPHERE:
A measure of pres-
sure, abbreviated “atm” and equal to the average pressure exerted by air at sea level. In English units, this is equal to 14.7 lb/in2, and in SI units, to 101,300 pascals.
A statement, derived by the
English chemist John Dalton (1766-1844), which holds that the total pressure of a gas is equal to the sum of its partial pressures—that is, the pressure exerted by each component of the gas mixture. GAS:
A phase of matter in which mole-
A statement,
cules move at high speeds, and therefore
derived by the Italian physicist Amedeo
exert little or no attraction toward one
Avogadro (1776-1856), which holds that as
another.
AVOGADRO’S
LAW:
the volume of gas increases under isothermal and isobarometric conditions, the number of molecules (expressed in terms of mole number), increases as well. Thus, the ratio of volume to mole number is a constant. BAROMETER:
GAS LAWS:
A series of statements
concerning the behavior of gases in response to changes in temperature, pressure, and volume. The gas laws, developed by scientists during the seventeenth, eighteenth, and nineteenth centuries, include
An
instrument
for
measuring atmospheric pressure.
Avogadro’s law, Boyle’s law, Charles’s law, Dalton’s law of partial pressures, Gay-Lussac’s law, and Henry’s law. These are
A statement, derived
summed up in the ideal gas law. The kinet-
by English chemist Robert Boyle (1627-
ic theory of gases is based on observations
1691), which holds that for gases in
garnered from these laws.
BOYLE’S LAW:
isothermal conditions, an inverse relationship exists between the volume and pressure of a gas. This means that the greater the pressure, the less the volume and vice versa, and therefore the product of pressure multiplied by volume yields a constant figure. CHARLES’S
GAY-LUSSAC’S LAW:
A statement,
derived by French physicist and chemist Joseph Gay-Lussac (1778-1850), which holds that the pressure of a gas is directly related to its absolute temperature. Hence, the ratio of pressure to absolute temperature is a constant.
LAW:
A
statement,
S C I E N C E O F E V E RY DAY T H I N G S
HENRY’S LAW:
A statement, derived
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Gases
KEY TERMS
CONTINUED
by English chemist William Henry (1774-
MOLE:
1836), which holds that the amount of gas
“amount of substance.” The quantity of
dissolved in a liquid is directly proportion-
molecules or atoms in a mole is, generally
al to the partial pressure of the gas above
speaking, the same as Avogadro’s number:
the solution. This holds true only for gases,
6.022137 • 1023. However, in the more pre-
such as hydrogen and oxygen, which do
cise SI definition, a mole is equal to the
not react chemically to liquids.
number of carbon atoms in 12.01 g of car-
IDEAL GAS LAW:
A proposition, also
bon. When two or
known as the combined gas law, which
PARTIAL PRESSURE:
draws on all the gas laws. The ideal gas law
more gases are present in a container, par-
can be expressed as the formula pV = nRT,
tial pressure is the pressure that one of
where p stands for pressure, V for volume,
them exerts if it alone is in the container.
n for number of moles, and T for tempera-
Dalton’s law of partial pressure and
ture. R is known as the universal gas con-
Henry’s law relate to the partial pressure of
stant, a figure equal to 0.0821 atm •
gases.
liter/mole • K. ISOTHERMAL:
PASCAL:
Referring to a situa-
tion in which temperature is kept constant. ISOBAROMETRIC:
Referring to a sit-
uation in which pressure is kept constant. KINETIC ENERGY:
The principle SI or metric
unit of pressure, abbreviated “Pa” and equal to 1 N/m2. PRESSURE:
The ratio of force to sur-
face area, when force is applied in a direction perpendicular to that surface.
The energy that
an object possesses by virtue of its motion.
THERMAL ENERGY:
A form of kinet-
ic energy—commonly called “heat”—that
A set
is produced by the movement of atomic or
of propositions describing a gas as consist-
molecular particles. The greater the
ing of numerous molecules, relatively far
motion of these particles relative to one
apart in space, which interact by colliding.
another, the greater the thermal energy.
KINETIC THEORY OF GASES:
These collisions are responsible for the production of thermal energy, because when the velocity of the molecules increases—as it does after collision—the temperature increases as well. MILLIMETER OF MERCURY:
TORR:
An SI unit, also known as the
millimeter of mercury, that represents the pressure required to raise a column of mercury 1 mm. The torr, equal to 133 Pascals, is named for the Italian physicist Evange-
Anoth-
er name for the torr, abbreviated mm Hg.
58
The SI fundamental unit for
lista Torricelli (1608-1647), who invented the barometer.
much, much more slowly. Two seconds after impact, which is an eternity in terms of the processes involved, the pressure inside the bag has returned to 1 atm.
The chemistry of the airbag is particularly interesting. The bag releases inert, or non-reactive, nitrogen gas, which poses no hazard to human life; yet one of the chemical ingredients in
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the airbag is so lethal that some environmentalist groups have begun to raise concerns over its presence in airbags. This is sodium azide (NaN3), one of three compounds—along with potassium nitrate (KNO3) and silicon dioxide (SiO2)—present in an airbag prior to inflation. The sodium azide and potassium nitrate react to one another, producing a burst of hot nitrogen gas in two back-to-back reactions. In the fractions of a second during which this occurs, the airbag becomes like a solid-rocket booster, experiencing a relatively slow detonation known as “deflagration.” The first reaction releases nitrogen gas, which fills the bag, while the second reaction leaves behind the by-products potassium oxide (K2O) and sodium oxide (Na2O). These combine with the silicon dioxide to produce a safe, stable compound known as alkaline silicate. The latter, similar to the sand used for making glass, is all that remains in the airbag after the nitrogen gas has escaped. WHERE TO LEARN MORE “Atmospheric Pressure: The Force Exerted by the Weight of Air” (Web site). (April 7, 2001).
S C I E N C E O F E V E RY DAY T H I N G S
“Chemical Sciences Structure: Structure of Matter: Nature of Gases” University of Alberta Chemistry Department (Web site). (May 12, 2001).
Gases
“Chemistry Units: Gas Laws.” (February 21, 2001). “Homework: Science: Chemistry: Gases” Channelone.com (Web site). (May 12, 2001). “Kinetic Theory of Gases: A Brief Review” University of Virginia Department of Physics (Web site). (April 15, 2001). Laws of Gases. New York: Arno Press, 1981. Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998. Mebane, Robert C. and Thomas R. Rybolt. Air and Other Gases. Illustrations by Anni Matsick. New York: Twenty-First Century Books, 1995. “Tutorials—6.” Chemistrycoach.com (Web site). (February 21, 2001). Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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S C I E N C E O F E V E R Y D AY T H I N G S real-life chemistry
AT O M S AND MOLECULES AT O M S AT O M I C M A S S ELECTRONS ISOTOPES I O N S A N D I O N I Z AT I O N MOLECULES
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Atoms
CONCEPT Our world is made up of atoms, yet the atomic model of the universe is nonetheless considered a “theory.” When scientists know beyond all reasonable doubt that a particular principle is the case, then it is dubbed a law. Laws address the fact that certain things happen, as well as how they happen. A theory, on the other hand, attempts to explain why things happen. By definition, an idea that is dubbed a theory has yet to be fully proven, and such is the case with the atomic theory of matter. After all, the atom cannot be seen, even with electron microscopes—yet its behavior can be studied in terms of its effects. Atomic theory explains a great deal about the universe, including the relationship between chemical elements, and therefore (as with Darwin’s theory concerning biological evolution), it is generally accepted as fact. The particulars of this theory, including the means by which it evolved over the centuries, are as dramatic as any detective story. Nonetheless, much still remains to be explained about the atom—particularly with regard to the smallest items it contains.
HOW IT WORKS Why Study Atoms? Many accounts of the atom begin with a history of the growth in scientists’ understanding of its structure, but here we will take the opposite approach, first discussing the atom in terms of what physicists and chemists today understand. Only then will we examine the many challenges scientists faced in developing the current atomic model: false starts, wrong theories, right roads not taken, incomplete models. In addition, we
S C I E N C E O F E V E R Y D AY T H I N G S
AT O M S
will explore the many insights added along the way as, piece by piece, the evidence concerning atomic behavior began to accumulate. People who are not scientifically trained tend to associate studies of the atom with physics, not chemistry. While it is true that physicists study atomic structure, and that much of what scientists know today about atoms comes from the work of physicists, atomic studies are even more integral to chemistry than to physics. At heart, chemistry is about the interaction of different atomic and molecular structures: their properties, their reactions, and the ways in which they bond. WHAT THE ATOM MEANS TO CHEMISTRY. Just as a writer in English
works with the 26 letters of the alphabet, a chemist works with the 100-plus known elements, the fundamental and indivisible substances of all matter. And what differentiates the elements, ultimately, from one another is not their color or texture, or even the phase of matter—solid, gas, or liquid—in which they are normally found. Rather, the defining characteristic of an element is the atom that forms its basic structure. The number of protons in an atom is the critical factor in differentiating between elements, while the number of neutrons alongside the protons in the nucleus serves to distinguish one isotope from another. However, as important as elements and even isotopes are to the work of a chemist, the components of the atom’s nucleus have little direct bearing on the atomic activity that brings about chemical reactions and chemical bonding. All the chemical “work” of an atom is done by particles vastly smaller in mass than
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element. In fact, these two definitions do not form a closed loop, as they would if it were stated that an element is something made up of atoms. Every item of matter that exists, except for the subatomic particles discussed in this essay, is made up of atoms. An element, on the other hand, is—as stated in its definition—made up of only one kind of atom. “Kind of atom” in this context refers to the number of protons in its nucleus.
Atoms
JOHN DALTON.
either the protons or neutrons—fast-moving little bundles of energy called electrons. Moving rapidly through the space between the nucleus and the edge of the atom, electrons sometimes become dislodged, causing the atom to become a positively charged ion. Conversely, sometimes an atom takes on one or more electrons, thus acquiring a negative charge. Ions are critical to the formation of some kinds of chemical bonds, but the chemical role of the electron is not limited to ionic bonds. In fact, what defines an atom’s ability to bond with another atom, and therefore to form a molecule, is the specific configuration of its electrons. Furthermore, chemical reactions are the result of changes in the arrangement of electrons, not of any activity involving protons or neutrons. So important are electrons to the interactions studied in chemistry that a separate essay has been devoted to them.
What an Atom Is BASIC ATOMIC STRUCTURE. The definitions of atoms and elements seems, at first glance, almost circular: an element is a substance made up of only one kind of atom, and an atom is the smallest particle of an element that retains all the chemical and physical properties of the
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Protons are one of three basic subatomic particles, the other two being electrons and neutrons. As we shall see, there appear to be particles even smaller than these, but before approaching these “sub-subatomic” particles, it is necessary to address the three most significant components of an atom. These are distinguished from one another in terms of electric charge: protons are positively charged, electrons are negative in charge, and neutrons have no electrical charge. As with the north and south poles of magnets, positive and negative charges attract one another, whereas like charges repel. Atoms have no net charge, meaning that the protons and electrons cancel out one another. EVOLVING MODELS OF THE ATOM. Scientists originally thought of an atom
as a sort of closed sphere with a relatively hard shell, rather like a ball bearing. Nor did they initially understand that atoms themselves are divisible, consisting of the parts named above. Even as awareness of these three parts emerged in the last years of the nineteenth century and the first part of the twentieth, it was not at all clear how they fit together. At one point, scientists believed that electrons floated in a cloud of positive charges. This was before the discovery of the nucleus, where the protons and neutrons reside at the heart of the atom. It then became clear that electrons were moving around the nucleus, but how? For a time, a planetary model seemed appropriate: in other words, electrons revolved around the nucleus much as planets orbit the Sun. Eventually, however—as is often the case with scientific discovery—this model became unworkable, and had to be replaced by another. The model of electron behavior accepted today depicts the electrons as forming a cloud around the nucleus—almost exactly the opposite of what physicists believed a century ago. The use of the term “cloud” may perhaps be a bit mis-
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leading, implying as it does something that simply hovers. In fact, the electron, under normal circumstances, is constantly moving. The paths of its movement around the nucleus are nothing like that of a planet’s orbit, except inasmuch as both models describe a relatively small object moving around a relatively large one.
Atoms
The furthest edges of the electron’s movement define the outer perimeters of the atom. Rather than being a hard-shelled little nugget of matter, an atom—to restate the metaphor mentioned above—is a cloud of electrons surrounding a nucleus. Its perimeters are thus not sharply delineated, just as there is no distinct barrier between Earth’s atmosphere and space itself. Just as the air gets thinner the higher one goes, so it is with an atom: the further a point is from the nucleus, the less the likelihood that an electron will pass that point on a given orbital path.
Nucleons NIELS BOHR.
MASS NUMBER AND ATOMIC NUMBER. The term nucleon is used generi-
cally to describe the relatively heavy particles that make up an atomic nucleus. Just as “sport” can refer to football, basketball, or baseball, or any other item in a similar class, such as soccer or tennis, “nucleon” refers to protons and neutrons. The sum of protons and neutrons is sometimes called the nucleon number, although a more commonly used term is mass number. Though the electron is the agent of chemical reactions and bonding, it is the number of protons in the nucleus that defines an atom as to its element. Atoms of the same element always have the same number of protons, and since this figure is unique for a given element, each element is assigned an atomic number equal to the number of protons in its nucleus. The atoms are listed in order of atomic number on the periodic table of elements. ATOMIC MASS AND ISOTOPES.
A proton has a mass of 1.673 • 10–24 g, which is very close to the established figure for measuring atomic mass, the atomic mass unit. At one time, the basic unit of atomic mass was equal to the mass of one hydrogen atom, but hydrogen is so reactive—that is, it tends to combine readily with other atoms to form a molecule, and hence a compound—that it is difficult to isolate. Instead, the atomic mass unit is today defined as 1/12 of
S C I E N C E O F E V E R Y D AY T H I N G S
the mass of a carbon-12 atom. That figure is exactly 1.66053873 • 10–24 grams. The mention of carbon-12, a substance found in all living things, brings up the subject of isotopes. The “12” in carbon-12 refers to its mass number, or the sum of protons and neutrons. Two atoms may be of the same element, and thus have the same number of protons, yet differ in their number of neutrons—which means a difference both in mass number and atomic mass. Such differing atoms of the same element are called isotopes. Isotopes are often designated by symbols showing mass number to the upper left of the chemical symbol or element symbol—for instance, 12C for carbon-12. ELECTRIC CHARGE. Protons have a positive electric charge of 1, designated either as 1+ or +1. Neutrons, on the other hand, have no electric charge. It appears that the 1+ charge of a proton and the 0 charge of a neutron are the products of electric charges on the part of even smaller particles called quarks. A quark may either have a positive electric charge of less than 1+, in which case it is called an “up quark”; or a negative charge of less than 1–, in which case it is called a “down quark.”
Research indicates that a proton contains two up quarks, each with a charge of 2/3+, and
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Atoms
THE
EVOLUTION OF ATOMIC THEORY.
one down quark with a charge of 1/3–. This results in a net charge of 1+. On the other hand, a neutron is believed to hold one up quark with a charge of 2/3+, and two down quarks with charges of 1/3– each. Thus, in the neutron, the up and down quarks cancel out one another, and the net charge is zero. A neutron has about the same mass as a proton, but other than its role in forming isotopes, the neutron’s function is not exactly clear. Perhaps, it has been speculated, it binds protons— which, due to their positive charges, tend to repel one another—together at the nucleus.
Electrons An electron is much smaller than a proton or neutron, and has much less mass; in fact, its mass is equal to 1/1836 that of a proton, and 1/1839 that of a neutron. Yet the area occupied by electrons—the region through which they move— constitutes most of the atom’s volume. If the nucleus of an atom were the size of a BB (which, in fact, is billions of times larger than a nucleus), the furthest edge of the atom would be equivalent to the highest ring of seats around an indoor sports arena. Imagine the electrons as incredibly fast-moving insects buzzing constantly through the arena, passing by the BB but then flitting to
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the edges or points in between, and you have something approaching an image of the atom’s interior. How fast does an electron move? Speeds vary depending on a number of factors, but it can move nearly as fast as light: 186,000 mi (299,339 km) per second. On the other hand, for an item of matter near absolute zero in temperature, the velocity of the electron is much, much less. In any case, given the fact that an electron has enough negative charge to cancel out that of the proton, it must be highly energized. After all, this would be like an electric generator weighing 1 lb having as much power as a generator that weighed 1 ton. According to what modern scientists know or hypothesize concerning the inner structure of the atom, electrons are not made up of quarks; rather, they are part of a class of particles called leptons. It appears that leptons, along with quarks and what are called exchange particles, constitute the elementary particles of atoms— particles on a much more fundamental level than that of the proton and neutron. Electrons are perhaps the most intriguing parts of an atom. Their mass is tiny, even in atomic terms, yet they possess enough charge to counteract a “huge” proton. They are capable, in certain situations, of moving from one atom to
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another, thus creating ions, and depending on their highly complex configuration and ability to rearrange their configuration, they facilitate or prevent chemical reactions.
REAL-LIFE AP P LICATIONS Ancient Greek Theories of Matter The first of the Greek philosophers, and the first individual in Western history who deserves to be called a scientist, was Thales (c. 625-c. 547 B.C.) of Miletus. (Miletus is in Greek Asia Minor, now part of Turkey.) Among his many achievements were the correct prediction of a solar eclipse, and one of the first-ever observations of electricity, when he noted the electrification of amber by friction. But perhaps the greatest of Thales’s legacies was his statement that “Everything is water.” This represented the first attempt to characterize the nature of all physical reality. It set off a debate concerning the fundamental nature of matter that consumed Greek philosophers for two centuries. Later, philosophers attempted to characterize matter in terms of fire or air. In time, however, there emerged a school of thought concerned not with identifying matter as one particular thing or another, but with recognizing a structural consistency in all of matter. Among these were the philosophers Leucippus (c. 480-c. 420 B.C.) and his student Democritus (c. 460-370 B.C.) DEMOCRITUS’S “ATOMS”. Leucippus and Democritus proposed a new and highly advanced model for the tiniest point of physical space. Democritus, who actually articulated these ideas (far less is known about Leucippus) began with a “thought experiment,” imagining what would happen if an item of matter were subdivided down to its smallest piece. This tiniest fragment, representing an item of matter that could not be cut into smaller pieces, he called by a Greek term meaning “no cut”: atomos.
Democritus was not necessarily describing matter in a concrete, scientific way: his “atoms” were idealized philosophical constructs rather than purely physical units. Yet, he came amazingly close, and indeed much closer than any thinker for the next 22 centuries, to identifying the fun-
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damental structure of physical reality. Why did it take so long for scientists to come back around to the atomic model? The principal culprit, who advanced an erroneous theory of matter, also happened to be one of the greatest thinkers of all time: Aristotle (384-322 B.C..) ARISTOTLE’S
Atoms
“ELEMENTS”.
Aristotle made numerous contributions to science, including his studies in botany and zoology, as well as his explanation of the four causes, a significant attempt to explain events by means other than myth or superstition. In the area of the physical sciences, however, Aristotle’s impact was less than beneficial. Most notably, in explaining why objects fall when dropped, he claimed that the ground was their “natural” destination— a fallacy later overturned with the gravitational model developed by Galileo Galilei (1564-1642) and Sir Isaac Newton (1642-1727). The ideas Aristotle put forward concerning what he called “natural motion” were a product of his equally faulty theories with regard to what today’s scientists refer to as chemistry. In ancient times, chemistry, as such, did not exist. Long before Aristotle’s time, Egyptian embalmers and metallurgists used chemical processes, but they did so in a practical, applied manner, exerting little effort toward what could be described as scientific theory. Philosophers such as Aristotle, who were some of the first scientists, made little distinction between physical and chemical processes. Thus, whereas physics is understood today as an important background for chemistry, Aristotle’s “physics” was actually an outgrowth of his “chemistry.” Rejecting Democritus’s atomic model, Aristotle put forward his own view of matter. Like Democritus, he believed that matter was composed of very small components, but these he identified not as atoms, but as “elements”: earth, air, fire, and water. He maintained that all objects consisted, in varying degrees, of one or more of these, and based his explanation of gravity on the relative weights of each element. Water sits on top of the earth, he explained, because it is lighter, yet air floats above the water because it is lighter still—and fire, lightest of all, rises highest. Furthermore, he claimed that the planets beyond Earth were made up of a “fifth element,” or quintessence, of which little could be known. In fairness to Aristotle, it should be pointed out that it was not his fault that science all but
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died out in the Western world during the period from about A.D. 200 to about 1200. Furthermore, he did offer an accurate definition of an element, in a general sense, as “one of those simple bodies into which other bodies can be decomposed, and which itself is not capable of being divided into others.” As we shall see, the definition used today is not very different from Aristotle’s. However, to define an element scientifically, as modern chemists do, it is necessary to refer to something Aristotle rejected: the atom. So great was his opposition to Democritus’s atomic theory, and so enormous was Aristotle’s influence on learning for more than 1,500 years following his death, that scientists only began to reconsider atomic theory in the late eighteenth century.
noted that elements always react with one another in the same proportions.
A Maturing Concept of Elements
of Lavoisier and Proust influenced a critical figure in the development of the atomic model: English chemist John Dalton (1766-1844). In A New System of Chemical Philosophy (1808), Dalton put forward the idea that nature is composed of tiny particles, and in so doing he adopted Democritus’s word “atom” to describe these basic units. This idea, which Dalton had formulated five years earlier, marked the starting-point of modern atomic theory.
BOYLE’S IDEA OF ELEMENTS.
One of the first steps toward an understanding of the chemical elements came with the work of English physicist and chemist Robert Boyle (1627-1691). Building on the usable definition of an element provided by Aristotle, Boyle maintained no substance was an element if it could be broken down into other substances. Thus, air could be eliminated from the list of “elements,” because, clearly, it could be separated into more than one elemental substance. (In fact, none of the four “elements” identified by Aristotle even remotely qualifies as an element in modern chemistry.) Boyle, nonetheless, still clung to aspects of alchemy, a pseudo-science based on the transformation of “base metals,” for example, the metamorphosis of iron into gold. Though true chemistry grew out of alchemy, the fundamental proposition of alchemy was faulty: if one metal can be turned into another, then that means that metals are not elements, which, in fact, they are. Nonetheless, Boyle’s studies led to the identification of numerous elements—that is, items that really are elements—in the years that followed. LAVOISIER AND PROUST: CONSTANT COMPOSITION. A few years after
Boyle came two French chemists who extended scientific understanding of the elements. Antoine Lavoisier (1743-1794) affirmed the definition of an element as a simple substance that could not be broken down into a simpler substance, and
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Joseph-Louis Proust (1754-1826) put forward the law of constant composition, which holds that a given compound always contains the same proportions of mass between elements. Another chemist of the era had claimed that the composition of a compound varies in accordance with the reactants used to produce it. Proust’s law of constant composition made it clear that any particular compound will always have the same composition.
Early Modern Understanding of the Atom DALTON AND AVOGADRO: ATOMS AND MOLECULES. The work
Dalton recognized that the structure of atoms in a particular element or compound is uniform, but maintained that compounds are made up of compound atoms: in other words, water, for instance, is a compound of “water atoms.” However, water is not an element, and thus, it was necessary to think of its atomic composition in a different way—in terms of molecules rather than atoms. Dalton’s contemporary Amedeo Avogadro (1776-1856), an Italian physicist, became the first scientist to clarify the distinction between atoms and molecules. The later development of the mole, which provided a means whereby equal numbers of molecules could be compared, paid tribute to Avogadro by designating the number of molecules in a mole as “Avogadro’s number.” Another contemporary, Swedish chemist Jons Berzelius (1779-1848), maintained that equal volumes of gases at the same temperature and pressure contained equal numbers of atoms. Using this idea, he compared the mass of various reacting gases, and developed a system of comparing the mass of various atoms in relation to the lightest one, hydrogen. Berzelius also introduced the system
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of chemical symbols—H for hydrogen, O for oxygen, and so on—in use today. BROWNIAN MOTION AND KINETIC THEORY. Yet another figure
whose dates overlapped with those of Dalton, Avogadro, and Berzelius was Scottish botanist Robert Brown (1773-1858). In 1827, Brown noted a phenomenon that later had an enormous impact on the understanding of the atom. While studying pollen grains under a microscope, Brown noticed that the grains underwent a curious zigzagging motion in the water. The pollen assumed the shape of a colloid, a pattern that occurs when particles of one substance are dispersed—but not dissolved—in another substance. At first, Brown assumed that the motion had a biological explanation—that is, it resulted from life processes within the pollen—but later, he discovered that even pollen from long-dead plants behaved in the same way. Brown never understood what he was witnessing. Nor did a number of other scientists, who began noticing other examples of what came to be known as Brownian motion: the constant but irregular zigzagging of colloidal particles, which can be seen clearly through a microscope. Later, however, Scottish physicist James Clerk Maxwell (1831-1879) and others were able to explain this phenomenon by what came to be known as the kinetic theory of matter. Kinetic theory is based on the idea that molecules are constantly in motion: hence, the water molecules were moving the pollen grains Brown observed. Pollen grains are many thousands of times as large as water molecules, but since there are so many molecules in even a drop of water, and their motion is so constant but apparently random, they are bound to move a pollen grain once every few thousand collisions.
Mendeleev and the Periodic Table In 1869, Russian chemist Dmitri Mendeleev (1834-1907) introduced a highly useful system for organizing the elements, the periodic table. Mendeleev’s table is far more than just a handy chart listing elements: at once simple and highly complex, it shows elements in order of increasing atomic mass, and groups together those exhibiting similar forms of chemical behavior and structure.
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Reading from right to left and top to bottom, the periodic table, as it is configured today, lists atoms in order of atomic number, generally reflected by a corresponding increase in average atomic mass. As Mendeleev observed, every eighth element on the chart exhibits similar characteristics, and thus the chart is organized in columns representing specific groups of elements.
Atoms
The patterns Mendeleev observed were so regular that for any “hole” in his table, he predicted that an element would be discovered that would fill that space. For instance, at one point there was a gap between atomic numbers 71 and 73 (lutetium and tantalum, respectively). Mendeleev indicated that an atom would be found for the space, and 15 years after this prediction, the element germanium was isolated. However, much of what defines an element’s place on the chart today relates to subatomic particles—protons, which determine atomic number, and electrons, whose configurations explain certain chemical similarities. Mendeleev was unaware of these particles: from the time he created his table, it was another three decades before the discovery of the first of these particles, the electron. Instead, he listed the elements in an order reflecting outward characteristics now understood to be the result of the quantity and distribution of protons and electrons.
Electromagnetism and Radiation The contribution of Mendeleev’s contemporary, Maxwell, to the understanding of the atom was not limited to his kinetic theory. Building on the work of British physicist and chemist Michael Faraday (1791-1867) and others, in 1865 he published a paper outlining a theory of a fundamental interaction between electricity and magnetism. The electromagnetic interaction, as it later turned out, explained something that gravitation, the only other form of fundamental interaction known at the time, could not: the force that held together particles in an atom. The idea of subatomic particles was still a long time in coming, but the model of electromagnetism helped make it possible. In the long run, electromagnetism was understood to encompass a whole spectrum of energy radiation, including radio waves; infrared, visible, and ultraviolet light; x rays; and gamma rays. But this,
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too, was the product of work on the part of numerous individuals, among whom was English physicist William Crookes (1832-1919).
electrons were like raisins, floating in a positively charged “pudding”—that is, an undifferentiated cloud of positive charges.
In the 1870s, Crookes developed an apparatus later termed a Crookes tube, with which he sought to analyze the “rays”—that is, radiation— emitted by metals. The tube consisted of a glass bulb, from which most of the air had been removed, encased between two metal plates or electrodes, referred to as a cathode and an anode. A wire led outside the bulb to an electric source, and when electricity was applied to the electrodes, the cathodes emitted rays. Crookes concluded that the cathode rays were particles with a negative electric charge that came from the metal in the cathode plate.
Kelvin’s temperature scale contributed greatly to the understanding of molecular motion as encompassed in the kinetic theory of matter. However, his model for the distribution of charges in an atom—charming as it may have been—was incorrect. Nonetheless, for several decades, the “plum pudding model,” as it came to be known, remained the most widely accepted depiction of the way that electric charges were distributed in an atom. The overturning of the plum pudding model was the work of English physicist Ernest Rutherford (1871-1937), a student of J. J. Thomson.
RADIATION. In 1895, German physicist Wilhelm Röntgen (1845-1923) noticed that photographic plates held near a Crookes tube became fogged, and dubbed the rays that had caused the fogging “x rays.” A year after Röntgen’s discovery, French physicist Henri Becquerel (1852-1908) left some photographic plates in a drawer with a sample of uranium. Uranium had been discovered more than a century before; however, there were few uses for it until Becquerel discovered that the uranium likewise caused a fogging of the photographic plates.
RUTHERFORD IDENTIFIES THE NUCLEUS. Rutherford did not set out to dis-
Thus radioactivity, a type of radiation brought about by atoms that experience radioactive decay was discovered. The term was coined by Polish-French physicist and chemist Marie Curie (1867-1934), who with her husband Pierre (1859-1906), a French physicist, was responsible for the discovery of several radioactive elements.
The Rise and Fall of the Plum Pudding Model Working with a Crookes tube, English physicist J. J. Thomson (1856-1940) hypothesized that the negatively charged particles Crookes had observed were being emitted by atoms, and in 1897, he gave a name to these particles: electrons. The discovery of the electron raised a new question: if Thomson’s particles exerted a negative charge, from whence did the counterbalancing positive charge come? An answer, of sorts, came from William Thomson, not related to the other Thomson and, in any case, better known by his title as Lord Kelvin (1824-1907). Kelvin compared the structure of an atom to an English plum pudding: the
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prove the plum pudding model; rather, he was conducting tests to find materials that would block radiation from reaching a photographic plate. The two materials he identified, which were, respectively, positive and negative in electric charge, he dubbed alpha and beta particles. (An alpha particle is a helium nucleus stripped of its electrons, such that it has a positive charge of 2; beta particles are either electrons or positively charged subatomic particles called positrons. The beta particle Rutherford studied was an electron emitted during radioactive decay.) Using a piece of thin gold foil with photographic plates encircling it, Rutherford bombarded the foil with alpha particles. Most of the alpha particles went straight through the foil—as they should, according to the plum pudding model. However, a few particles were deflected from their course, and some even bounced back. Rutherford later said it was as though he had fired a gun at a piece of tissue paper, only to see the tissue deflect the bullets. Analyzing these results, Rutherford concluded that there was no “pudding” of positive charges: instead, the atom had a positively charged nucleus at its center.
The Nucleus Emerges PROTONS AND ISOTOPES. In addition to defining the nucleus, Rutherford also gave a name to the particles that imparted its positive charge: protons. But just as the identification of the electron had raised new questions that, in being answered, led to the discovery of the proton, Rutherford’s achievement only
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brought up new anomalies concerning the behavior of the nucleus. Together with English chemist Frederick Soddy (1877-1956), Rutherford discovered that when an atom emitted alpha or beta particles, its atomic mass changed. Soddy had a name for atoms that displayed this type of behavior: isotopes. Certain types of isotopes, Soddy and Rutherford went on to conclude, had a tendency to decay, moving toward stabilization, and this decay explained radioactivity. CLARIFYING THE PERIODIC TABLE. Soddy concluded that atomic mass, as
measured by Berzelius, was actually an average of the mass figures for all isotopes within that element. This explained a problem with Mendeleev’s periodic table, in which there seemed to be irregularities in the increase of atomic mass from element to element. The answer to these variations in mass, it turned out, related to the number of isotopes associated with a given element: the greater the number of isotopes, the more these affected the overall measure of the element’s mass. By this point, physicists and chemists had come to understand that various levels of energy in matter emitted specific electromagnetic wavelengths. Welsh physicist Henry Moseley (18871915) experimented with x rays, bombarding atoms of different elements with high levels of energy and observing the light they gave off as they cooled. In the course of these tests, he uncovered an astounding mathematical relationship: the amount of energy a given element emitted was related to its atomic number. Furthermore, the atomic number corresponded to the number of positive charges—this was in 1913, before Rutherford had named the proton—in the nucleus. Mendeleev had been able to predict the discovery of new elements, but such predictions had remained problematic. When scientists understood the idea of atomic number, however, it became possible to predict the existence of undiscovered elements with much greater accuracy. NEUTRONS. Yet again, discoveries—the nucleus, protons, and the relationship between these and atomic number—only created new questions. (This, indeed, is one of the hallmarks of an active scientific theory. Rather than settling questions, science is about raising new ones, and thus improving the quality of the questions that
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are asked.) Once Rutherford had identified the proton, and Moseley had established the number of protons, the mystery at the heart of the atom only grew deeper.
Atoms
Scientists had found that the measured mass of atoms could not be accounted for by the number of protons they contained. Certainly, the electrons had little to do with atomic mass: by then it had been shown that the electron weighed about 0.06% as much as a proton. Yet for all elements other than protium (the first of three hydrogen isotopes), there was a discrepancy between atomic mass and atomic number. Clearly, there had to be something else inside the nucleus. In 1932, English physicist James Chadwick (1891-1974) identified that “something else.” Working with radioactive material, he found that a certain type of subatomic particle could penetrate lead. All other known types of radiation were stopped by the lead, and therefore, Chadwick reasoned that this particle must be neutral in charge. In 1932, he won the Nobel Prize in Physics for his discovery of the neutron.
The Nuclear Explosion ISOTOPES AND RADIOACTIVITY. Chadwick’s discovery clarified another mys-
tery, that of the isotope, which had been raised by Rutherford and Soddy several decades earlier. Obviously, the number of protons in a nucleus did not change, but until the identification of the neutron, it had not been clear what it was that did change. At that point, it was understood that two atoms may have the same atomic number— and hence be of the same element—yet they may differ in number of neutrons, and thus be isotopes. As the image of what an isotope was became clearer, so too did scientists’ comprehension of radioactivity. Radioactivity, it was discovered, was most intense where an isotope was the most unstable—that is, in cases where an isotope had the greatest tendency to experience decay. Uranium had a number of radioactive isotopes, such as 235U, and these found application in the burgeoning realm of nuclear power—both the destructive power of atomic bombs, and later the constructive power of nuclear energy plants. FISSION VS. FUSION. In nuclear fission, or the splitting of atoms, uranium isotopes (or other radioactive isotopes) are bom-
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barded with neutrons, splitting the uranium nucleus in half and releasing huge amounts of energy. As the nucleus is halved, it emits several extra neutrons, which spin off and split more uranium nuclei, creating still more energy and setting off a chain reaction. This explains the destructive power in an atomic bomb, as well as the constructive power—providing energy to homes and businesses—in a nuclear power plant. Whereas the chain reaction in an atomic bomb becomes an uncontrolled explosion, in a nuclear plant the reaction is slowed and controlled. Yet nuclear fission is not the most powerful form of atomic reaction. As soon as scientists realized that it was possible to force particles out of a nucleus, they began to wonder if particles could be forced into the nucleus. This type of reaction, known as fusion, puts even nuclear fission, with its awesome capabilities, to shame: nuclear fusion is, after all, the power of the Sun. On the surface of that great star, hydrogen atoms reach incredible temperatures, and their nuclei fuse to create helium. In other words, one element actually transforms into another, releasing enormous amounts of energy in the process. NUCLEAR ENERGY IN WAR AND PEACE. The atomic bombs dropped by the
United States on Japan in 1945 were fission bombs. These were the creation of a group of scientists—legendary figures such as American physicist J. Robert Oppenheimer (1904-1967), American mathematician John von Neumann (1903-1957), American physicist Edward Teller (1908-), and Italian physicist Enrico Fermi (1901-1954)—involved in the Manhattan Project at Las Alamos, New Mexico. Some of these geniuses, particularly Oppenheimer, were ambivalent about the moral implications of the enormous destructive power they created. However, most military historians believe that far more lives—both Japanese and American—would have been lost if America had been forced to conduct a land invasion of Japan. As it was, the Japanese surrendered shortly after the cities of Hiroshima and Nagasaki suffered the devastating effects of fission-based explosions. By 1952, U.S. scientists had developed a “hydrogen,” or fusion bomb, thus raising the stakes greatly. This was a bomb that possessed far more destructive capability than the ones dropped over Japan. Fortunately, the Hiroshima and Nagasaki bombs were the only ones dropped
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in wartime, and a ban on atmospheric nuclear testing has greatly reduced the chances of human exposure to nuclear fallout of any kind. With the end of the arms race between the United States and the Soviet Union, the threat of nuclear destruction has receded somewhat—though it will perhaps always be a part of human life. Nonetheless, fear of nuclear power, spawned as a result of the arms race, continues to cloud the future of nuclear plants that generate electricity—even though these, in fact, emit less radioactive pollution than coal- or gas-burning power plants. At the same time, scientists continue to work on developing a process of power generation by means of nuclear fusion, which, if and when it is achieved, will be one of the great miracles of science. PARTICLE ACCELERATORS. One of the tools used by scientists researching nuclear fusion is the particle accelerator, which moves streams of charged particles—protons, for instance—faster and faster. These fast particles are then aimed at a thin plate composed of a light element, such as lithium. If the proton manages to be “captured” in the nucleus of a lithium atom, the resulting nucleus is unstable, and breaks into alpha particles.
This method of induced radioactivity is among the most oft- used means of studying nuclear structure and subatomic particles. In 1932, the same year that Chadwick discovered the neutron, English physicist John D. Cockcroft (1897-1967) and Irish physicist Ernest Walton (1903-1995) built the first particle accelerator. Some particle accelerators today race the particles in long straight lines or, to save space, in ringed paths several miles in diameter.
Quantum Theory and Beyond THE CONTRIBUTION OF RELATIVITY. It may seem strange that in this lengthy
(though, in fact, quite abbreviated!) overview of developments in understanding of the atom, no mention has been made of the figure most associated with the atom in the popular mind: German-American physicist Albert Einstein (18791955). The reasons for this are several. Einstein’s relativity theory addresses physical, rather than chemical, processes, and did not directly contribute to enhanced understanding of atomic structure or elements. The heart of relativity the-
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ory is the famous formula E = mc2, which means that every item of matter possesses energy proportional to its mass multiplied by the squared speed of light.
of the electron; but before this could be fully achieved, scientists had to develop a new understanding of the way electrons move around the nucleus.
The value of mc2, of course, is an enormous amount of energy, and in order to be released in significant quantities, an article of matter must experience the kinetic energy associated with very, very high speeds—speeds close to that of light. Obviously, the easiest thing to accelerate to such a speed is an atom, and hence, nuclear energy is a result of Einstein’s famous equation. Nonetheless, it should be stressed that although Einstein is associated with unlocking the power of the atom, he did little to explain what atoms are.
BOHR’S PLANETARY MODEL OF THE ATOM. As was often the case in the his-
However, in the course of developing his relativity theory in 1905, Einstein put to rest a question about atoms and molecules that still remained unsettled after more than a century. Einstein’s analysis of Brownian motion, combined with the confirmation of his results by French physicist Jean Baptiste Perrin (18701942), showed conclusively that yes, atoms and molecules do exist. It may seem amazing that as recently as 1905, this was still in doubt; however, this only serves to illustrate the arduous path scientists must tread in developing a theory that accurately explains the world. PLANCK’S QUANTUM THEORY.
A figure whose name deserves to be as much a household word as Einstein’s—though it is not— is German physicist Max Planck (1858-1947). It was Planck who initiated the quantum theory that Einstein developed further, a theory that prevails today in the physical sciences. At the atomic level, Planck showed, energy is emitted in tiny packets or “quanta.” Each of these energy packets is indivisible, and the behavior of quanta redefine the old rules of physics handed down from Newton and Maxwell. Thus, it is Planck’s quantum theory, rather than Einstein’s relativity, that truly marks the watershed, or “before and after,” between classical physics and modern physics. Quantum theory is important not only to physics, but to chemistry as well. It helps to explain the energy levels of electrons, which are not continuous, as in a spectrum, but jump between certain discrete points. The quantum model is now also applied to the overall behavior
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Atoms
tory of the atom, a man otherwise respected as a great scientist put forward a theory of atomic structure that at first seemed convincing, but ultimately turned out to be inaccurate. In this case, it was Danish physicist Niels Bohr (18851962), a seminal figure in the development of nuclear fission. Using the observation, derived from quantum theory, that electrons only occupied specific energy levels, Bohr hypothesized that electrons orbited around a nucleus in the same way that planets orbit the Sun. There is no reason to believe that Bohr formed this hypothesis for any sentimental reasons—though, of course, scientists are just as capable of prejudice as anyone. His work was based on his studies; nonetheless, it is easy to see how this model seemed appealing, showing as it did an order at the subatomic level reflecting an order in the heavens. ELECTRON CLOUDS. Many people
today who are not scientifically trained continue to think that an atom is structured much like the Solar System. This image is reinforced by symbolism, inherited from the 1950s, that represents “nuclear power” by showing a dot (the nucleus) surrounded by ovals at angles to one another, representing the orbital paths of electrons. However, by the 1950s, this model of the atom had already been overturned. In 1923, French physicist Louis de Broglie (1892-1987) introduced the particle-wave hypothesis, which indicated that electrons could sometimes have the properties of waves—an eventuality not encompassed in the Bohr model. It became clear that though Bohr was correct in maintaining that electrons occupy specific energy levels, his planetary model was inadequate for explaining the behavior of electrons. Two years later, in 1925, German physicist Werner Heisenberg (1901-1976) introduced what came to be known as the Heisenberg Uncertainty Principle, showing that the precise position and speed of an electron cannot be known at the same time. Austrian physicist Erwin Schrödinger (1887-1961) developed an
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Atoms
KEY TERMS The smallest particle of an ele-
ELECTRON: Negatively charged parti-
ment that retains all the chemical and
cles in an atom. Electrons, which spin
physical properties of the element. An
around the protons and neutrons that
atom can exist either alone or in combina-
make up the atom’s nucleus, constitute a
tion with other atoms in a molecule. Atoms
very small portion of the atom’s mass. The
are made up of protons, neutrons, and
number of electrons and protons is the
electrons.
same, thus canceling out one another; on
ATOM:
ATOMIC
MASS
UNIT:
An SI unit
(abbreviated amu), equal to 1.66 • 10-24 g,
electrons, it becomes an ion.
for measuring the mass of atoms.
ELEMENT SYMBOL: Another term for
ATOMIC
NUMBER:
The number of
chemical symbol. An atom or atoms that has lost or
protons in the nucleus of an atom. Since
ION:
this number is different for each element,
gained one or more electrons, and thus has
elements are listed on the periodic table of
a net electric charge.
elements in order of atomic number.
ISOTOPES: Atoms that have an equal
AVERAGE ATOMIC MASS: A figure
number of protons, and hence are of the
used by chemists to specify the mass—in
same element, but differ in their number of
atomic mass units—of the average atom in
neutrons.
a large sample.
MASS NUMBER: The sum of protons
CHEMICAL SYMBOL: A one- or two-
and neutrons in an atom’s nucleus.
letter abbreviation for the name of an
MOLECULE: A group of atoms, usually
element.
(but not always) representing more A substance made up of
than one element, joined in a structure.
atoms of more than one element. These
Compounds are typically made up of
atoms are usually joined in molecules.
molecules.
COMPOUND:
equation for calculating how an electron with a certain energy moves, identifying regions in an atom where an electron possessing a certain energy level is likely to be. Schrödinger’s equation cannot, however, identify the location exactly. Rather than being called orbits, which suggest the orderly pattern of Bohr’s model, Schrödinger’s regions of probability are called orbitals. Moving within these orbitals, electrons describe the shape of a cloud, as discussed much earlier in this essay; as a result, the “electron cloud” theory prevails today. This theory incorporates aspects of Bohr’s model, inasmuch as
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the other hand, if an atom loses or gains
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electrons move from one orbital to another by absorbing or emitting a quantum of energy.
WHERE TO LEARN MORE “The Atom.” Thinkquest (Web site). (May 18, 2001). “Elements” (Web site). (May 18, 2001). “Explore the Atom” CERN—European Organization for Nuclear Research (Web site). (May 18, 2001).
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Atoms
KEY TERMS
CONTINUED
A subatomic particle that
together form the nucleus around which
has no electric charge. Neutrons are found
electrons spin, have approximately the
at the nucleus of an atom, alongside
same mass—a mass that is many times
protons.
greater than that of an electron.
NEUTRON:
A generic term for the
QUARK: A particle believed to be a com-
heavy particles—protons and neutrons—
ponent of protons and neutrons. A quark
that make up the nucleus of an atom.
may either have a positive electric charge of
NUCLEON:
less than 1+, in which case it is called an NUCLEON NUMBER:
Another term
for mass number. NUCLEUS: The center of an atom, a
“up quark”; or a negative charge of less than 1-, in which case it is called a “down quark.”
region where protons and neutrons are
RADIATION:
located, and around which electrons spin.
tion can refer to anything that travels in a
PERIODIC TABLE OF ELEMENTS: A
chart that shows the elements arranged in order of atomic number, along with chem-
In a general sense, radia-
stream, whether that stream be composed of subatomic particles or electromagnetic waves. In a more specific sense, the term relates to the radiation from radioactive
ical symbol and the average atomic mass
materials, which can be harmful to human
(in atomic mass units) for that particular
beings.
element. Vertical columns within the periodic table indicate groups or “families” of elements with similar chemical character-
RADIOACTIVITY:
A term describing a
phenomenon whereby certain isotopes are subject to a form of decay brought about
istics.
by the emission of high-energy particles or PROTON:
A positively charged particle
in an atom. Protons and neutrons, which
Gallant, Roy A. The Ever-Changing Atom. New York: Benchmark Books, 1999. Goldstein, Natalie. The Nature of the Atom. New York: Rosen Publishing Group, 2001.
radiation, such as alpha particles, beta particles, or gamma rays.
“A Science Odyssey: You Try It: Atom Builder.” PBS—Public Broadcasting System (Web site). (May 18, 2001).
“A Look Inside the Atom” (Web site). (May 18, 2001).
Spangenburg, Ray and Diane K. Moser. The History of Science in the Nineteenth Century. New York: Facts on File, 1994.
“Portrait of the Atom” (Web site). (May 18, 2001).
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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AT O M I C M A S S Atomic Mass
CONCEPT Every known item of matter in the universe has some amount of mass, even if it is very small. But what about something so insignificant in mass that comparing it to a gram is like comparing a millimeter to the distance between Earth and the nearest galaxy? Obviously, special units are needed for such measurements; then again, one might ask why it is necessary to weigh atoms at all. One answer is that everything is made of atoms. More specifically, the work of a chemist requires the use of accurate atomic proportions in forming the molecules that make up a compound. The measurement of atomic mass was thus a historic challenge that had to be overcome, and the story of the ways that scientists met this challenge is an intriguing one.
HOW IT WORKS Why Mass and Not Weight? Some textbooks and other sources use the term atomic weight instead of atomic mass. The first of these is not as accurate as the second, which explains why atomic mass was chosen as the subject of this essay. Indeed, the use of “atomic weight” today merely reflects the fact that scientists in the past used that expression and spoke of “weighing” atoms. Though “weigh” is used as a verb in this essay, this is only because it is less cumbersome than “measure the mass of.” (In addition, “atomic weight” may be mentioned when discussing studies by scientists of the nineteenth century, who applied that term rather than atomic mass.)
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One might ask why such pains have been taken to make the distinction. Mass is, after all, basically the same as weight, is it not? In fact it is not, though people are accustomed to thinking in those terms since most weight scales provide measurements in both pounds and kilograms. However, the pound is a unit of weight in the English system, whereas a kilogram is a unit of mass in the metric and SI systems. Though the two are relatively convertible on Earth, they are actually quite different. (Of course it would make no more sense to measure atoms in pounds or kilograms than to measure the width of a hair in light-years; but pounds and kilograms are the most familiar units of weight and mass respectively.) Weight is a measure of force affected by Earth’s gravitational pull. Therefore a person’s weight varies according to gravity, and would be different if measured on the Moon, whereas mass is the same throughout the universe. Its invariability makes mass preferable to weight as a parameter of scientific measure.
Putting an Atom’s Size and Mass in Context Mass does not necessarily relate to size, though there is enough of a loose correlation that more often than not, we can say that an item of very small size will have very small mass. And atoms are very, very small—so much so that, until the early twentieth century, chemists and physicists had no accurate means of isolating them to determine their mass. The diameter of an atom is about 10-8 cm. This is equal to about 0.000000003937 in—or to put it another way, an inch is about as long as 250
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million atoms lined up side by side. Obviously, special units are required for describing the size of atoms. Usually, measurements are provided in terms of the angstrom, equal to 10-10 m. (In other words, there are 10 million angstroms in a millimeter.)
Atomic Mass
Measuring the spatial dimensions of an atom, however, is not nearly as important for chemists’ laboratory work as measuring its mass. The mass of an atom is almost inconceivably small. It takes about 5.0 • 1023 carbon atoms to equal just one gram in mass. At first, 1023 does not seem like such a huge number, until one considers that 106 is already a million, meaning that 1023 is a million times a million times a million times 100,000. If 5.0 • 1023 angstrom lengths—angstroms, not meters or even millimeters—were laid end to end, they would stretch from Earth to the Sun and back 107,765 times!
Atomic Mass Units It is obvious, then, that an entirely different unit is needed for measuring the mass of an atom, and for this purpose, chemists and other scientists use an atom mass unit (abbreviated amu), which is equal to 1.66 • 10-24 g. Though the abbreviation amu is used in this book, atomic mass units are sometimes designated simply by a u. On the other hand, they may be presented as numbers without any unit of measure—as for instance on the periodic table of elements. Within the context of biochemistry and microbiology, often the term dalton (abbreviated Da or D) is used. This is useful for describing the mass of large organic molecules, typically rendered in kilodaltons (kDa). The Latin prefix kiloindicates 1,000 of something, and “kilodalton” is much less of a tongue-twister than “kilo-amu”. The term “dalton” honors English chemist John Dalton (1766-1844), who, as we shall see, introduced the concept of the atom to science. AVERAGE ATOMIC MASS. Since
1960, when its value was standardized, the atomic mass unit has been officially known as the “unified atomic mass unit.” The addition of the word “unified” reflects the fact that atoms are not weighed individually—a labor that would be problematic at the very least. In any case, to do so would be to reinvent the wheel, as it were,
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ERNEST RUTHERFORD.
because average atomic mass figures have been established for each element. Average atomic mass figures range from 1.008 amu for hydrogen, the first element listed on the periodic table of elements, to over 250 amu for elements of very high atomic number. Figures for average atomic mass can be used to determine the average mass of a molecule as well, since a molecule is just a group of atoms joined in a structure. The mass of a molecule can be determined simply by adding together average atomic mass figures for each atom the molecule contains. A water molecule, for instance, consists of two hydrogen atoms and one oxygen atom; therefore, its mass is equal to the average atomic mass of hydrogen multiplied by two, and added to the average atomic mass of oxygen.
Avogadro’s Number and the Mole Atomic mass units and average atomic mass are not the only components necessary for obtaining accurate mass figures where atoms are concerned. Obviously, as suggested several times already, it would be fruitless to determine the mass of individual atoms or molecules. Nor would it do to measure the mass of a few hundred, or even a few million, of these particles.
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becomes clear: as noted, carbon has an average atomic mass of 12.01 amu, and multiplication of the average atomic mass by Avogadro’s number yields a figure in grams equal to the value of the average atomic mass in atomic mass units.
Atomic Mass
REAL-LIFE A PPLICAT I O N S Early Ideas of Atomic Mass Dalton was not the first to put forth the idea of the atom: that concept, originated by the ancient Greeks, had been around for more than 2,000 years. However, atomic theory had never taken hold in the world of science—or, at least, what passed for science prior to the seventeenth century revolution in thinking brought about by Galileo Galilei (1564-1642) and others.
FREDERICK SODDY.
After all, as we have seen, it takes about 500,000 trillion million carbon atoms to equal just one gram—and a gram, after all, is still rather small in mass compared to most objects encountered in daily life. (There are 1,000 g in a kilogram, and a pound is equal to about 454 g.) In addition, scientists need some means for comparing atoms or molecules of different substances in such a way that they know they are analyzing equal numbers of particles. This cannot be done in terms of mass, because the number of atoms in each sample varies: a gram of hydrogen, for instance, contains about 12 times as many atoms as a gram of carbon, which has an average atomic mass of 12.01 amu. What is needed, instead, is a way to designate a certain number of atoms or molecules, such that accurate comparisons are possible. In order to do this, chemists make use of a figure known as Avogadro’s number. Named after Italian physicist Amedeo Avogadro (1776-1856), it is equal to 6.022137 x 1023. Avogadro’s number, which is 6,022,137 followed by 17 zeroes, designates the quantity of molecules in a mole (abbreviated mol). The mole, a fundamental SI unit for “amount of substance,” is defined precisely as the number of carbon atoms in 12.01 g of carbon. It is here that the value of Avogadro’s number
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Influenced by several distinguished predecessors, Dalton in 1803 formulated the theory that nature is formed of tiny particles, an idea he presented in A New System of Chemical Philosophy (1808). Dalton was the first to treat atoms as fully physical constructs; by contrast, ancient proponents of atomism conceived these fundamental particles in ideal or spiritual terms. Dalton described atoms as hard, solid, indivisible particles with no inner spaces—a definition that did not endure, as later scientific inquiry revealed the complexities of the atom. Yet he was correct in identifying atoms as having weight—or, as scientists say today, mass. THE FIRST TABLE OF ATOMIC WEIGHTS. The question was, how could any-
one determine the weight of something as small as an atom? A year after the publication of Dalton’s book, a discovery by French chemist and physicist Joseph Gay-Lussac (1778-1850) and German naturalist Alexander von Humboldt (1769-1859) offered a clue. Humboldt and GayLussac—famous for his gas law associating pressure and temperature—found that gases combine to form compounds in simple proportions by volume. For instance, as Humboldt and Gay-Lussac discovered, water is composed of only two elements: hydrogen and oxygen, and these two combine in a whole-number ratio of 8:1. By separating water into its components, they found that for every part of oxygen, there were eight parts of hydrogen. Today we know that water molecules
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are formed by two hydrogen atoms, with an average atomic mass of 1.008 amu each, and one oxygen atom. The ratio between the average atomic mass of oxygen (16.00 amu) and that of the two hydrogen atoms is indeed very nearly 8:1. In the early nineteenth century, however, chemists had no concept of molecular structure, or any knowledge of the atomic masses of elements. They could only go on guesswork: hence Dalton, in preparing the world’s first “Table of Atomic Weights,” had to make some assumptions based on Humboldt’s and Gay-Lussac’s findings. Presumably, Dalton reasoned, only one atom of hydrogen combines with one atom of oxygen to form a “water atom.” He assigned to hydrogen a weight of 1, and according to this, calculated the weight of oxygen as 8. AVOGADRO AND BERZELIUS IMPROVE ON DALTON’S WORK. The
implications of Gay-Lussac’s discovery that substances combined in whole-number ratios were astounding. (Gay-Lussac, who studied gases for much of his career, is usually given more credit than Humboldt, an explorer and botanist who had his hand in many things.) On the one hand, the more scientists learned about nature, the more complex it seemed; yet here was something amazingly simple. Instead of combining in proportions of, say, 8.3907 to 1.4723, oxygen and hydrogen molecules formed a nice, clean, ratio of 8 to 1. This served to illustrate the fact that, as Dalton had stated, the fundamental particles of matter must be incredibly tiny; otherwise, it would be impossible for every possible quantity of hydrogen and oxygen in water to have the same ratio. Intrigued by the work of Gay-Lussac, Avogadro in 1811 proposed that equal volumes of gases have the same number of particles if measured at the same temperature and pressure. He also went on to address a problem raised by Dalton’s work. If atoms were indivisible, as Dalton had indicated, how could oxygen exist both as its own atom and also as part of a water “atom”? Water, as Avogadro correctly hypothesized, is not composed of atoms but of molecules, which are themselves formed by the joining of two hydrogen atoms with one oxygen atom. Avogadro’s molecular theory opened the way to the clarification of atomic mass and the development of the mole, which, as we have seen, makes it possible to determine mass for large
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quantities of molecules. However, his ideas did not immediately gain acceptance. Only in 1860, four years after Avogadro’s death, did Italian chemist Stanislao Cannizzaro (1826-1910) resurrect the concept of the molecule as a way of addressing disagreements among scientists regarding the determination of atomic mass.
Atomic Mass
In the meantime, Swedish chemist Jons Berzelius (1779-1848) had adopted Dalton’s method of comparing all “atomic weights” to that of hydrogen. In 1828, Berzelius published a table of atomic weights, listing 54 elements along with their weight relative to that of hydrogen. Thus carbon, in Berzelius’s system, had a weight of 12. Unlike Dalton’s figures, Berzelius’s are very close to those used by scientists today. By the time Russian chemist Dmitri Ivanovitch Mendeleev (1834-1907) created his periodic table in 1869, there were 63 known elements. That first table retained the system of measuring atomic mass in comparison to hydrogen.
The Discovery of Subatomic Structures Until scientists began to discover the existence of subatomic structures, measurements of atomic mass could not really progress. Then in 1897, English physicist J. J. Thomson (1856-1940) identified the electron. A particle possessing negative charge, the electron contributes little to an atom’s mass, but it pointed the way to the existence of other particles within an atom. First of all, there had to be a positive charge to offset that of the electron, and secondly, the item or items providing this positive charge had to account for the majority of the atom’s mass. Early in the twentieth century, Thomson’s student Ernest Rutherford (1871-1937) discovered that the atom has a nucleus, a center around which electrons move, and that the nucleus contains positively charged particles called protons. Protons have a mass 1,836 times as great as that of an electron, and thus seemed to account for the total atomic mass. Later, however, Rutherford and English chemist Frederick Soddy (18771956) discovered that when an atom emitted certain types of particles, its atomic mass changed. ISOTOPES AND ATOMIC MASS.
Rutherford and Soddy named these atoms of differing mass isotopes, though at that point— because the neutron had yet to be discovered—
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they did not know exactly what had caused the change in mass. Certain types of isotopes, Soddy and Rutherford concluded, had a tendency to decay, moving (sometimes over a great period of time) toward stabilization. Such isotopes were radioactive. Soddy concluded that atomic mass, as measured by Berzelius, was actually an average of the mass figures for all isotopes within that element. This explained a problem with Mendeleev’s periodic table, in which there seemed to be irregularities in the increase of atomic mass from element to element. The answer to these variations in mass, it turned out, related to the number of isotopes associated with a given element: the greater the number of isotopes, the more these affected the overall measure of the element’s mass. A NEW DEFINITION OF ATOMIC NUMBER. Up to this point, the term “atomic
number” had a different, much less precise, meaning than it does today. As we have seen, the early twentieth century periodic table listed elements in order of their atomic mass in relation to hydrogen, and thus atomic number referred simply to an element’s position in this ordering. Then, just a few years after Rutherford and Soddy discovered isotopes, Welsh physicist Henry Moseley (1887-1915) determined that every element has a unique number of protons in its nucleus. Today, the number of protons in the nucleus, rather than the mass of the atom, determines the atomic number of an element. Carbon, for instance, has an atomic number of 6, not because there are five elements lighter—though this is also true—but because it has six protons in its nucleus. The ordering by atomic number happens to correspond to the ordering by atomic mass, but atomic number provides a much more precise means of distinguishing elements. For one thing, atomic number is always a whole integer—1 for hydrogen, for instance, or 17 for chlorine, or 92 for uranium. Figures for mass, on the other hand, are almost always rendered with decimal fractions (for example, 1.008 for hydrogen). NEUTRONS COMPLETE THE PICTURE. As with many other discoveries
along the way to uncovering the structure of the atom, Moseley’s identification of atomic number with the proton raised still more questions. In particular, if the unique number of protons identified an element, what was it that made isotopes
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of the same element different from one another? Hydrogen, as it turned out, indeed had a mass very nearly equal to that of one proton—thus justifying its designation as the basic unit of atomic mass. Were it not for the isotope known as deuterium, which has a mass nearly twice as great as that of hydrogen, the element would have an atomic mass of exactly 1 amu. A discovery by English physicist James Chadwick (1891-1974) in 1932 finally explained what made an isotope an isotope. It was Chadwick who identified the neutron, a particle with no electric charge, which resides in the nucleus alongside the protons. In deuterium, which has one proton, one neutron, and one electron, the electron accounts for only 0.0272% of the total mass—a negligible figure. The proton, on the other hand, makes up 49.9392% of the mass. Until the discovery of the neutron, there had been no explanation of the other 50.0336% of the mass in an atom with just one proton and one electron.
Average Atomic Mass Today Thanks to Chadwick’s discovery of the neutron, it became clear why deuterium weighs almost twice as much as ordinary hydrogen. This in turn is the reason why a large sample of hydrogen, containing as it does a few molecules of deuterium here and there, does not have the same average atomic mass as a proton. Today scientists know that there are literally thousands of isotopes—many of them stable, but many more of them unstable or radioactive—for the 100-plus elements on the periodic table. Each isotope, of course, has a slightly different atomic mass. This realization has led to clarification of atomic mass figures. One might ask how figures of atomic mass are determined. In the past, as we have seen, it was largely a matter of guesswork, but today chemists and physicist use a highly sophisticated instrument called a mass spectrometer. First, atoms are vaporized, then changed to positively charged ions, or cations, by “knocking off ” electrons. The cations are then passed through a magnetic field, and this causes them to be deflected by specific amounts, depending on the size of the charge and its atomic mass. The particles eventually wind up on a deflector plate, where the amount of deflection can be measured and compared with the charge. Since 1 amu has
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been calculated to equal approximately 931.494 MeV, or mega electron-volts, very accurate figures can be determined. CALIBRATION OF THE ATOMIC MASS UNIT. When 1 is divided by Avo-
gadro’s number, the result is 1.66 • 10-24—the value, in grams, of 1 amu. However, in accordance with a 1960 agreement among members of the international scientific community, measurements of atomic mass take as their reference point the mass of carbon-12. Not only is the carbon-12 isotope found in all living things, but hydrogen is a problematic standard because it bonds so readily with other elements. According to the 1960 agreement, 1 amu is officially 1/12 the mass of a carbon-12 atom, whose exact value (retested in 1998), is 1.6653873 • 10-24 g. 12
Carbon-12, sometimes represented as ᎏ6ᎏC, contains six protons and six neutrons. (As explained in the essay on Isotopes, where an isotope is indicated, the number to the upper left of the chemical symbol indicates the total number of protons and neutrons. Sometimes this is the only number shown; but if a number is included on the lower left, this indicates only the number of protons, which remains the same for each element.) The value of 1 amu thus obtained is, in effect, an average of the mass for a proton and neutron—a usable figure, given the fact that a neutron weighs only 0.163% more than a proton. Of all the carbon found in nature (as opposed to radioactive isotopes created in laboratories), 98.89% of it is carbon-12. The remainder is mostly carbon-13, with traces of carbon14, an unstable isotope produced in nature. By definition, carbon-12 has an atomic mass of exactly 12 amu; that of carbon-13 (about 1.11% of all carbon) is 13 amu. Thus the atomic mass of carbon, listed on the periodic table as 12.01 amu, is obtained by taking 98.89% of the mass of carbon-12, combined with 1.11% of the mass of carbon-13. ATOMIC MASS UNITS AND THE PERIODIC TABLE. The periodic table as it
is used today includes figures, in atomic mass units, for the average mass of each atom. As it turns out, Berzelius was not so far off in his use of hydrogen as a standard, since its mass is almost exactly 1 amu—but not quite, because (as noted above) deuterium increases the average mass somewhat. Figures increase from there along the
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periodic table, though not by a regular pattern. Sometimes the increase from one element to the next is by just over 1 amu, and in other cases, the increase is by more than 3 amu. This only serves to prove that atomic number, rather than atomic mass, is a more straightforward means of ordering the elements.
Atomic Mass
Mass figures for many elements that tend to appear in the form of radioactive isotopes are usually shown in parentheses. This is particularly true for elements with atomic numbers above 92, because samples of these elements do not stay around long enough to be measured. Some have a half-life—the period in which half the isotopes decay to a stable form—of just a few minutes, and for others, the half-life is but a fraction of a second. Therefore, atomic mass figures represent the mass of the longest-lived isotope.
Uses of Atomic Mass in Chemistry MOLAR MASS. Just as the value of atomic mass units has been calibrated to the mass of carbon-12, the mole is no longer officially defined in terms of Avogadro’s number, though in general its value has not changed. By international scientific agreement, the mole equals the number of carbon atoms in 12.01 g of carbon. Note that, as stated earlier, carbon has an average atomic mass of 12.01 amu.
This is no coincidence, of course: multiplication of the average atomic mass by Avogadro’s number yields a figure in grams equal to the value of the average atomic mass in amu. A mole of helium, with an average atomic mass of 4.003, is 4.003 g. Iron, on the other hand, has an average atomic mass of 55.85, so a mole of iron is 55.85 g. These figures represent the molar mass—the mass of 1 mole—for each of the elements mentioned. THE NEED FOR EXACT PROPORTIONS. When chemists discover new
substances in nature or create new ones in the laboratory, the first thing they need to determine is the chemical formula—in other words, the exact quantities and proportions of elements in each molecule. By chemical means, they separate the compound into its constituent elements, then determine how much of each element is present.
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Atomic Mass
KEY TERMS ATOM:
The smallest particle of an ele-
NUMBER:
A figure,
ment that retains all the chemical and
named after Italian physicist Amedeo Avo-
physical properties of that element.
gadro (1776-1856), equal to 6.022137 x
ATOMIC
MASS
UNIT:
An SI unit
(abbreviated amu), equal to 1.66 • 10-24 g, for measuring the mass of atoms. ATOMIC
NUMBER:
The number of
protons in the nucleus of an atom. Since this number is different for each element, elements are listed on the periodic table of elements in order of atomic number.
1023. Avogadro’s number indicates the number of atoms or molecules in a mole. COMPOUND:
A substance made up of
atoms of more than one element. These atoms are usually joined in molecules. DALTON:
An alternate term for atomic
mass units, used in biochemistry and microbiology for describing the mass of large organic molecules. The dalton
An old term for
(abbreviated Da or D) is named after
atomic mass. Since weight varies depend-
English chemist John Dalton (1766-1844),
ing on gravitational field, whereas mass is
who introduced the concept of the atom to
the same throughout the universe, scien-
science.
ATOMIC WEIGHT:
tists typically use the term “atomic mass”
ELEMENT:
A substance made up of only
instead.
one kind of atom, which cannot be chemi-
AVERAGE ATOMIC MASS: A figure
cally broken into other substances.
used by chemists to specify the mass—in
HALF-LIFE: The length of time it takes a
atomic mass units—of the average atom in
substance to diminish to one-half its initial
a large sample.
amount.
Since they are using samples in relatively large quantities, molar mass figures for each element make it possible to determine the chemical composition. To use a very simple example, suppose a quantity of water is separated, and the result is 2.016 g of hydrogen and 16 g of oxygen. The latter is the molar mass of oxygen, and the former is the molar mass of hydrogen multiplied by two. Thus we know that there are two moles of hydrogen and one mole of oxygen, which combine to make one mole of water. Of course the calculations used by chemists working in the research laboratories of universities, government institutions, and corporations are much, much more complex than the example we have given. In any case, it is critical that a chemist be exact in making these determinations,
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so as to know the amount of reactants needed to produce a given amount of product, or the amount of product that can be produced from a given amount of reactant. When a company produces millions or billions of a single item in a given year, a savings of very small quantities in materials—thanks to proper chemical measurement—can result in a savings of billions of dollars on the bottom line. Proper chemical measurement can also save lives. Again, to use a very simple example, if a mole of compounds weighs 44.01 g and is found to contain two moles of oxygen and one of carbon, then it is merely carbon dioxide—a compound essential to plant life. But if it weighs 28.01 g and has one mole of oxygen with one mole of carbon, it is poisonous carbon monoxide.
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Atomic Mass
KEY TERMS ION:
An atom or group of atoms that has
lost or gained one or more electrons, and thus has a net electric charge.
CONTINUED
SI definition, a mole is equal to the number of carbon atoms in 12.01 g of carbon. MOLECULE: A group of atoms, usually,
ISOTOPES: Atoms of the same element
but
(that is, they have the same number of pro-
than one element, joined in a structure.
tons) that differ in terms of mass. Isotopes
Compounds are typically made of up
may be either stable or unstable. The latter
molecules.
type, known as radioisotopes, are radioactive.
not
always, representing
more
PERIODIC TABLE OF ELEMENTS: A
chart that shows the elements arranged in
MASS: The amount of matter an object
order of atomic number, along with chem-
contains.
ical symbol and the average atomic mass
MOLAR MASS: The mass, in grams, of
(in atomic mass units) for that particular
1 mole of a given substance. The value in
element.
grams of molar mass is always equal to the
RADIOACTIVITY:
value, in atomic mass units, of the average
phenomenon whereby certain isotopes
atomic mass of that substance. Thus car-
known as radioisotopes are subject to a
bon has a molar mass of 12.01 g, and an
form of decay brought about by the emis-
average atomic mass of 12.01 amu.
sion of high-energy particles. “Decay” does
A term describing a
The SI fundamental unit for
not mean that the isotope “rots”; rather, it
“amount of substance.” A mole is, general-
decays to form another isotope, until even-
ly speaking, Avogadro’s number of atoms
tually (though this may take a long time), it
or molecules; however, in the more precise
becomes stable.
MOLE:
WHERE TO LEARN MORE “Atomic Weight” (Web site). (May 23, 2001). “An Experiment with ‘Atomic Mass’” (Web site). (May 23, 2001). Knapp, Brian J. and David Woodroffe. The Periodic Table. Danbury, CT: Grolier Educational, 1998. Oxlade, Chris. Elements and Compounds. Chicago: Heinemann Library, 2001.
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“Periodic Table: Atomic Mass.” ChemicalElements.com (Web site). (May 23, 2001). “Relative Atomic Mass” (Web site). (May 23, 2001). “What Are Atomic Number and Atomic Weight?” (Web site). (May 23, 2001).
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ELECTRONS Electrons
CONCEPT No one can see an electron. Even an electron microscope, used for imaging the activities of these subatomic particles, does not offer a glimpse of an electron as one can look at an amoeba; instead, the microscope detects the patterns of electron deflection. In any case, a singlecell organism is gargantuan in comparison to an electron. Even when compared to a proton or a neutron, particles at the center of an atom, electrons are minuscule, being slightly more than 1/2000 the size of either. Yet the electron is the key to understanding the chemical process of bonding, and electron configurations clarify a number of aspects of the periodic table that may, at first, seem confusing.
HOW IT WORKS The Electron’s Place in the Atom The atom is discussed in detail elsewhere in this book; here, the particulars of atomic structure will be presented in an abbreviated form, so that the discussion of electrons may proceed. At the center of an atom, the smallest particle of an element, there is a nucleus, which contains protons and neutrons. Protons are positive in charge, while neutrons exert no charge. Moving around the nucleus are electrons, negatively charged particles whose mass is very small in comparison to the proton or neutron: 1/1836 and 1/1839 the mass of the proton and neutron respectively. The mass of an electron is 9.109389 • 10–33 g. Compare the number 9 to the number
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1,000,000,000,000,000,000,000,000,000,000,000, and this gives some idea of the ratio between an electron’s mass and a gram. The large number— 1 followed by 33 zeroes—is many trillions of times longer than the age of the universe in seconds. IONS AND CHEMICAL BONDS.
Electrons, though very small, are exceedingly powerful, and they are critical to both physical and chemical processes. The negative charge of an electron, designated by the symbol 1- or -1, is enough to counteract the positive charge (1+ or +1) of a proton, even though the proton has much greater mass. As a result, atoms (because they possess equal numbers of protons and electrons) have an electric charge of zero. Sometimes an atom will release an electron, or a released electron will work its way into the structure of another atom. In either case, an atom that formerly had no electric charge acquires one, becoming an ion. In the first of the instances described, the atom that has lost an electron or electrons becomes a positively charged ion, or cation. In the second instance, an atom that gains an electron or electrons becomes a negatively charged ion, or anion. One of the first forms of chemical bonding discovered was ionic bonding, in which electrons clearly play a role. In fact, electrons are critical to virtually all forms of chemical bonding, which relates to the interactions between electrons of different atoms. MOVEMENT OF THE ELECTRON ABOUT THE NUCLEUS. If the size of the
nucleus were compared to a grape, the edge of the atom itself would form a radius of about a mile. Because it is much smaller than the nucle-
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Electrons
z
y
y
2py
y
x
x
TWO-LOBED
z
z
2px
x
2p2
ORBITALS.
us, an electron might be depicted in this scenario as a speck of dust—but a speck of dust with incredible energy, which crosses the mile radius of this enlarged atom at amazing speeds. In an item of matter that has been frozen to absolute zero, an electron moves relatively little. On the other hand, it can attain speeds comparable to that of the speed of light: 186,000 mi (299,339 km) per second. The electron does not move around the nucleus as a planet orbits the Sun—a model of electron behavior that was once accepted, but which has since been overturned. On the other hand, as we shall see, the electron does not simply “go where it pleases”: it acts in accordance with complex patterns described by the quantum theory of physics. Indeed, to some extent the behavior of the electron is so apparently erratic that the word “pattern” seems hardly to describe it. However, to understand the electron clearly, one has to set aside all ideas about how objects behave in the physical world.
Emerging Models of Electron Behavior The idea that matter is composed of atoms originated in ancient Greece, but did not take hold until early in the nineteenth century, with the
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atomic theory of English chemist John Dalton (1766-1844). In the years that followed, numerous figures—among them Russian chemist Dmitri Mendeleev (1834-1907), father of the periodic table of elements—contributed to the emerging understanding of the atomic model. Yet Mendeleev, despite his awareness that the mass of an atom differentiated one element from another, had no concept of subatomic particles. No one did: until very late in the nineteenth century, the atom might as well have been a hardshelled ball of matter, for all that scientists understood about its internal structure. The electron was the first subatomic particle discovered, in 1897—nearly a century after the scientific beginning of atomic theory. Yet the first hints regarding its existence had begun to appear some 60 years before. DISCOVERY OF THE ELECTRON. In 1838, British physicist and chemist
Michael Faraday (1791-1867) was working with a set of electrodes—metal plates used to emit or collect electric charge—which he had placed at either end of an evacuated glass tube. (In other words, most of the air and other matter had been removed from the tube.) He applied a charge of several thousand volts between the electrodes, and discovered that an electric current flowed between them.
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Electrons
A
COMPUTER-GENERATED MODEL OF A NEON ATOM.
THE
NUCLEUS, AT CENTER, IS TOO SMALL TO BE SEEN AT THIS SURROUNDING THE NUCLEUS ARE THE ATOM’S ELECTRON SPHERE), AND 2P (LOBED). (Photograph by Kenneth Eward/BioGrafx. National
SCALE AND IS REPRESENTED BY THE FLASH OF LIGHT. ORBITALS:
1S (SMALL
SPHERE),
2S (LARGE
Audubon Society Collection/Photo Researchers, Inc. Reproduced by permission.)
This seemed to suggest the existence of particles carrying an electric charge, and four decades later, English physicist William Crookes (1832-1919) expanded on these findings with his experiments using an apparatus that came to be known as a Crookes tube. As with Faraday’s device, the Crookes tube used an evacuated glass tube encased between two electrodes—a cathode at the negatively charged end, and an anode at the positively charged end. A wire led outside the bulb to an electric source, and when electricity was applied to the electrodes, the cathodes emitted rays. Crookes concluded that the cathode rays were particles with a negative electric charge that came from the metal in the cathode plate. English physicist J. J. Thomson (1856-1940) hypothesized that the negatively charged particles Crookes had observed were being emitted by atoms, and in 1897 he gave a name to these particles: electrons. The discovery of the electron raised questions concerning its place in the atom: obviously, there had to be a counterbalancing positive charge, and if so, from whence did it come? FROM PLUM PUDDINGS TO PLANETS. Around the beginning of the
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twentieth century, the prevailing explanation of atomic structure was the “plum pudding model,” which depicted electrons as floating like raisins in a “pudding” of positive charges. This was overturned by the discovery of the nucleus, and, subsequently, of the proton and neutron it contained. In 1911, the great Danish physicist Niels Bohr (1885-1962) studied hydrogen atoms, and concluded that electrons move around the nucleus in much the same way that planets move around the Sun. This worked well when describing the behavior of hydrogen, which, in its simplest form—the isotope protium—has only one electron and one proton, without any neutrons. The model did not work as well when applied to other elements, however, and within less than two decades Bohr’s planetary model was overturned. As it turns out, the paths of an electron’s movement around the nucleus are nothing like that of a planet’s orbit—except inasmuch as both models describe a relatively small object moving around a relatively large one. The reality is much more complex, and to comprehend the secret of the electron’s apparently random behavior is
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truly a mind-expanding experience. Yet Bohr is still considered among the greatest scientists of the twentieth century: it was he, after all, who first explained the quantum behavior of electrons, examined below.
on a continuum; rather, there are only certain energy levels possible for an atom of a given element. The energy levels are therefore said to be quantized.
Electrons
The Wave Mechanical Model
REAL-LIFE AP P LICATIONS Quantum Theory and the Atom Much of what scientists understand today about the atom in general, and the electron in particular, comes from the quantum theory introduced by German physicist Max Planck (1858-1947). Planck showed that, at the atomic level, energy is emitted in tiny packets, or “quanta.” Applying this idea to the electron, Bohr developed an idea of the levels at which an electron moves around the nucleus. Though his conclusions led him to the erroneous planetary model, Bohr’s explanation of energy levels still prevails. As has been suggested, the interaction between electrons and protons is electromagnetic, and electromagnetic energy is emitted in the form of radiation, or a stream of waves and particles. The Sun, for instance, emits electromagnetic radiation along a broad spectrum that includes radio waves, infrared light, visible light, ultraviolet light, x rays, and gamma rays. These are listed in ascending order of their energy levels, and the energy emitted can be analyzed in terms of wavelength and frequency: the shorter the wavelength, the greater the frequency and the greater the energy level. When an atom is at its ordinary energy level, it is said to be in a ground state, but when it acquires excess energy, it is referred to as being in an excited state. It may release some of that energy in the form of a photon, a particle of electromagnetic radiation. The amount of energy involved can be analyzed in terms of the wavelengths of light the atom emits in the form of photons, and such analysis reveals some surprising things about the energy levels of atoms. If one studies the photons emitted by an atom as it moves between a ground state and an excited state, one discovers that it emits only certain kinds of photons. From this, Bohr concluded that the energy levels of an atom do not exist
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In everyday terms, quantization can be compared to the way that a person moves up a set of stairs: by discrete steps. If one step directly follows another, there is no step in between, nor is there any gradual way of moving from step to step, as one would move up a ramp. The movement of electrons from one energy level to another is not a steady progression, like the movement of a person up a ramp; rather, it is a series of quantum steps, like those a person makes when climbing a set of stairs. The idea of quantization was ultimately applied to describing the paths that an electron makes around the nucleus, but this required some clarification along the way. It had been believed that an electron could move through any point between the nucleus and the edge of the atom (again, like a ramp), but it later became clear that the electrons could only move along specific energy levels. As we have seen, Bohr believed that these corresponded to the orbits of planets around the Sun; but this explanation would be discarded in light of new ideas that emerged in the 1920s. During the early part of that decade, French physicist Louis de Broglie (1892-1987) and Austrian physicist Erwin Schrödinger (1887-1961) introduced what came to be known as the wave mechanical model, also known as the particle-wave hypothesis. Because light appeared to have the properties of both particles and waves, they reasoned, electrons (possessing electromagnetic energy as they did) might behave in the same fashion. In other words, electrons were not just particles: in some sense, they were waves as well. UNDERSTANDING
ORBITALS.
The wave mechanical model depicted the movement of electrons, not as smooth orbits, but as orbitals—regions in which there is the highest probability that an electron will be found. An orbital is nothing like the shape of a solar system, but, perhaps ironically, it can be compared to the photographs astronomers have taken of galaxies. In most of these photographs, one sees an area of
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intense light emitted by the stars in the center. Further from this high-energy region, the distribution of stars (and hence of light) becomes increasingly less dense as one moves from the center of the galaxy to the edges. Replace the center of the galaxy with the nucleus of the atom, and the stars with electrons, and this is an approximation of an orbital. Just as a galaxy looks like a cloud of stars, scientists use the term electron cloud to describe the pattern formed by orbitals. The positions of electrons cannot be predicted; rather, it is only possible to assign probabilities as to where they will be. Naturally, they are most drawn to the positive charges in the nucleus, and hence an orbital depicts a high-density region of probabilities at the center—much like the very bright center of a galaxy. The further away from the nucleus, the less the probability that an electron will be in that position. Hence in models of an orbital, the dots are concentrated at the center, and become less dense the further away from the nucleus they are. As befits the comparison to a cloud, the edge of an orbital is fuzzy. Contrary to the earlier belief that an atom was a clearly defined little pellet of matter, there is no certainty regarding the exact edge of a given atom; rather, scientists define the sphere of the atom as the region encompassing 90% of the total electron probability. THE MYSTERIOUS ELECTRON.
As complex as this description of electron behavior may seem, one can rest assured that the reality is infinitely more complex than this simplified explanation suggests. Among the great mysteries of the universe is the question of why an electron moves as it does, or even exactly how it does so. Nor does a probability model give us any way of knowing when an electron will occupy a particular position. In fact, as German physicist Werner Heisenberg (1901-1976) showed with what came to be known as the Heisenberg Uncertainty Principle, it is impossible to know both the speed of an electron and its precise position at the same time. This, of course, goes against every law of physics that prevailed until about 1920, and in fact quantum theory offers an entirely different model of reality than the one accepted during the seventeenth, eighteenth, and nineteenth centuries.
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Orbitals Given the challenges involved in understanding electron behavior, it is amazing just how much scientists do know about electrons—particularly where energy levels are concerned. This, in turn, makes possible an understanding of the periodic table that would astound Mendeleev. Every element has a specific configuration of energy levels that becomes increasingly complex as one moves along the periodic table. In the present context, these configurations will be explained as simply as possible, but the reader is encouraged to consult a reliable chemistry textbook for a more detailed explanation. PRINCIPAL ENERGY LEVELS AND SUBLEVELS. The principal energy
level of an atom indicates a distance that an electron may move away from the nucleus. This is designated by a whole-number integer, beginning with 1 and moving upward: the higher the number, the further the electron is from the nucleus, and hence the greater the energy in the atom. Each principal energy level is divided into sublevels corresponding to the number n of the principal energy level: thus principal energy level 1 has one sublevel, principal energy level 2 has two, and so on. The simplest imaginable atom, a hydrogen atom in a ground state, has an orbital designated as 1s1. The s indicates that an electron at energy level 1 can be located in a region described by a sphere. As for the significance of the superscript 1, this will be explained shortly. Suppose the hydrogen atom is excited enough to be elevated to principal energy level 2. Now there are two sublevels, 2s (for now we will dispense with the superscript 1) and 2p. A p orbital is rather like the shape of a figure eight, with its center of gravity located on the nucleus, and thus unlike the s sublevel, p orbitals can have a specific directional orientation. Depending on whether it is oriented along an x-, y-, or zaxis, orbitals in sublevel p are designated as 2px, 2py, or 2pz. If the hydrogen atom is further excited, and therefore raised to principal energy level 3, it now has three possible sublevels, designated as s, p, and d. Some of the d orbitals can be imagined as two figure eights at right angles to one another, once again with their centers of gravity along the nucleus of the atom. Because of their more com-
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plex shape, there are five possible spatial orientations for orbitals at the d sublevel. Even more complex is the model of an atom at principal level 4, with four sublevels—s,p, d, and f, which has a total of seven spatial orientations. Obviously, things get very, very complex at increased energy levels. The greater the energy level, the further the electron can move from the nucleus, and hence the greater the possible number of orbitals and corresponding shapes. ELECTRON SPIN AND THE PAULI EXCLUSION PRINCIPLE.
Every electron spins in one of two directions, and these are indicated by the symbols ↑ and ↓. According to the Pauli exclusion principle, named after the Austrian-Swiss physicist Wolfgang Pauli (1900-1958), no more than two electrons can occupy the same orbital, and those two electrons must have spins opposite one another. This explains the use of the superscript 1, which indicates the number of electrons in a given orbital. This number is never greater than two: hence, the electron configuration of helium is written as 1s2. It is understood that these two electrons must be spinning in opposite directions, but sometimes this is indicated by an orbital diagram showing both an upward- and downward-pointing arrow in an orbital that has been filled, or only an upward-pointing arrow in an orbital possessing just one electron.
Electron Configuration and the Periodic Table THE FIRST 18 ELEMENTS. As one moves up the periodic table from atomic number 1 (hydrogen) to 18 (argon), a regular pattern emerges. The orbitals are filled in a neat progression: from helium (atomic number 2) onward, all of principal level 1 is filled; beginning with beryllium (atomic number 4), sublevel 2s is filled; from neon (atomic number 10), sublevel 2p— and hence principal level 2 as a whole—is filled, and so on. The electron configuration for neon, thus, is written as 1s22s22p6.
Note that if one adds together all the superscript numbers, one obtains the atomic number of neon. This is appropriate, of course, since atomic number is defined by the number of protons, and an atom in a non-ionized state has an equal number of protons and electrons. In noticing the electron configurations of an element, pay close attention to the last or highest principal
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energy level represented. These are the valence electrons, the ones involved in chemical bonding. By contrast, the core electrons, or the ones that are at lower energy levels, play no role in the bonding of atoms.
Electrons
SHIFTS IN ELECTRON CONFIGURATION PATTERNS. After argon, how-
ever, as one moves to the element occupying the nineteenth position on the periodic table— potassium—the rules change. Argon has an electron configuration of 1s22s22p63s23p6, and by the pattern established with the first 18 elements, potassium should begin filling principal level 3d. Instead, it “skips” 3d and moves on to 4s. The element following argon, calcium, adds a second electron to the 4s level. After calcium, the pattern again changes. Scandium (atomic number 21) is the first of the transition metals, a group of elements on the periodic table in which the 3d orbitals are filled. This explains why the transition metals are indicated by a shading separating them from the rest of the elements on the periodic table. But what about the two rows at the very bottom of the chart, representing groups of elements that are completely set apart from the periodic table? These are the lanthanide and actinide series, which are the only elements that involve f sublevels. In the lanthanide series, the seven 4f orbitals are filled, while the actinide series reflects the filling of the seven 5f orbitals. As noted earlier, the patterns involved in the f sublevel are ultra-complex. Thus it is not surprising than the members of the lanthanide series, with their intricately configured valence electrons, were very difficult to extract from one another, and from other elements: hence their old designation as the “rare earth metals.” However, there are a number of other factors—relating to electrons, if not necessarily electron configuration—that explain why one element bonds as it does to another. CHANGES IN ATOMIC SIZE. With the tools provided by the basic discussion of electrons presented in this essay, the reader is encouraged to consult the essays on Chemical Bonding, as well as The Periodic Table of the Elements, both of which explore the consequences of electron arrangement in chemistry. Not only are electrons the key to chemical bonding, understanding their configurations is critical to an understanding of the periodic table.
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Electrons
KEY TERMS ANION:
The negative ion that results
when an atom gains one or more electrons.
describe the pattern formed by orbitals.
ANODE: An electrode at the positively
EXCITED STATE:
charged end of a supply of electric current.
characteristics of an atom that has
ATOM:
The smallest particle of an
element. ATOMIC
acquired excess energy. GROUND STATE:
NUMBER:
The number of
A term describing the
A term describing
the state of an atom at its ordinary energy
protons in the nucleus of an atom. Since
level.
this number is different for each element,
ION:
elements are listed on the periodic table of
gained one or more electrons, and thus has
elements in order of atomic number.
a net electric charge.
CATHODE: An electrode at the negative-
ISOTOPES: Atoms that have an equal
ly charged end of a supply of electric cur-
number of protons, and hence are of the
rent.
same element, but differ in their number of
CATION:
The positive ion that results
An atom or atoms that has lost or
neutrons.
when an atom loses one or more electrons.
NEUTRON:
ELECTRODE: A structure, often a metal
has no electric charge. Neutrons are found
plate or grid, that conducts electricity, and
in the nucleus of an atom, alongside
which is used to emit or collect electric
protons.
charge.
NUCLEUS: The center of an atom, a
ELECTRON: A negatively charged parti-
region where protons and neutrons are
cle in an atom.
located, and around which electrons spin.
One of the curious things about the periodic table, for instance, is the fact that the sizes of atoms decrease as one moves from left to right across a row or period, even though the sizes increase as one moves from top to bottom along a column or group. The latter fact—the increase of atomic size in a group, as a function of increasing atomic number—is easy enough to explain: the higher the atomic number, the higher the principal energy level, and the greater the distance from the nucleus to the furthest probability range. On the other hand, the decrease in size across a period (row) is a bit more challenging to comprehend. However, all the elements in a period have their outermost electrons at a particular principal energy level corresponding to the num-
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ELECTRON CLOUD: A term used to
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A subatomic particle that
ber of the period. For instance, the elements on period 5 all have principal energy levels 1 through 5. Yet as one moves along a period from left to right, there is a corresponding increase in the number of protons within the nucleus. This means a stronger positive charge pulling the electrons inward; therefore, the “electron cloud” is drawn ever closer toward the increasingly powerful charge at the center of the atom.
WHERE TO LEARN MORE “Chemical Bond” (Web site). (May 18, 2001). “The Discovery of the Electron” (Web site). (May 18, 2001).
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Electrons
KEY TERMS
CONTINUED
A pattern of probabilities
ber integer, beginning with 1 and moving
regarding the regions that an electron can
upward. The higher the number, the fur-
occupy within an atom in a particular
ther the electron is from the nucleus, and
energy state. The orbital, complex and
hence the greater the energy in the atom.
ORBITAL:
imprecise as it may seem, is a much more accurate depiction of electron behavior
PROTON:
than the model once used, which depicted
in an atom.
A positively charged particle
electrons moving in precisely defined A term describing any
orbits around the nucleus, rather as planets
QUANTIZATION:
move around the Sun.
property that has only certain discrete values, as opposed to values distributed along
PERIODIC TABLE OF ELEMENTS: A
chart that shows the elements arranged in order of atomic number. Vertical columns within the periodic table indicate groups
a continuum. The quantization of an atom means that it does not have a continuous range of energy levels; rather, it can exist
or “families” of elements with similar
only at certain levels of energy from the
chemical characteristics.
ground state through various excited
PHOTON:
A particle of electromagnetic
radiation. PRINCIPAL ENERGY LEVEL: A value
states. RADIATION:
In a general sense, radia-
tion can refer to anything that travels in a
indicating the distance that an electron
stream, whether that stream be composed
may move away from the nucleus of an
of subatomic particles or electromagnetic
atom. This is designated by a whole-num-
waves.
Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: Houghton Mifflin, 1995. Gallant, Roy A. The Ever-Changing Atom. New York: Benchmark Books, 1999. Goldstein, Natalie. The Nature of the Atom. New York: Rosen Publishing Group, 2001. “Life, the Universe, and the Electron” (Web site).
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“A Look Inside the Atom” (Web site). (May 18, 2001). “Valence Shell Electron Pair Repulsion (VSEPR).” (May 18, 2001). “What Are Electron Microscopes?” (Web site). (May 18, 2001). Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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ISOTOPES Isotopes
CONCEPT Isotopes are atoms of the same element that have different masses due to differences in the number of neutrons they contain. Many isotopes are stable, meaning that they are not subject to radioactive decay, but many more are radioactive. The latter, also known as radioisotopes, play a significant role in modern life. Carbon-14, for instance, is used for estimating the age of objects within a relatively recent span of time—up to about 5,000 years—whereas geologists and other scientists use uranium-238 to date minerals of an age on a scale with that of the Earth. Concerns over nuclear power and nuclear weapons testing in the atmosphere have heightened awareness of the dangers posed by certain kinds of radioactive isotopes, which can indeed be hazardous to human life. However, the reality is that people are subjected to considerably more radiation from nonnuclear sources.
THE NUCLEUS AND ELECTRONS. Together with protons in the nucleus
Atoms and Elements
are neutrons, which exert no charge. The discovery of these particles, integral to the formation of isotopes, is discussed below. The nucleus, with a diameter about 1/10,000 that of the atom itself, makes up only a tiny portion of the atom’s volume, but the vast majority of its mass. Thus a change in the mass of a nucleus, as occurs when an isotope is formed, is reflected by a noticeable change in the mass of the atom itself.
The elements are substances that cannot be broken down into other matter by chemical means, and an atom is the fundamental particle in an element. As of 2001, there were 112 known elements, 88 of which occur in nature; the rest were created in laboratories. Due to their high levels of radioactivity, they exist only for extremely short periods of time. Whatever the number of elements—and obviously that number will increase over time, as new elements are synthesized—the same number of basic atomic structures exists in the universe.
Far from the nucleus (in relative terms, of course), at the perimeter of the atom, are the electrons, which have a negative electric charge. Whereas the protons and neutrons have about the same mass, the mass of an electron is less than 0.06% of either a proton or neutron. Nonetheless, electrons play a highly significant role in chemical reactions and chemical bonding. Just as isotopes are the result of changes in the number of neutrons, ions—atoms that are either positive or negative in electric charge—are the result of changes in the number of electrons.
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92
What distinguishes one element from another is the number of protons, subatomic particles with a positive electric charge, in the nucleus, or center, of the atom. The number of protons, whatever it may be, is unique to an element. Thus if an atom has one proton, it is an atom of hydrogen, because hydrogen has an atomic number of 1, as shown on the periodic table of elements. If an atom has 109 protons, on the other hand, it is meitnerium. (Meitnerium, synthesized at a German laboratory in 1982, is the last element on the periodic table to have been assigned a name as of 2001.)
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Unless it loses or gains an electron, thus becoming an ion, an atom is neutral in charge, and it maintains this electric-charge neutrality by having an equal number of protons and electrons. There is, however, no law of the universe stating that an atom must have the same number of neutrons as it does protons and electrons: some do, but this is far from universal, as we shall see.
Isotopes
Neutrons The number of neutrons is variable within an element precisely because they exert no charge, and thus while their addition or removal changes the mass, it does not affect the electric charge of the atom. Therefore, whereas the importance of the proton and the electron is very clear to anyone who studies atomic behavior, neutrons, on the other hand, might seem at first glance as though they are only “along for the ride.” Yet they are all-important to the formation of isotopes. Not surprisingly, given their lack of electric charge, neutrons were the last of the three major subatomic particles to be discovered. English physicist J. J. Thomson (1856-1940) identified the electron in 1897, and another English physicist, Ernest Rutherford (1871-1937), discovered the proton in 1914. Rutherford’s discovery overturned the old “plum pudding” model, whereby atoms were depicted as consisting of electrons floating in a positively charged cloud, rather like raisins in an English plum pudding. As Rutherford showed, the atom must have a nucleus—yet protons alone could not account for the mass of the nucleus. There must be something else at the heart of the atom, and in 1932, yet another English physicist, James Chadwick (1891-1974), identified what it was. Working with radioactive material, he found that a certain type of subatomic particle could penetrate lead. All types of radiation known at the time were stopped by the lead, and therefore Chadwick reasoned that this particle must be neutral in charge. In 1932, he won the Nobel Prize in physics for his discovery of the neutron. NEUTRONS AND NUCLEAR FUSION. Neutrons played a critical role in the
development of the atomic bomb during the 1940s. In nuclear fission, atoms of uranium are bombarded with neutrons. The result is that the uranium nucleus splits in half, releasing huge
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A
MUSHROOM CLOUD RISES AFTER THE DETONATION OF
A HYDROGEN BOMB BY
FRANCE
IN A
1968
TEST.
DEU-
TERIUM IS A CRUCIAL PART OF THE DETONATING DEVICE FOR HYDROGEN BOMBS. (Bettmann/Corbis. Reproduced by per-
mission.)
amounts of energy. As it does so, it emits several extra neutrons, which split more uranium nuclei, creating still more energy and setting off a chain reaction. This explains the destructive power in an atomic bomb, as well as the constructive power—providing energy to homes and businesses—in a nuclear power plant. Whereas the chain reaction in an atomic bomb becomes an uncontrolled explosion, in a nuclear plant, the reaction is slowed and controlled. One of the means used to do this is by the application of “heavy water,” which, as we shall see, is water made with a hydrogen isotope.
Isotopes: The Basics Two atoms may have the same number of protons, and thus be of the same element, yet differ in their number of neutrons. Such atoms are called isotopes, atoms of the same element having different masses. The name comes from the Greek phrase isos topos, meaning “same place”: because they have the same atomic number,
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Isotopes
ENRICO FERMI.
isotopes of the same element occupy the same position on the periodic table. Also called nuclides, isotopes are represented m symbolically as follows: ᎏaᎏS, where S is the symbol of the element, a is the atomic number, and m is the mass number—the sum of protons and neutrons in the atom’s nucleus. For the stable sil93 ver isotope designated as ᎏ4ᎏ7 Ag, for instance, Ag is the element symbol; 47 its atomic number; and 93 the mass number. From this, it is easy to discern that this particular stable isotope has 46 neutrons in its nucleus. Because the atomic number of any element is established, sometimes isotopes are represented simply with the mass number, thus: 93Ag. They may also be designated with a subscript notation indicating the number of neutrons, so that this
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information can be obtained at a glance without having to do the arithmetic. For the silver isotope 93 shown here, this is written as ᎏ4ᎏ7 Ag46. Isotopes can also be indicated by simple nomenclature: for instance, carbon-12 or carbon-13.
Stable and Unstable Isotopes Radioactivity is a term describing a phenomenon whereby certain materials are subject to a form of decay brought about by the emission of highenergy particles or radiation. Forms of particles or energy emitted in radiation include alpha particles (positively charged helium nuclei); beta particles (either electrons or subatomic particles called positrons); or gamma rays, which occupy the highest energy level in the electromagnetic
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radiation emitted by the Sun. Radioactivity will be discussed below, but for the present, the principal concern is with radioactive properties as a distinguishing factor between the two varieties of isotope. Isotopes are either stable or unstable. The unstable variety, known as radioisotopes, are subject to radioactive decay, but in this context, “decay” does not mean what it usually does. A radioisotope does not “rot”; it decays by turning into another isotope of the same element—or even into another element entirely. (For example, uranium-238 decays by emitting alpha particles, ultimately becoming lead-206.) A stable isotope, on the other hand, has already become what it is going to be, and will not experience further decay. Most elements have between two and six stable isotopes. On the other hand, a few elements—for example, technetium—have no stable isotopes. Twenty elements, among them gold, fluorine, sodium, aluminum, and phosphorus, have only one stable isotope each. The element with the most stable isotopes is easy to remember because its name is almost the same as its number of stable isotopes: tin, with 10. As for unstable isotopes, there are over 1,000, some of which exist in nature, but most of which have been created synthetically in laboratories. This number is not fixed; in any case, it is not necessarily important, because many of these highly radioactive isotopes last only for fractions of a second before decaying to form a stable isotope. Yet radioisotopes in general have so many uses, in comparison to stable isotopes, that they are often referred to simply as “isotopes.”
words, the lowest mass number is increasingly high in comparison to the atomic number. For example, uranium has an atomic number of 92, but the lowest mass number for a uranium isotope is not 184, or 92 multiplied by two; it is 218. The ratio of neutrons to protons necessary for a stable isotope creeps upward along the periodic table: tin, with an atomic number of 50, has a stable isotope with a mass number of 120, indicating a 1.4 to 1 ratio of neutrons to protons. For mercury-200, the ratio is 1.5 to 1. The higher the atomic number, by definition, the greater the number of protons in the nucleus. This means that more neutrons are required to “bind” the nucleus together. In fact, all nuclei with 84 protons or more (i.e., starting at polonium and moving along the periodic table) are radioactive, for the simple reason that it is increasingly difficult for the neutrons to withstand the strain of keeping so many protons in place. One can predict the mode of radioactive decay by noting whether the nucleus is neutronrich or neutron-poor. Neutron-rich nuclei undergo beta emission, which decreases the numbers of protons in the nucleus. Neutronpoor nuclei typically undergo positron emission or electron capture, the first of these being more prevalent among the lighter nuclei. Elements with atomic numbers of 84 or greater generally undergo alpha emission, which decreases the numbers of protons and neutrons by two each.
REAL-LIFE A PPLICAT ION S
Understanding Isotopes
Deuterium and Tritium
Before proceeding with a discussion of isotopes and their uses, it is necessary to address a point raised earlier, when it was stated that some atoms do have the same numbers of neutrons and protons, but that this is far from universal. In fact, nuclear stability is in part a function of neutronto-proton ratio.
Only three isotopes are considered significant enough to have names of their own, as opposed to being named after a parent atom (for example, carbon-12, uranium-238). These are protium, deuterium, and tritium, all three isotopes of hydrogen. Protium, or 1H, is hydrogen in its most basic form—one proton, no neutrons—and the name “protium” is only applied when necessary to distinguish it from the other two isotopes. Therefore we will focus primarily on the two others.
Stable nuclei with low atomic numbers (up to about 20) have approximately the same number of neutrons and protons. For example, the most stable and abundant form of carbon is carbon-12, with six protons and six neutrons. Beyond atomic number 20 or so, however, the number of neutrons begins to grow: in other
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Isotopes
Deuterium, designated as 2H, is a stable isotope, whereas tritium—3H—is radioactive. Both, in fact, have chemical symbols (D and T respec-
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tively), just as though they were elements on the periodic table. What makes these two so special? They are, as it were, “the products of a good home”—in other words, their parent atom is the most basic and plentiful element in the universe. Indeed, the vast majority of the universe is hydrogen, along with helium, which is formed by the fusion of hydrogen atoms. If all atoms were numbers, then hydrogen would be 1; but of course, this is more than a metaphor, since its atomic number is indeed 1. Ordinary hydrogen or protium, as noted, consists of a single proton and a single electron, the simplest possible atomic form possible. Its simplicity has made it a model for understanding the atom, and therefore when physicists discovered the existence of two hydrogen atoms that were just a bit more complex, they were intrigued. Just as hydrogen represented the standard against which atoms could be measured, scientists reasoned, deuterium and tritium could offer valuable information regarding stable and unstable isotopes respectively. Furthermore, the pronounced tendency of hydrogen to bond with other substances—it almost never appears by itself on Earth—presented endless opportunities for study regarding hydrogen isotopes in association with other elements. ISOLATION
OF
DEUTERIUM.
Deuterium is sometimes called “heavy hydrogen,” and its nucleus—with one proton and one neutron—is called a deuteron. It was first isolated in 1931 by American chemist Harold Clayton Urey (1893-1981), who was awarded the 1934 Nobel Prize in Chemistry for his discovery. Serving at that time as a professor of chemistry at Columbia University in New York City, Urey started with the assumption that any hydrogen isotopes other than protium must exist in very minute quantities. This assumption, in turn, followed from an awareness that hydrogen’s average atomic mass—measured in atomic mass units—was only slightly higher than 1. There must be, as Urey correctly reasoned, a very small quantity of “heavy hydrogen” on Earth. To separate deuterium, Urey collected a relatively large sample of liquid hydrogen: 4.2 quarts (4 l). Then he allowed the liquid to evaporate very slowly, predicting that the more abundant protium would evaporate more quickly than the
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isotope whose existence he had hypothesized. After all but 0.034 oz (1 ml) of the sample had evaporated, he submitted the remainder to a form of analysis called spectroscopy, adding a burst of energy to the atoms and then analyzing the light spectrum they emitted for evidence of differing varieties of atom. OF
CHARACTERISTICS AND USES DEUTERIUM. Deuterium, with an
atomic mass of 2.014102 amu, is almost exactly twice as heavy as protium, which has an atomic mass of 1.007825. Its melting point, or the temperature at which it changes from a solid to a liquid -426°F (-254°C), is much higher than for protium, which melts at -434°F (-259°C). The same relationship holds for its boiling point, or the temperature at which it changes from a liquid to its normal state on Earth, as a gas: -417°F (-249°C), as compared to -423°F (-253°C) for protium. Deuterium is also much, much less plentiful than protium: protium represents 99.985% of all the hydrogen that occurs naturally, meaning that deuterium accounts for just 0.015%. Often, deuterium is applied as a tracer, an atom or group of atoms whose participation in a chemical, physical, or biological reaction can be easily observed. Radioisotopes are most often used as tracers, precisely because of their radioactive emissions; deuterium, on the other hand, is effective due to its almost 2:1 mass ratio in comparison to protium. In addition, it bonds with other atoms in a fashion slightly different from that of protium, and this contrast makes its presence easier to trace. Its higher boiling and melting points mean that when deuterium is combined with oxygen to form “heavy water” (D2O), the water likewise has higher boiling and melting points than ordinary water. Heavy water is often used in nuclear fission reactors to slow down the fission process, or the splitting of atoms. DEUTERIUM IN NUCLEAR FUSION. Deuterium is also applied in a type of
nuclear reaction much more powerful that fission: fusion, or the joining of atomic nuclei. The Sun produces energy by fusion, a thermonuclear reaction that takes places at temperatures of many millions of degrees Celsius. In solar fusion, it appears that two protium nuclei join to form a single deuteron.
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During the period shortly after World War II, physicists developed a means of duplicating the thermonuclear fusion process. The result was the hydrogen bomb—more properly called a fusion bomb—whose detonating device was a compound of lithium and deuterium called lithium deuteride. Vastly more powerful than the “atomic” (that is, fission) bombs dropped by the United States over Japan in 1945, the hydrogen bomb greatly increased the threat of worldwide nuclear annihilation in the postwar years. Yet the power that could destroy the world also has the potential to provide safe, abundant fusion energy from power plants—a dream that as yet remains unrealized. Among the approaches being attempted by physicists studying nuclear fusion is a process in which two deuterons are fused. The result is a triton, the nucleus of tritium, along with a single proton. The triton and deuteron would then be fused to create a helium nucleus, with a resulting release of vast amounts of energy. TRITIUM. Whereas deuterium has a single neutron, tritium—as its mass number of 3 indicates—has two. And just as deuterium has approximately twice the mass of protium, tritium has about three times the mass, 3.016 amu. As is expected, the thermal properties of tritium are different from those of protium. Again, the melting and boiling points are higher: thus tritium heavy water (T2O) melts at 40°F (4.5°C), as compared with 32°F (0°C) for H2O.
Because it is radioactive, tritium is often described in terms of half-life, the length of time it takes for a substance to diminish to one-half its initial amount. The half-life of tritium is 12.26 years. As it decays, its nucleus emits a low-energy beta particle, and this results in the creation of the helium-3 isotope. Due to the low energy levels involved, the radioactive decay of tritium poses little danger to humans. Like deuterium, tritium is applied in nuclear fusion, though due to its scarcity, it is usually combined with deuterium. Furthermore, tritium decay requires that hydrogen bombs containing the radioisotope be recharged periodically. Also, like deuterium, tritium is an effective tracer. Sometimes it is released in small quantities into groundwater as a means of monitoring subterranean water flow. It is also used as a tracer in biochemical processes.
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Separating Isotopes Isotopes
As noted in the discussion of deuterium, tritium can only be separated from protium due to the differences in mass. The chemical properties of isotopes with the same parent element make them otherwise indistinguishable, and hence purely chemical means cannot be used to separate them. Physicists working on the Manhattan Project, the U.S. effort to develop atomic weaponry during World War II, were faced with the need to separate 235U from 238U. Uranium-238 is far more abundant, but what they wanted was the uranium-235, highly fissionable and thus useful in the processes they were attempting. Their solution was to allow a gaseous uranium compound to diffuse, or separate, the uranium through porous barriers. Because uranium238 was heavier, it tended to move more slowly through the barriers, much like grains of rice getting caught in a sifter. Another means of separating isotopes is by mass spectrometry.
Radioactivity One of the scientists working on the Manhattan Project was Italian physicist Enrico Fermi (19011954), who used radium and beryllium powder to construct a neutron source for making new radioactive materials. Fermi and his associates succeeded in producing radioisotopes of sodium, iron, copper, gold, and numerous other elements. As a result of Fermi’s work, for which he won the 1938 Nobel Prize in Physics, scientists have been able to develop radioactive versions of virtually all elements. Interestingly, the ideas of radioactivity, fission reactions, and fusion reactions collectively represent the realization of a goal sought by the medieval alchemists: the transformation of one element into another. The alchemists, forerunners of chemists, believed they could transform ordinary metals into gold by using various potions—an impossible dream. Yet as noted in the preceding paragraph, among the radioisotopes generated by Fermi’s neutron source was gold. The “catch,” of course, is that this gold was unstable; furthermore, the amount of energy and human mental effort required to generate it far outweighed the monetary value of the gold itself. Radioactivity is, in the modern imagination, typically associated with fallout from nuclear
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war, or with hazards resulting from nuclear power—hazards that, as it turns out, have been greatly exaggerated. Nor is radioactivity always harmful to humans. For instance, with its applications in medicine—as a means of diagnosing and treating thyroid problems, or as a treatment for cancer patients—it can actually save lives. HAZARDS ASSOCIATED WITH RADIOACTIVITY. It is a good thing that
radiation, even the harmful variety known as ionizing radiation, is not fatal in small doses, because every person on Earth is exposed to small quantities of radiation every year. About 82% of this comes from natural sources, and 18% from manmade sources. Of course, some people are at much greater risk of radiation exposure than others: coal miners are exposed to higher levels of the radon-222 isotope present underground, while cigarette smokers ingest much higher levels of radiation than ordinary people, due to the polonium-210, lead-210, and radon-222 isotopes present in the nitrogen fertilizers used to grow tobacco. Nuclear weapons, as most people know, produce a great deal of radioactive pollution. However, atmospheric testing of nuclear armaments has long been banned, and though the isotopes released in such tests are expected to remain in the atmosphere for about a century, they do not constitute a significant health hazard to most Americans. (It should be noted that nations not inclined to abide by international protocols might still conduct atmospheric tests in defiance of the test bans.) Nuclear power plants, despite the great deal of attention they have received from the media and environmentalist groups, do not pose the hazard that has often been claimed: in fact, coal- and oil-burning power plants are responsible for far more radioactive pollution in the United States. This is not to say that nuclear energy poses no dangers, as the disaster at Chernobyl in the former Soviet Union has shown. In April 1986, an accident at a nuclear reactor in what is now the Ukraine killed 31 workers immediately, and ultimately led to the deaths of some 10,000 people. The fact that the radiation was allowed to spread had much to do with the secretive tactics of the Communist government, which attempted to cover up the problem rather than evacuate the area.
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Another danger associated with nuclear power plants is radioactive waste. Spent fuel rods and other waste products from these plants have to be dumped somewhere, but it cannot simply be buried in the ground because it will create a continuing health hazard through the water supply. No fully fail-safe storage system has been developed, and the problem of radioactive waste poses a continuing threat due to the extremely long half-lives of some of the isotopes involved.
Dating Techniques In addition to their uses in applications related to nuclear energy, isotopes play a significant role in dating techniques. The latter may sound like a subject that has something to do with romance, but it does not: dating techniques involve the use of materials, including isotopes, to estimate the age of both organic and inorganic materials. Uranium-238, for instance, has a half-life of 4.47 • 109 years, which is nearly the age of Earth; in fact, uranium-dating techniques have been used to determine the planet’s age, which is estimated at about 4.7 billion years. As noted elsewhere in this volume, potassium-argon dating, which involves the isotopes potassium-40 and argon-40, has been used to date volcanic layers in east Africa. Because the half-life of potassium-40 is 1.3 billion years, this method is useful for dating activities that are distant in the human scale of time, but fairly recent in geological terms. Another dating technique is radiocarbon dating, used for estimating the age of things that were once alive. All living things contain carbon, both in the form of the stable isotope carbon-12 and the radioisotope carbon-14. While a plant or animal is living, there is a certain proportion between the amounts of these two isotopes in the organism’s body, with carbon-12 being far more abundant. When the organism dies, however, it ceases to acquire new carbon, and the carbon-14 present in the body begins to decay into nitrogen-14. The amount of nitrogen-14 that has been formed is thus an indication of the amount of time that has passed since the organism was alive. Because it has a half-life of 5,730 years, carbon-14 is useful for dating activities within the span of human history, though it is not without controversy. Some scientists contend, for instance, that samples may be contaminated by carbon from the surrounding soils, thus affecting ratios and leading to inaccurate dates.
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KEY TERMS ATOM:
The smallest particle of an ele-
ION:
An atom or atoms that has lost or
ment. Atoms are made up of protons, neu-
gained one or more electrons, and thus has
trons, and electrons. Atoms that have the
a net electric charge.
same number of protons—that is, are of the same element—but differ in number of neutrons are known as isotopes.
ISOTOPES: Atoms that have an equal
number of protons, and hence are of the same element, but differ in their number of
An SI unit
neutrons. This results in a difference of
(abbreviated amu), equal to 1.66 • 10-24 g,
mass. Isotopes may be either stable or
for measuring the mass of atoms.
unstable. The latter type is known as a
ATOMIC
MASS
UNIT:
radioisotope. ATOMIC
NUMBER:
The number of
protons in the nucleus of an atom. Since this number is different for each element, elements are listed on the periodic table of elements in order of atomic number. AVERAGE ATOMIC MASS: A figure
used by chemists to specify the mass—in atomic mass units—of the average atom in a large sample.
NEUTRON:
A subatomic particle that
has no electric charge. Neutrons are found at the nucleus of an atom, alongside protons. NUCLEUS: The center of an atom, a
region where protons and neutrons are located, and around which electrons spin. The plural of “nucleus” is nuclei. NUCLIDES: Another name for isotopes.
ELEMENT: A substance made up of only
one kind of atom. Hence an element can-
PERIODIC TABLE OF ELEMENTS: A
not be chemically broken into other sub-
chart that shows the elements arranged in
stances.
order of atomic number.
ELECTRON: Negatively charged parti-
cles in an atom, which spin around the protons and neutrons that make up the atom’s nucleus.
PROTON:
A positively charged particle
in an atom. Protons and neutrons, which together form the nucleus around which electrons spin, have approximately the same mass—a mass that is many times
HALF-LIFE: The length of time it takes a
greater than that of an electron. The num-
substance to diminish to one-half its initial
ber of protons in the nucleus of an atom is
amount.
the atomic number of an element.
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KEY TERMS In a general sense, radia-
about by the emission of high-energy par-
tion can refer to anything that travels in a
ticles or radiation, including alpha parti-
stream, whether that stream be composed
cles, beta particles, or gamma rays.
of subatomic particles or electromagnetic
RADIOISOTOPE:
waves. In a more specific sense, the term
the decay associated with radioactivity. A
relates to the radiation from radioactive
radioisotope is thus an unstable isotope.
RADIATION:
materials, which can be harmful to human beings.
An isotope subject to
TRACER: An atom or group of atoms
whose participation in a chemical, physiA term describing a
cal, or biological reaction can be easily
phenomenon whereby certain materials
observed. Radioisotopes are often used as
are subject to a form of decay brought
tracers.
RADIOACTIVITY:
WHERE TO LEARN MORE “Carbon 14 Dating Calculator” (Web site). (May 15, 2001). Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: Houghton Mifflin, 1995. “Exploring the Table of Isotopes” (Web site). (May 15, 2001).
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CONTINUED
“Isotopes” University of Colorado Department of Physics (Web site). (May 15, 2001). Milne, Lorus Johnson and Margery Milne. Understanding Radioactivity. Illustrated by Bill Hiscock. New York: Atheneum, 1989. Smith, Norman F. Millions and Billions of Years Ago: Dating Our Earth and Its Life. New York: F. Watts, 1993.
Goldstein, Natalie. The Nature of the Atom. New York: Rosen Publishing Group, 2001.
“Stable Isotope Group.” Martek Biosciences (Web site). (May 15, 2001).
“The Isotopes” (Web site). (May 15, 2001).
“Tracking with Isotopes” (Web site). (May 15, 2001).
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I O N S A N D I O N I Z AT I O N
CONCEPT Atoms have no electric charge; if they acquire one, they are called ions. Ions are involved in a form of chemical bonding that produces extremely strong bonds between metals, or between a metal and a nonmetal. These substances, of which table salt is an example, are called ionic compounds. Ionization is the process whereby electrons are removed from an atom or molecule, as well as the process whereby an ionic substance, such as salt, is dissociated into its component ions in a solution such as water. There are several varieties of ionization, including field ionization, which almost everyone has experienced in the form of static electricity. Ion exchange, or the replacement of one ion by another, is used in applications such as water purification, while chemists and physicists use ions in mass spectrometry, to discover mass and structural information concerning atoms and molecules. Another example of ions at work (and a particularly frightening example at that) is ionizing radiation, associated with the radioactive decay following a nuclear explosion.
HOW IT WORKS Ions: Positive and Negative Atoms have no electric charge, because they maintain an equal number of protons (positively charged subatomic particles) and electrons, subatomic particles with a negative charge. In certain situations, however, the atom may lose or gain one or more electrons and acquire a net charge, becoming an ion.
S C I E N C E O F E V E R Y D AY T H I N G S
Aluminum, for instance, has an atomic number of 13, which tells us that an aluminum atom will have 13 protons. Given the fact that every proton has a positive charge, and that most atoms tend to be neutral in charge, this means that there are usually 13 electrons, with a negative charge, present in an atom of aluminum. Yet like all metals, aluminum is capable of forming an ion by losing electrons—in this case, three. CATIONS. Initially, the aluminum atom had a charge of +13 + (–13) = 0; in other words, its charge was neutral due to the equal numbers of protons and electrons. When it becomes an ion, it loses 3 electrons, leaving behind only 10. Now the charge is +13 + (–10) = +3. Thus the remaining aluminum ion is said to have a net positive charge of 3, represented as +3 or 3+. Chemists differ as to whether they represent the plus sign (or the minus sign, in the case of a negatively charged ion) before or after the number. Because both systems of notation are used, these will be applied interchangeably throughout the course of this essay.
When a neutral atom loses one or more electrons, the result is a positively charged ion, or cation (pronounced KAT-ie-un). Cations are usually represented by a superscript number and plus sign: Al+3 or Al3+, for instance, represents the aluminum cation described above. A cation is named after the element of which it is an ion: thus the ion we have described is either called the aluminum ion, or the aluminum cation. ANIONS. When a neutrally charged atom gains electrons, acquiring a negative charge as a result, this type of ion is known as an anion (ANie-un). Anions can be represented symbolically in much the same way as cations: Cl-, for
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A
COMMON FORM OF FIELD IONIZATION IS STATIC ELECTRICITY.
HERE,
A GIRL PLACES HER HAND ON A STATIC ELEC-
TRICITY GENERATOR. (Paul A. Souders/Corbis. Reproduced by permission.)
instance, is an anion of chlorine that forms when it acquires an electron, thus assuming a net charge of –1. Note that the 1 is not represented in the superscript notation, much as people do not write 101. In both cases, the 1 is assumed, but any number higher than 1 is shown. The anion described here is never called a chlorine anion; rather, anions have a special nomenclature. If the anion represents, as was the case here, a single element, it is named by adding the suffix -ide to the name of the original element name: chloride. Such is the case, for instance, with a deadly mixture of carbon and nitrogen (CN-), better known as cyanide. Most often the -ide suffix is used, but in the case of most anions involving more than one element (polyatomic anions), as well as with oxyanions (anions containing oxygen), the rules can get fairly complicated. The general principles for naming anions are as follows: • -ide: A single element with a negative charge. Note, however, that both hydroxide (OH–) and cyanide (CN–) also receive the -ide suffix, even though they involve more than one element. • -ate: An oxyanion with the normal number of oxygen atoms, a number that depends on
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•
•
•
•
the nature of the compound. Examples include oxalate (C2O4- 2) or chlorate (ClO3-). -ite: An oxyanion containing 1 less oxygen than normal. Examples include chlorite (ClO2–). hypo____ite: An oxyanion with 2 less oxygens than normal, but with the normal charge. An example is hypochlorite, or ClO–. per____ate: An oxyanion with 1 more oxygen than normal, but with the normal charge. Perchlorate, or ClO4–, is an example. thio-: An anion in which sulfur has replaced an oxygen. Thus, SO4–2 is called sulfate, whereas S2O3–2 is called thiosulfate.
Elements and Ion Charges As one might expect, given the many differences among families of elements on the periodic table, different elements form ions in different ways. Yet precisely because many of these can be grouped into families, primarily according to the column or group they occupy on the periodic table, it is possible to predict the ways in which they will form ions. The table below provides a few rules of thumb. (All group numbers refer to the North American version of the periodic table;
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THE
DAMAGED REACTOR AT THE
CHERNOBYL
NUCLEAR PLANT IN THE FORMER
SOVIET UNION. THE 1986
ACCIDENT
AT THE PLANT RELEASED IONIZING RADIATION INTO THE ATMOSPHERE. (AP/Wide World Photos. Reproduced by permission.)
see Periodic Table of Elements essay for an explanation of the differences between this and the IUPAC version.) • Alkali metals (Group 1) form 1+ cations. For example, the ion of lithium (Li) is always Li+. • Alkaline earth metals (Group 2) form 2+ cations. Thus, beryllium (Be), for instance, forms a Be2+ ion. • Most Group 3 metals (aluminum, gallium, and indium) form 3+ cations. The cation of aluminum, thus, is designated as Al3+. • Group 6 nonmetals and metalloids (oxygen, sulfur, selenium, and tellurium) form 2– anions. Oxygen, in its normal ionized state, is shown as O2–. • Halogens (Group 7) form 1– anions. Fluorine’s anion would therefore be designated as Fl–. The metals always form positive ions, or cations; indeed, one of the defining characteristics of a metal is that it tends to lose electrons. However, the many elements of the transition metals family form cations with a variety of different charges; for this reason, there is no easy way to classify the ways in which these elements form cations.
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Likewise, it should be evident from the above table that nonmetals, such as oxygen or fluorine, gain electrons to form anions. This, too, is a defining characteristic of this broad grouping of elements. The reasons why these elements— both metals and nonmetals—behave as they do are complex, involving the numbers of valence electrons (the electrons involved in chemical bonding) for each group on the periodic table, as well as the octet rule of chemical bonding, whereby elements typically bond so that each atom has eight valence electrons.
REAL-LIFE A PPLICAT ION S Ionic Bonds, Compounds, and Solids German chemist Richard Abegg (1869-1910), whose work with noble gases led to the discovery of the octet rule, hypothesized that atoms combine with one another because they exchange electrons in such a way that both end up with eight valence electrons. This was an early model of ionic bonding, which results from attractions between ions with opposite electric charges:
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when they bond, these ions “complete” one another. As noted, ionic bonds occur when a metal bonds with a nonmetal, and these bonds are extremely strong. Salt, for instance, is formed by an ionic bond between the metal sodium (a +1 cation) and the nonmetal chlorine, a -1 anion. Thus Na+ joins with Cl- to form NaCl, or table salt. The strength of the bond in salt is reflected by its melting point of 1,472°F (800°C), which is much higher than that of water at 32°F (0°C). In ionic bonding, two ions start out with different charges and end up forming a bond in which both have eight valence electrons. In a covalent bond, as is formed between nonmetals, two atoms start out as most atoms do, with a net charge of zero. Each ends up possessing eight valence electrons, but neither atom “owns” them; rather, they share electrons. Today, chemists understand that most bonds are neither purely ionic nor purely covalent; rather, there is a wide range of hybrids between the two extremes. The degree to which elements attract one another is a function of electronegativity, or the relative ability of an atom to attract valence electrons. IONIC COMPOUNDS AND SOLIDS. Not only is salt formed by an ionic
bond, but it is an ionic compound—that is, a compound containing at least one metal and nonmetal, in which ions are present. Salt is also an example of an ionic solid, or a crystalline solid that contains ions. A crystalline solidis a type of solid in which the constituent parts are arranged in a simple, definite geometric pattern that is repeated in all directions. There are three types of crystalline solid: a molecular solid (for example, sucrose or table sugar), in which the molecules have a neutral electric charge; an atomic solid (a diamond, for instance, which is pure carbon); and an ionic solid. Salt is not formed of ordinary molecules, in the way that water or carbon dioxide are. (Both of these are molecular compounds, though neither is a solid at room temperature.) The internal structure of salt can be depicted as a repeating series of chloride anions and sodium cations packed closely together like oranges in a crate. Actually, it makes more sense to picture them as cantaloupes and oranges packed together, with the larger chloride anions as the cantaloupes and the smaller sodium cations as the oranges.
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If a grocer had to pack these two fruits together in a crate, he would probably put down a layer of cantaloupes, then follow this with a layer of oranges in the spaces between the cantaloupes. This pattern would be repeated as the crate was packed, with the smaller oranges filling the spaces. Much the same is true of the way that chlorine “cantaloupes” and sodium “oranges” are packed together in salt. This close packing of positive and negative charges helps to form a tight bond, and therefore salt must be heated to a high temperature before it will melt. Solid salt does not conduct electricity, but when melted, it makes for an extremely good conductor. When it is solid, the ions are tightly packed, and thus there is no freedom of movement to carry the electric charge along; but when the structure is disturbed by melting, movement of ions is therefore possible.
Ionization and Ionization Energy Water is not a good conductor, although it will certainly allow an electric current to flow through it, which is why it is dangerous to operate an electrical appliance near water. We have already seen that salt becomes a good conductor when melted, but this can also be achieved by dissolving it in water. This is one type of ionization, which can be defined as the process in which one or more electrons are removed from an atom or molecule to create an ion, or the process in which an ionic solid, such as salt, dissociates into its component ions upon being dissolved in a solution. The amount of energy required to achieve ionization is called ionization energy or ionization potential. When an atom is at its normal energy level, it is said to be in a ground state. At that point, electrons occupy their normal orbital patterns. There is always a high degree of attraction between the electron and the positively charged nucleus, where the protons reside. The energy required to move an electron to a higher orbital pattern increases the overall energy of the atom, which is then said to be in an excited state. The excited state of the atom is simply a step along the way toward ionizing it by removing the electron. “Step” is an appropriate metaphor, because electrons do not simply drift along a continuum from one energy level to the next, the way a person walks gently up a ramp. Rather,
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they make discrete steps, like a person climbing a flight of stairs or a ladder. This is one of the key principles of quantum mechanics, a cuttingedge area of physics that also has numerous applications to chemistry. Just as we speak of a sudden change as a “quantum leap,” electrons make quantum jumps from one energy level to another. Due to the high attraction between the electron and the nucleus, the first electron to be removed is on the outermost orbital—that is, one of the valence electrons. This amount of energy is called the first ionization energy. To remove a second electron will be considerably more difficult, because now the atom is a cation, and the positive charge of the protons in the nucleus is greater than the negative charge of the electrons. Hence the second ionization energy, required to remove a second electron, is much higher than the first ionization energy. IONIZATION ENERGIES OF ELEMENTS AND COMPOUNDS. First and
second ionization energy levels for given elements have been established, though it should be noted that hydrogen, because it has only one electron, has only a first ionization energy. In general, the figures for ionization energy increase from left to right along a period or row on the periodic table, and decrease from top to bottom along a column or group. The reason ionization energy increases along a period is that nonmetals, on the right side of the table, have higher ionization energies than metals, which are on the left side. Ionization energies decrease along a group because elements lower on the table have higher atomic numbers, which means more protons and thus more electrons. It is therefore easier for them to give up one of their electrons than it is for an element with a lower atomic number—just as it would be easier for a millionaire to lose a dollar than it would be for a person earning minimum wage. For molecules in compounds, the ionization energies are generally related to those of the elements whose atoms make up the molecule. Just as elements with fewer electrons are typically less inclined to give up one, so are molecules with only a few atoms. Thus the ionization energy of carbon dioxide (CO2), with just three atoms, is relatively high. Conversely, in larger molecules as with larger atoms, there are more electrons to
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give up, and therefore it is easier to separate one of these from the molecules.
Ions and Ionization
A number of methods are used to produce ions for mass spectrometry (discussed below) or other applications. The most common of these methods is electron impact, produced by bombarding a sample of gas with a stream of fast-moving electrons. Though easier than some other methods, this one is not particularly efficient, because it supplies more energy than is needed to remove the electron. An electron gun, usually a heated tungsten wire, produces huge amounts of electrons, which are then fired at the gas. Because electrons are so small, this is rather like using a rapid-fire machine gun to kill mosquitoes: it is almost inevitable that some of the mosquitoes will get hit, but plenty of the rounds will fire into the air without hitting a single insect. IONIZATION
PROCESSES.
Another ionization process is field ionization, in which ionization is produced by subjecting a molecule to a very intense electric field. Field ionization occurs in daily life, when static electricity builds up on a dry day: the small spark that jumps from the tip of your finger when you touch a doorknob is actually a stream of electrons. In field ionization as applied in laboratories, fine, sharpened wires are used. This process is much more efficient than electron impact ionization, employing far less energy in relation to that required to remove the electrons. Because it deposits less energy into the ion source, the parent ion, it is often used when it is necessary not to damage the ionized specimen. Chemical ionization employs a method similar to that of electron impact ionization, except that instead of electrons, a beam of positively charged molecular ions is used to bombard and ionize the sample. The ions used in this bombardment are typically small molecules, such as those in methane, propane, or ammonia. Nonetheless, the molecular ion is much larger than an electron, and these collisions are highly reactive, yet they tend to be much more efficient than electron impact ionization. Many mass spectrometers use a source capable of both electron impact and chemical ionization. Ionization can also be supplied by electromagnetic radiation, with wavelengths shorter than those of visible light—that is, ultraviolet light, x rays, or gamma rays. This process, called photoionization, can ionize small molecules,
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such as those of oxygen (O2). Photoionization occurs in the upper atmosphere, where ultraviolet radiation from the Sun causes ionization of oxygen and nitrogen (N2) in their molecular forms. In addition to these other ionization processes, ionization can be produced in a fairly simple way by subjecting atoms or molecules to the heat from a flame. The temperatures, however, must be several thousand degrees to be effective, and therefore specialized flames, such as an electrical arc, spark, or plasma, are typically used. MASS SPECTROMETRY. As not-ed, a number of the ionization methods described above are used in mass spectrometry, a means of obtaining structure and mass information concerning atoms or molecules. In mass spectrometry, ionized particles are accelerated in a curved path through an electromagnetic field. The field will tend to deflect lighter particles from the curve more easily than heavier ones. By the time the particles reach the detector, which measures the ratio between mass and charge, the ions will have been separated into groups according to their respective mass-to-charge ratios.
When molecules are subjected to mass spectrometry, fragmentation occurs. Each molecule breaks apart in a characteristic fashion, and this makes it possible for a skilled observer to interpret the mass spectrum of the particles generated. Mass spectrometry is used to establish values for ionization energy, as well as to ascertain the mass of substances when that mass is not known. It can also be used to determine the chemical makeup of a substance. Mass spectrometry is applied by chemists, not only in pure research, but in applications within the environmental, pharmaceutical, and forensic (crime-solving) fields. Chemists for petroleum companies use it to analyze hydrocarbons, as do scientists working in areas that require flavor and fragrance analysis.
Ion Exchange The process of replacing one ion with another of a similar charge is called ion exchange. When an ionic solution—for example, salt dissolved in water—is placed in contact with a solid containing ions that are only weakly bonded within its crystalline structure, ion exchange is possible. Throughout the exchange, electric neutrality is maintained: in other words, the total number of
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positive charges in the solid and solution equals the total number of negative charges. The only thing that changes is the type of ion in the solid and in the solution. There are natural ion exchangers, such as zeolites, a class of minerals that contain aluminum, silicon, oxygen, and a loosely held cation of an alkali metal or alkaline earth metal (Group 1 and Group 2 of the periodic table, respectively). When the zeolite is placed in an ionic solution, exchange occurs between the loosely held zeolite cation and the dissolved cation. In synthetic ion exchangers, used in laboratories, a charged group is attached to a rigid structural framework. One end of the charged group is permanently fixed to the frame, while a positively or negatively charged portion kept loose at the other end attracts other ions in the solution. RESINS AND SEMIPERMEABLE MEMBRANES. Anion resins and cation
resins are both solid materials, but in an anion resin, the positive ions are tightly bonded, while the negative ions are loosely bonded. The negative ions will exchange with negative ions in the solution. The reverse is true for a cation resin, in which the negative ions are tightly bonded, while the loosely bonded positive ions exchange with positive ions in the solution. These resins have applications in scientific studies, where they are used to isolate and collect various types of ionic substances. They are also used to purify water, by removing all ions. Semipermeable membranes are natural or synthetic materials with the ability to selectively permit or retard the passage of charged and uncharged molecules through their surfaces. In the cells of living things, semipermeable membranes regulate the balance between sodium and potassium cations. Kidney dialysis, which removes harmful wastes from the urine of patients with kidneys that do not function properly, is an example of the use of semipermeable membranes to purify large ionic molecules. When seawater is purified by removal of salt, or otherwise unsafe water is freed of its impurities, the water is passed through a semipermeable membrane in a process known as reverse osmosis.
Ionizing Radiation We have observed a number of ways in which ionization is useful, and indeed part of nature. But ionizing radiation, which causes ionization
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Ions and Ionization
KEY TERMS The negatively charged ion that results when an atom gains one or more electrons. An anion (pronounced “AN-ieun”) of a single element is named by adding the suffix -ide to the name of the original element—hence, “chloride.” Other rules apply for more complex anions. ANION:
The positively charged ion that results when an atom loses one or more electrons. A cation (pronounced KAT-ieun) is named after the element of which it is an ion and, thus, is called, for instance, the aluminum ion or the aluminum cation. CATION:
CRYSTALLINE SOLID: A type of solid
in which the constituent parts have a simple and definite geometric arrangement that is repeated in all directions. Types of crystalline solids include atomic solids, ionic solids, and molecular solids. ELECTRON: Negatively charged parti-
cles in an atom. The number of electrons and protons in an atom is the same, thus canceling out one another. When an atom loses or gains one or more electrons, however—thus becoming an ion—it acquires a net electric charge. A term describing the characteristics of an atom that has acquired excess energy. EXCITED STATE:
A term describing the characteristics of an atom that is at its ordinary energy level. GROUND STATE:
An atom or group of atoms that has lost or gained one or more electrons, and thus has a net electric charge. There are two types of ions: anions and cations. ION:
The process of replacing one ion with another of similar charge. ION
EXCHANGE:
IONIC BONDING:
A form of chemical
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bonding that results from attractions between ions with opposite electric charges. IONIC
COMPOUND:
A compound
(two or more elements chemically bonded to one another), in which ions are present. Ionic compounds contain at least one metal and nonmetal, joined by an ionic bond. IONIC SOLID:
A form of crystalline
solid that contains ions. When mixed with a solvent such as water, ions from table salt—an example of an ionic solid—move freely throughout the solution, making it possible to conduct an electric current. IONIZATION:
A term that refers to two
different processes. In one kind of ionization, one or more electrons are removed from an atom or molecule to create an ion. A second kind of ionization occurs when an ionic solid, such as salt dissociates into its component ions upon being dissolved in a solution. IONIZATION ENERGY: The amount of
energy required to achieve ionization in which one or more electrons are removed from an atom or molecule. Another term for this is ionization potential. NUCLEUS: The center of an atom, a
region where protons and neutrons are located, and around which electrons spin. ORBITAL:
A pattern of probabilities
regarding the position of an electron for an atom in a particular energy state. OXYANION:
An
anion
containing
oxygen. POLYATOMIC
ANION:
An
anion
involving more than one element. PROTON:
A positively charged particle
in an atom.
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in the substance through which it passes, is extremely harmful. It should be noted that not all radiation is unhealthy: after all, Earth receives heat and light from the Sun by means of radiation. Ionizing radiation, on the other hand, is the kind of radiation associated with radioactive fallout from nuclear warfare, and with nuclear disasters such as the one at Chernobyl in the former Soviet Union in 1986. Whereas thermal radiation from the Sun can be harmful if one is exposed to it for too long, ionizing radiation is much more so, and involves much greater quantities of energy deposited per area per second. In ionizing radiation, an ionizing particle knocks an electron off an atom or molecule in a living system (that is, human, animal, or plant), freeing an electron. The molecule left behind becomes a free radical, a highly reactive group of atoms with unpaired electrons. These can spawn other free radicals, inducing chemical changes that can cause cancer and genetic damage. WHERE TO LEARN MORE “The Atom.” Thinkquest (Web site). (May 18, 2001).
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“Explore the Atom” CERN—European Organization for Nuclear Research (Web site). (May 18, 2001). Gallant, Roy A. The Ever-Changing Atom. New York: Benchmark Books, 1999. “Ion Exchange Chromatography” (Web site). (June 1, 2001). “Just After Big Bang, Colliding Gold Ions Exploded.” UniSci: Daily University Science News (Web site). (June 1, 2001). “A Look Inside the Atom” (Web site). (May 18, 2001). “Portrait of the Atom” (Web site). (May 18, 2001). “A Science Odyssey: You Try It: Atom Builder.” PBS—Public Broadcasting System (Web site). (May 18, 2001). “Table of Inorganic Ions and Rules for Naming Inorganic Compounds.” Augustana College (Web site.) (June 1, 2001). “Virtual Chemistry Lab.” University of Oxford Department of Chemistry (Web site). (June 1, 2001).
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Molecules
CONCEPT Prior to the nineteenth century, chemists pursued science simply by taking measurements, before and after a chemical reaction, of the substances involved. This was an external approach, rather like a person reaching into a box and feeling of the contents without actually being able to see them. With the evolution of atomic theory, chemistry took on much greater definition: for the first time, chemists understood that the materials with which they worked were interacting on a level much too small to see. The effects, of course, could be witnessed, but the activities themselves involved the interactions of atoms in molecules. Just as an atom is the most basic particle of an element, a molecule is the basic particle of a compound. Whereas there are only about 90 elements that occur in nature, many millions of compounds are formed naturally or artificially. Hence the study of the molecule is at least as important to the pursuit of modern chemistry as the study of the atom. Among the most important subjects in chemistry are the ways in which atoms join to form molecules—not just the numbers and types of atoms involved, but the shape that they form together in the molecular structure.
HOW IT WORKS Introduction to the Molecule Sucrose or common table sugar, of course, is grainy and sweet, yet it is made of three elements that share none of those characteristics. The formula for sugar is C12H22O1 1, meaning that each
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MOLECULES
molecule is formed by the joining of 12 carbon atoms, 22 hydrogens, and 11 atoms of oxygen. Coal is nothing like sugar—for one thing, it is as black as sugar is white, yet it is almost pure carbon. Carbon, at least, is a solid at room temperature, like sugar. The other two components of sugar, on the other hand, are gases, and highly flammable ones at that. The question of how elements react to one another, producing compounds that are altogether unlike the constituent parts, is one of the most fascinating aspects of chemistry and, indeed, of science in general. Combined in other ways and in other proportions, the elements in sugar could become water (H2O), carbon dioxide (CO2), or even petroleum, which is formed by the joining of carbon and hydrogen. Two different compounds of hydrogen and oxygen serve to further illustrate the curiosities involved in the study of molecules. As noted, hydrogen and oxygen are both flammable, yet when they form a molecule of water, they can be used to extinguish most fires. On the other hand, when two hydrogens join with two oxygens to form a molecule of hydrogen peroxide (H2O2), the resulting compound is quite different from water. In relatively high concentrations, hydrogen peroxide can burn the skin, and in still higher concentrations, it is used as rocket fuel. And whereas water is essential to life, pure hydrogen peroxide is highly toxic. THE QUESTION OF MOLECULAR STRUCTURE. It is not enough, how-
ever, to know that a certain combination of atoms forms a certain molecule, because molecules may have identical formulas and yet be quite different substances. In English, for
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Molecules
MODELS
OF VARIOUS ELEMENTS.
instance, there is the word “rose.” Simply seeing the word, however, does not tell us whether it is a noun, referring to a flower, or a verb, as in “she rose through the ranks.” Similarly, the formula of a compound does not necessarily tell what it is, and this can be crucial. For instance, the formula C2H6O identifies two very different substances. One of these is ethyl alcohol, the type of alcohol found in beer and wine. Note that the elements involved are the same as those in sugar, though the proportions are different: in fact, some aspects of the body’s reaction to ethyl alcohol are not so different from its response to sugar, since both lead to unhealthy weight gain. In reasonable small quantities, of course, ethyl alcohol is not toxic, or at least only mildly so; yet methyl ether—which has an identical formula—is a toxin. But the distinction is not simply an external one, as simple as the difference between beer and a substance such as methyl ether, sometimes used as a refrigerant. To put it another way, the external difference reflects an internal disparity: though the formulas for ethyl alcohol and methyl ether are the same, the arrangements of the atoms within the molecules of each are not. The substances are therefore said to be isomers.
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In fact C2H6O is just one of three types of formula for a compound: an empirical formula, or one that shows the smallest possible wholenumber ratio of the atoms involved. By contrast, a molecular formula—a formula that indicates the types and numbers of atoms involved— shows the actual proportions of atoms. If the formula for glucose, a type of sugar (C6H12O6 ), were rendered in empirical form, it would be CH2O, which would reveal less about its actual structure. Most revealing of all, however, is a structural formula—a diagram that shows how the atoms are bonded together, complete with lines representing covalent bonds. (Structural formulas such as those that apply the Couper or Lewis systems are discussed in the Chemical Bonding essay, which also examines the subject of covalent bonds.) Chemists involved in the area of stereochemistry, discussed below, attempt to develop three-dimensional models to show how atoms are arranged in a molecule. Such models for ethyl alcohol and methyl ether, for instance, would reveal that they are quite different, much as the two definitions of rose mentioned above illustrate the two distinctly different meanings. Because stereochemistry is a highly involved and complex subject, it can only be touched upon very briefly in this essay; nonetheless, an under-
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Molecules
TWO
HIGH SCHOOL STUDENTS POSE WITH A MODEL OF A
standing of a molecule’s actual shape is critical to the work of a professional chemist. MOLECULES AND COMPOUNDS. A molecule can be most properly
defined as a group of atoms joined in a specific structure. A compound, on the other hand, is a substance made up of more than one type of atom—in other words, more than one type of element. Not all compounds are composed of discrete molecules, however. For instance, table salt (NaCl) is an ionic compound formed by endlessly repeating clusters of sodium and chlorine that are not, in the strictest sense of the word, molecules. Salt is an example of a crystalline solid, or a solid in which the constituent parts are arranged in a simple, definite geometric pattern repeated in all directions. There are three kinds of crystalline solids, only one of which has a truly molecular structure. In an ionic solid such as table salt, ions (atoms, or groups of atoms, with an electric charge) bond a metal to a nonmetal— in this case, the metal sodium and the nonmetal chlorine. Another type of crystalline solid, an atomic solid, is formed by atoms of one element bonding to one another. A diamond, made of pure carbon, is an example. Only the third type of crystalline solid is truly molecular in structure:
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DNA
MOLECULE. (James A. Sugar/Corbis. Reproduced by permission.)
a molecular solid—sugar, for example—is one in which the molecules have a neutral electric charge. Not all solids are crystalline; nor, of course, are all compounds solids: water, obviously, is a liquid at room temperature, while carbon dioxide is a gas. Nor is every molecule composed of more than one element. Oxygen, for instance, is ordinarily diatomic, meaning that even in its elemental form, it is composed of two atoms that join in an O2 molecule. It is obvious, then, that the defining of molecules is more complex than it seems. One can safely say, however, that the vast majority of compounds are made up of molecules in which atoms are arranged in a definite structure. In the essay that follows, we will discuss the ways atoms join to form molecules, a subject explored in more depth within the Chemical Bonding essay. (In addition, compounds themselves are examined in somewhat more detail within the Compounds essay.) We will also briefly examine how molecules bond to other molecules in the formation of solids and liquids. First, however, a little history is in order: as noted in the introduction to this essay, chemists did not always possess a clear understanding of the nature of a molecule.
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A Brief History of the Molecule In ancient and medieval times, early chemists— some of whom subscribed to an unscientific system known as alchemy—believed that one element could be transformed into another. Thus many an alchemist devoted an entire career to the vain pursuit of turning lead into gold. The alchemists were at least partially right, however: though one element cannot be transformed into another (except by nuclear fusion), it is possible to change the nature of a compound by altering the relations of the elements within it. Modern understanding of the elements began to emerge in the seventeenth century, but the true turning point came late in the eighteenth century. It was then that French chemist Antoine Lavoisier (1743-1794) defined an element as a simple substance that could not be separated into simpler substances by chemical means. Around the same time, another French chemist, JosephLouis Proust (1754-1826) stated that a given compound always contained the same proportions of mass between elements. The ideas of Lavoisier and Proust were revolutionary at the time, and these concepts pointed to a substructure, invisible to the naked eye, underlying all matter. In 1803, English chemist John Dalton (17661844) defined that substructure by introducing the idea that the material world is composed of tiny particles called atoms. Despite the enormous leap forward that his work afforded to chemists, Dalton failed to recognize that matter is not made simply of atoms. Water, for instance, is not just a collection of “water atoms”: clearly, there is some sort of intermediary structure in which atoms are combined. This is the molecule, a concept introduced by Italian physicist Amedeo Avogadro (1776-1856). AVOGADRO AND THE IDEA OF THE MOLECULE. French chemist and
physicist Joseph Gay-Lussac (1778-1850) had announced in 1809 that gases combine to form compounds in simple proportions by volume. As Gay-Lussac explained, the ratio, by weight, between hydrogen and oxygen in water is eight to one. The fact that this ratio was so “clean,” involving whole numbers rather than decimals, intrigued Avogadro, who in 1811 proposed that equal volumes of gases have the same number of particles if measured at the same temperature
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and pressure. This, in turn, led him to the hypothesis that water is not composed simply of atoms, but of molecules in which hydrogen and oxygen combine. For several decades, however, chemists largely ignored Avogadro’s idea of the molecule. Only in 1860, four years after his death, was the concept resurrected by Italian chemist Stanislao Cannizzaro (1826-1910). Of course, the understanding of the molecule has progressed enormously in the years since then, and much of this progress is an outcome of advances in the study of subatomic structure. Only in the early twentieth century did physicists finally identify the electron, the negatively charged subatomic particle critical to the bonding of atoms.
REAL-LIFE A PPLICAT I O N S Molecular Mass Just as the atoms of elements have a definite mass, so do molecules—a mass equal to that of the combined atoms in the molecule. The figures for the atomic mass of all elements are established, and can be found on the periodic table; therefore, when one knows the mass of a hydrogen atom and an oxygen atom, as well as the fact that there are two hydrogens and one oxygen in a molecule of water, it is easy to calculate the mass of a water molecule. Individual molecules cannot easily be studied; therefore, the mass of molecules is compared by use of a unit known as the mole. The mole contains 6.022137 ⫻ 1023 molecules, a figure known as Avogadro’s number, in honor of the man who introduced the concept of the molecule. When necessary, it is possible today to study individual molecules, or even atoms and subatomic particles, using techniques such as mass spectrometry.
Bonding Within Molecules Note that the mass of an atom in a molecule does not change; nor, indeed, do the identities of the individual atoms. An oxygen atom in water is the same oxygen atom in sugar, or in any number of other compounds. With regard to compounds, it should be noted that these are not the same thing as a mixture, or a solution. Sugar or salt can be dissolved in water at the appropriate tempera-
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tures, but the resulting solution is not a compound; the substances are joined physically, but they are not chemically bonded. Chemical bonding is the joining, through electromagnetic force, of atoms representing different elements. Each atom possesses a certain valency, which determines its ability to bond with atoms of other elements. Valency, in turn, is governed by the configuration of valence electrons at the highest energy level (the shell) of the atom. While studying noble gases, noted for their tendency not to bond, German chemist Richard Abegg (1869-1910) discovered that these gases always have eight valence electrons. This led to the formation of the octet rule: most elements (with the exception of hydrogen and a few others) are inclined to bond in such a way that they end up with eight valence electrons. When a metal bonds to a nonmetal, this is known as ionic bonding, which results from attractions between ions with opposite electric charges. In ionic bonding, two ions start out with different charges and form a bond in which both have eight valence electrons. Nonmetals, however, tend to form covalent bonds. In a covalent bond, two atoms start out as most atoms do, with a net charge of zero. Each ends up possessing eight valence electrons, but neither atom “owns” them; rather, they share electrons. ELECTRONEGATIVITY. Not all elements bond covalently in the same way. Each has a certain value of electronegativity—the relative ability of an atom to attract valence electrons. Elements capable of bonding are assigned an electronegativity value ranging from a minimum of 0.7 for cesium to a maximum of 4.0 for fluorine. The greater the electronegativity value, the greater the tendency of an element to attract valence electrons.
When substances of differing electronegativity values form a covalent bond, this is described as polar covalent bonding. Water is an example of a molecule with a polar covalent bond. Because oxygen has a much higher electronegativity (3.5) than hydrogen (2.1), the electrons tend to gravitate toward the oxygen atom. By contrast, molecules of petroleum, a combination of carbon and hydrogen, tend to be nonpolar, because carbon (2.5) and hydrogen have very similar electronegativity values.
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A knowledge of electronegativity values can be used to make predictions concerning bond polarities. Bonds that involve atoms whose electronegativities differ by more than 2 units are substantially ionic, whereas bonds between atoms whose electronegativities differ by less than 2 units are polar covalent. If the atoms have the same or similar electronegativity values, the bond is covalent.
Molecules
Attractions Between Molecules The energy required to pull apart a molecule is known as bond energy. Covalent bonds that involve hydrogen are among the weakest bonds between atoms, and hence it is relatively easy to separate water into its constituent parts, hydrogen and oxygen. (This is sometimes done by electrolysis, which involves the use of an electric current to disperse atoms.) Double and triple covalent bonds are stronger, but strongest of all is an ionic bond. The strength of the bond energy in salt, for instance, is reflected by its melting point of 1,472°F (800°C), much higher than that of water, at 32°F (0°C). Bond energy relates to the attraction between atoms in a molecule, but in considering various substances, it is also important to recognize the varieties of bonds between molecules— that is, intermolecular bonding. For example, the polar quality of a water molecule gives it a great attraction for ions, and thus ionic substances such as salt and any number of minerals dissolve easily in water. On the other hand, we have seen that petroleum is essentially nonpolar, and therefore, an oil molecule offers no electric charge to bond it with a water molecule. For this reason, oil and water do not mix. The bonding between water molecules is known as a dipole-dipole attraction. This type of intermolecular bond can be fairly strong in the liquid or solid state, though it is only about 1% as strong as a covalent bond within a molecule. When a substance containing molecules joined by dipole-dipole attraction is heated to become a gas, the molecules spread far apart, and these bonds become very weak. On the other hand, when hydrogen bonds to an atom with a high value of electronegativity (fluorine, for example), the dipole-dipole attraction between these molecules is particularly strong. This is known as hydrogen bonding.
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Molecules
KEY TERMS AVOGADRO’S
A figure,
NUMBER:
A chemical
named after Italian physicist Amedeo Avo-
formula that shows the smallest possible
gadro (1776-1856), equal to 6.022137 x
whole-number ratio of the atoms involved.
1023.
Compare with molecular formula and
Avogadro’s number indicates the
number of molecules in a mole.
structural formula.
BOND ENERGY: The energy required
HYDROGEN
to pull apart the atoms in a chemical bond.
dipole-dipole attraction between mole-
The joining,
cules formed of hydrogen along with an
CHEMICAL BONDING:
through electromagnetic force, of atoms
COMPOUND:
A substance made up of
atoms of more than one element. These atoms are usually joined in molecules. COVALENT
BONDING:
bonding that exists between molecules. This is not to be confused with chemical bonding, the bonding of atoms within a molecule.
share valence electrons.
ION:
An atom or group of atoms that has
lost or gained one or more electrons, and thus has a net electric charge.
A term describing an ele-
ment that exists as molecules composed of two atoms. DIPOLE-DIPOLE
A kind of
element having a high electronegativity.
A type of
chemical bonding in which two atoms
DIATOMIC:
BONDING:
INTERMOLECULAR BONDING: The
representing different elements.
IONIC BONDING:
bonding
A form of chemical
resulting
from
attractions
between ions with opposite electric ATTRACTION:
A
form of intermolecular bonding between molecules formed by a polar covalent bond.
charges. ISOMERS: Substances having the same
chemical formula, but which are chemically dissimilar due to differences in the
ELECTRON: A negatively charged parti-
arrangement of atoms.
cle in an atom.
LONDON DISPERSION FORCES: A
The relative
term describing the weak intermolecular
ability of an atom to attract valence
bond between molecules that are not
electrons.
formed by a polar covalent bond.
ELECTRONEGATIVITY:
Even a nonpolar molecule, however, must have some attraction to other nonpolar molecules. The same is true of helium and the other noble gases, which are highly nonattractive but can be turned into liquids or even solids at extremely low temperatures. The type of intermolecular attraction that exists in such a situation is described by the term London dispersion forces. The name has nothing to do with the capital of England: it is a reference to German-
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VOLUME 1: REAL-LIFE CHEMISTRY
American physicist Fritz Wolfgang London (1900-1954), who in the 1920s studied the molecule from the standpoint of quantum mechanics. Because electrons are not uniformly distributed around the nucleus of an atom at every possible moment, instantaneous dipoles are formed when most of the electrons happen to be on one side of an atom. Of course, this only happens for an infinitesimal fraction of time, but it serves to create a weak attraction. Only at very low tem-
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Molecules
KEY TERMS
CONTINUED
The SI fundamental unit for
POLAR COVALENT BONDING: The
“amount of substance.” A mole is, general-
type of chemical bonding between atoms
ly speaking, Avogadro’s number of mole-
that have differing values of electronegativ-
cules; however, in the more precise SI defi-
ity. Water molecules are an example of a
nition, a mole is equal to the number of
polar covalent bond.
MOLE:
carbon atoms in 12.01 g of carbon. MOLECULAR FORMULA: A chemical
formula that indicates the types and num-
SHELL:
The orbital pattern of the
valence electrons at the outside of an atom.
bers of atoms involved, showing the actual
STEREOCHEMISTRY:
proportions of atoms in a molecule. Com-
chemistry devoted to the three-dimension-
pare with empirical formula and structural
al arrangement of atoms in a molecule.
The area of
formula. MOLECULAR SOLID: A form of crys-
talline solid—a solid in which the constituent parts have a simple and definite geometric arrangement repeated in all directions—in which the molecules have a
STRUCTURAL FORMULA: A diagram
that shows how the atoms are bonded together, complete with lines representing covalent bonds. Compare with empirical formula and molecular formula.
neutral electric charge. Table sugar
VALENCE
(sucrose) is an example.
that occupy the highest energy levels in an
MOLECULE: A group of atoms, usually
atom. These are the only electrons involved
but not always representing more than one
in chemical bonding.
element,
joined
in
a
structure.
Compounds are typically made up of molecules.
ELECTRONS:
Electrons
VALENCY: The property of the atom of
one element that determines its ability to bond with atoms of other elements.
OCTET RULE: A term describing the
distribution of valence electrons that takes
VSEPR
place in chemical bonding for most ele-
TRON PAIR REPULSION) MODEL: A
ments, which end up with eight valence
means of representing the three-dimen-
electrons.
sional structure of atoms in a molecule.
peratures do London dispersion forces become strong enough to result in the formation of a solid. (Thus, for instance, oil and rubbing alcohol freeze only at low temperatures.)
Molecular Structure The Couper system and Lewis structures, discussed in the Chemical Bonding essay, provide a means of representing the atoms that make up a molecule. Though Lewis structures show the dis-
S C I E N C E O F E V E R Y D AY T H I N G S
(VALENCE
SHELL
ELEC-
tribution of valence electrons, they do not represent the three-dimensional structure of the molecule. As noted earlier in this essay, the structure is highly important, because two compounds may be isomers, meaning that they have the same proportions of the same elements, yet are different substances. Stereochemistry is the realm of chemistry devoted to the three-dimensional arrangement of atoms in a molecule. One of the most impor-
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tant methods used is known as the VSEPR model (valence shell electron pair repulsion). In bonding, elements always share at least one pair of electrons, and the VSEPR model begins with the assumption that the electron pairs must be as far apart as possible to minimize their repulsion, since like charges repel. VSEPR structures can be very complex, and the rules governing them will not be discussed here, but a few examples can be given. If there are just two electron pairs in a bond between three atoms, the structure of a VSEPR model is like that of a stick speared through a ball, with two other balls attached at each end. The “ball” is an atom, and the “stick” represents the electron pairs. In water, there are four electron pairs, but still only three atoms and two bonds. In order to keep the electron pairs as far apart as possible, the angle between the two hydrogen atoms attached to the oxygen is 109.5°.
116
Elements of Chemistry for Beginning Life Science Students. Merced, CA: Bioventure Associates, 1990. Burnie, David. Microlife. New York: DK Publishing, 1997. “Common Molecules” (Web site). (June 2, 2001). Cooper, Christopher. Matter. New York: DK Publishing, 2000. Mebane, Robert C. and Thomas R. Rybolt. Adventures with Atoms and Molecules, Book V: Chemistry Experiments for Young People. Springfield, NJ: Enslow Publishers, 1995. “The Molecules of Life” (Web site). (June 2, 2001). “Molecules of the Month.” University of Oxford (Web site). (June 2, 2001). “Molecules with Silly or Unusual Names” (Web site). (June 2, 2001).
WHERE TO LEARN MORE
“Theory of Atoms in Molecules” (Web site). (June 2, 2001).
Basmajian, Ronald; Thomas Rodella; and Allen E. Breed. Through the Molecular Maze: A Helpful Guide to the
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
VOLUME 1: REAL-LIFE CHEMISTRY
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S C I E N C E O F E V E R Y D AY T H I N G S real-life chemistry
ELEMENTS ELEMENTS P E R I O D I C TA B L E O F E L E M E N T S FA M I L I E S O F E L E M E N T S
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Elements
CONCEPT The elements are at the heart of chemistry, and indeed they are at the heart of life as well. Every physical substance encountered in daily life is either an element, or more likely a compound containing more than one element. There are millions of compounds, but only about 100 elements, of which only 88 occur naturally on Earth. How can such vast complexity be created from such a small amount of elements? Consider the English alphabet, with just 26 letters, with which an almost infinite number of things can be said or written. Even more is possible with the elements, which greatly outnumber the letters of the alphabet. Despite the relatively great quantity of elements, however, just two make up almost the entire mass of the universe—and these two are far from abundant on Earth. A very small number of elements, in fact, are essential to life on this planet, and to the existence of human beings.
HOW IT WORKS The Focal Point of Chemistry Like physics, chemistry is concerned with basic, underlying processes that explain how the universe works. Indeed, these two sciences, along with astronomy and a few specialized fields, are the only ones that address phenomena both on the Earth and in the universe as a whole. By contrast, unless or until life on another planet is discovered, biology has little concern with existence beyond Earth’s atmosphere, except inasmuch as the processes and properties in outer space affect astronauts.
S C I E N C E O F E V E R Y D AY T H I N G S
ELEMENTS
While physics and chemistry address many of the same fundamental issues, they do so in very different ways. To make a gross generalization—subject to numerous exceptions, but nonetheless useful in clarifying the basic difference between the two sciences—physicists are concerned with external phenomena, and chemists with internal ones. For instance, when physicists and chemists study the interactions between atoms, unless physicists focus on some specialized area of atomic research, they tend to treat all atoms as more or less the same. Chemists, on the other hand, can never treat atoms as though they are just undifferentiated particles colliding in space. The difference in structure between one kind of atom and another, in fact, is the starting-point of chemical study.
Structure of the Atom An atom is the fundamental particle in a chemical element, or a substance that cannot be broken down into another substance by chemical means. Clustered at the center, or nucleus, of the atom are protons, which have a positive electric charge, and neutrons, which possess no charge. Spinning around the nucleus are electrons, which are negatively charged. The vast majority of the atom’s mass is made up by the protons and neutrons, which have approximately the same mass, whereas that of the electron is much smaller. The mass of an electron is about 1/1836 that of proton, and 1/1839 that of a neutron. It should be noted that the nucleus, though it constitutes most of the atom’s mass, is only a tiny portion of the atom’s volume. If the nucleus were the size of a grape, in fact, the electrons would, on average, be located about a mile away.
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Elements
THE
MOST COMMON AND/OR IMPORTANT CHEMICAL ELEMENTS.
Isotopes Atoms of the same element always have the same number of protons, and since this figure is unique for a given element, each element is
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assigned an atomic number equal to the number of protons in its nucleus. Two atoms may have the same number of protons, and thus be of the same element, yet differ in their number of neutrons. Such atoms are called isotopes.
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Isotopes are generally represented as follows: where S is the symbol of the element, a is the atomic number, and m is the mass number—the sum of protons and neutrons in the atom’s nucleus. For the stable silver isotope designated as 93 ᎏᎏAg, for instance, Ag is the element symbol (dis47 cussed below); 47 its atomic number; and 93 the mass number. From this, it is easy to discern that this particular stable isotope has 46 neutrons in its nucleus. m ᎏᎏS, a
Because the atomic number of any element is established, sometimes isotopes are represented simply with the mass number thus: 93Ag. They may also be designated with a subscript notation indicating the number of neutrons, so that one can obtain this information at a glance without having to do the arithmetic. For the silver isotope 93 shown here, this is written as ᎏ4ᎏ7 Ag46. Isotopes are sometimes indicated by simple nomenclature as well: for instance, carbon-12 or carbon-13.
Ions The number of electrons in an atom is usually the same as the number of protons, and thus most atoms have a neutral charge. In certain situations, however, the atom may lose or gain one or more electrons and acquire a net charge, becoming an ion. The electrons are not “lost” when an atom becomes an ion: they simply go elsewhere. Aluminum (Al), for instance, has an atomic number of 13, which tells us that an aluminum atom will have 13 protons. Given the fact that every proton has a positive charge, and that most atoms tend to be neutral in charge, this means that there are usually 13 electrons, with a negative charge, present in an atom of aluminum. Aluminum may, however, form an ion by losing three electrons.
represents the aluminum cation described above. (Some chemists represent this with the plus sign before the number—for example, Al+3.) A cation is named after the element of which it is an ion: thus the ion we have described is called either the aluminum ion, or the aluminum cation. ANIONS. When a neutrally charged atom gains electrons, and as a result acquires a negative charge, this type of ion is known as an anion (AN-ie-un). Anions can be represented symbolically in much the same way of cations: C1-, for instance, is an anion of chlorine that forms when it acquires an electron, thus assuming a net charge of –1. Note that the 1 is not represented in the superscript notation, much as people do not write 101. In both cases, the 1 is assumed, whereas any number higher than 1 is shown.
The anion described here is never called a chlorine anion; rather, anions have a special nomenclature. If the anion represents, as is the case here, a single element, it is named by adding the suffix -ide to the name of the original element name: hence it would be called chloride. Other anions involve more than one element, and in these cases other rules apply for designating names. A few two-element anions use the -ide ending; such is the case, for instance, with a deadly mixture of carbon and nitrogen (CN–), better known as cyanide. For anions involving oxygen, there may be different prefixes and suffixes, depending on the relative number of oxygen atoms in the anion.
REAL-LIFE A PPLICAT ION S The Periodic Table
CATIONS. After its three electrons have departed, the remaining aluminum ion has a net positive charge of 3, represented as +3. How do we know this? Initially the atom had a charge of +13 + (–13) = 0. With the exit of the 3 electrons, leaving behind only 10, the picture changes: now the charge is +13 + (–10) = +3.
Note that an ion is never formed by a change in the number of protons: that number, as noted earlier, is a defining characteristic of an element. If all we know about a particular atom is that it has one proton, we can be certain that it is an atom of hydrogen. Likewise, if an atom has 79 protons, it is gold.
When a neutral atom loses one or more electrons, the result is a positively charged ion, or cation (pronounced KAT-ie-un). Cations are represented by a superscript number and plus sign after the element symbol: Al3+, for instance,
Knowing these quantities is not a matter of memorization: rather, one can learn this and much more by consulting the periodic table of elements. The periodic table is a chart, present in virtually every chemistry classroom in the world,
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showing the elements arranged in order of atomic number. Elements are represented by boxes containing the atomic number, element symbol, and average atomic mass, in atomic mass units, for that particular element. Vertical columns within the periodic table indicate groups or “families” of elements with similar chemical characteristics. These groups include alkali metals, alkaline earth metals, halogens, and noble gases. In the middle of the periodic table is a wide range of vertical columns representing the transition metals, and at the bottom of the table, separated from it, are two other rows for the lanthanides and actinides.
An Overview of the Elements As of 2001, there 112 elements, of which 88 occur naturally on Earth. (Some sources show 92 naturally occurring elements; however, a few of the elements with atomic numbers below 92 have not actually been found in nature.) The others were created synthetically, usually in a laboratory, and because these are highly radioactive, they exist only for fractions of a second. The number of elements thus continues to grow, but these “new” elements have little to do with the daily lives of ordinary people. Indeed, this is true even for some of the naturally occurring elements: few people who are not chemically trained, for instance, are able to identify thulium, which has an atomic number of 69. Though an element can theoretically exist as a gas, liquid, or a solid, in fact the vast majority of elements are solids. Only 11 elements—the six noble gases, along with hydrogen, nitrogen, oxygen, fluorine, and chlorine—exist in the gaseous state at a normal temperature of about 77°F (25°C). Just two are liquids at normal temperature: mercury, a metal, and the non-metal bromine. (The metal gallium becomes liquid at just 85.6°F, or 29.76°C.) The rest are all solids. The noble gases are monatomic, meaning that they exist purely as single atoms. So too are the “noble metals,” such as gold, silver, and platinum. “Noble” in this context means “set apart”: noble gases and noble metals are known for their tendency not to react to, and hence not to bond with, other elements. On the other hand, a number of other elements are described as diatomic, meaning that two atoms join to form a molecule.
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Names of the Elements ELEMENT SYMBOL. As noted above, the periodic table includes the element symbol or chemical symbol—a one-or two-letter abbreviation for the name of the element. Many of these are simple one-letter designations: O for oxygen, or C for carbon. Others are two-letter abbreviations, such as Ne for neon or Si for silicon. Note that the first letter is always capitalized, and the second is always lowercase.
In many cases, the two-letter symbols indicate the first and second letters of the element’s name, but this is far from universal. Cadmium, for example, is abbreviated Cd, while platinum is Pt. In other cases, the symbol seems to have nothing to do with the element name as it is normally used: for instance, Au for gold or Fe for iron. Many of the one-letter symbols indicate elements discovered early in history. For instance, carbon is represented by C, and later “C” elements took two-letter designations: Ce for cerium, Cr for chromium, and so on. But many of those elements with apparently strange symbols were among the first discovered, and this is precisely why the symbols make little sense to a person who does not recognize the historical origins of the name. HISTORICAL BACKGROUND ON SOME ELEMENT NAMES. For many
years, Latin was the language of communication between scientists from different nations; hence the use of Latin names such as aurum (“shining dawn”) for gold, or ferrum, the Latin word for iron. Likewise, lead (Pb) and sodium (Na) are designated by their Latin names, plumbum and natrium, respectively. Some chemical elements are named for Greek or German words describing properties of the element—for example, bromine (Br), which comes from a Greek word meaning “stench.” The name of cobalt comes from a German term meaning “underground gnome,” because miners considered the metal a troublemaker. The names of several elements with high atomic numbers reflect the places where they were originally discovered or created: francium, germanium, americium, californium. Americium and californium, with atomic numbers of 95 and 98 respectively, are among those elements that do not occur naturally, but
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were created artificially. The same is true of several elements named after scientists—among them einsteinium, after Albert Einstein (18791955), and nobelium after Alfred Nobel (18331896), the Swedish inventor of dynamite who established the Nobel Prize.
Elements
Abundance of Elements IN THE UNIVERSE. The first two elements on the periodic table, hydrogen and helium, represent 99.9% of the matter in the entire universe. This may seem astounding, but Earth is a tiny dot within the vastness of space, and hydrogen and helium are the principal elements in stars.
All elements, except for those created artificially, exist both on Earth and throughout the universe. Yet the distribution of elements on Earth is very, very different from that in other places—as well it should be, given the fact that Earth is the only planet known to support life. Hydrogen, for instance, constitutes only about 0.87%, by mass, of the elements found in the planet’s crust, waters, and atmosphere. As for helium, it is not even among the 18 most abundant elements on Earth. ON EARTH. That great element essential to animal life, oxygen, is by far the most plentiful on Earth, representing nearly half—49.2%—of the total mass of atoms found on this planet. (Here the term “mass” refers to the known elemental mass of the planet’s atmosphere, waters, and crust; below the crust, scientists can only speculate, though it is likely that much of Earth’s interior consists of iron.) Together with silicon (25.7%), oxygen accounts for almost exactly three-quarters of the elemental mass of Earth. Add in aluminum (7.5%), iron (4.71%), calcium (3.39%), sodium (2.63%), potassium (2.4%), and magnesium (1.93%), and these eight elements make up about 97.46% of Earth’s material.
In addition to hydrogen, whose distribution is given above, nine other elements account for a total of 2% of Earth’s composition: titanium (0.58%), chlorine (0.19%), phosphorus (0.11%), manganese (0.09%), carbon (0.08%), sulfur (0.06%), barium (0.04%), nitrogen (0.03%), and fluorine (0.03%). The remaining 0.49% is made up of various elements.
S C I E N C E O F E V E R Y D AY T H I N G S
THIS
WOMAN’S GOITER IS PROBABLY THE RESULT OF A
LACK OF IODINE IN HER DIET. (Lester V. Bergman/Corbis. Repro-
duced by permission.)
Elements In the Human Body Fans of science-fiction are familiar with the phrase “carbon-based life form,” which is used, for instance, by aliens in sci-fi movies to describe humans. In fact, the term is a virtual redundancy on Earth, since all living things contain carbon. Essential though it is to life, carbon as a component of the human body takes second place to oxygen, which is an even larger proportion of the body’s mass—65.0%—than it is of the Earth. Carbon accounts for 18%, and hydrogen for 10%, meaning that these three elements make up 93% of the body’s mass. Most of the remainder is taken up by 10 other elements: nitrogen (3%), calcium (1.4%), phosphorus (1.0%), magnesium (0.50%), potassium (0.34%), sulfur (0.26%), sodium (0.14%), chlorine (0.14%), iron (0.004%), and zinc (0.003%). TRACE ELEMENTS. As small as the amount of zinc is in the human body, there are still other elements found in even smaller quantities. These are known as trace elements, because only traces of them are present in the body. Yet they are essential to human well-being: without enough iodine, for instance, a person can devel-
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Elements
KEY TERMS The negative ion that results when an atom gains one or more electrons. An anion (pronounced “AN-ie-un”) of an element is never called, for instance, the chlorine anion. Rather, for an anion involving a single element, it is named by adding the suffix -ide to the name of the original element—hence, “chloride.” Other rules apply for more complex anions.
ANION:
The smallest particle of an element. An atom can exist either alone or in combination with other atoms in a molecule. Atoms are made up of protons, neutrons, and electrons. An atom that loses or gains one or more electrons, and thus has a net charge, is an ion. Atoms that have the same number of protons—that is, are of the same element—but differ in number of neutrons are known as isotopes. ATOM:
An SI unit (abbreviated amu), equal to 1.66 • 10-24 g, for measuring the mass of atoms. ATOMIC
MASS
UNIT:
The number of protons in the nucleus of an atom. Since this number is different for each element, elements are listed on the periodic table in order of atomic number. ATOMIC
NUMBER:
AVERAGE ATOMIC MASS: A figure
used by chemists to specify the mass—in atomic mass units—of the average atom in
op a goiter, a large swelling in the neck area. Chromium helps the body metabolize sugars, which is why people concerned with losing weight and/or toning their bodies through exercise may take a chromium supplement. Even arsenic, lethal in large quantities, is a trace element in the human body, and medicines for treating illnesses such as the infection known as “sleeping sickness” contain tiny amounts of arsenic. Other trace elements include cobalt, cop-
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a large sample. If a substance is a compound, the average atomic mass of all atoms in a molecule of that substance must be added together to yield the average molecular mass of that substance. The positive ion that results when an atom loses one or more electrons. A cation (pronounced KAT-ie-un) is named after the element of which it is an ion and thus is called, for instance, the aluminum ion or the aluminum cation. CATION:
CHEMICAL SYMBOL:
Another term
for element symbol. A substance made up of atoms of more than one element. These atoms are usually joined in molecules.
COMPOUND:
A term describing an element that exists as molecules composed of two atoms. This is in contrast to monatomic elements.
DIATOMIC:
ELECTRON: Negatively charged parti-
cles in an atom. Electrons, which spin around the protons and neutrons that make up the atom’s nucleus, constitute a very small portion of the atom’s mass. The number of electrons and protons is the same, thus canceling out one another. But when an atom loses or gains one or more electrons, however—thus becoming an ion—it acquires a net electric charge.
per, fluorine, manganese, molybdenum, nickel, selenium, silicon, and vanadium. MAINTAINING AND IMPROVING HEALTH. Though these elements are present
in trace quantities within the human body, that does not mean that exposure to large amounts of them is healthy. Arsenic, of course, is a good example; so too is aluminum. Aluminum is present in unexpected places: in baked goods, for instance, where a compound containing alu-
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Elements
KEY TERMS
CONTINUED
ELEMENT: A substance made up of only
Compounds are typically made of up
one kind of atom. Unlike compounds, elements cannot be chemically broken into other substances.
molecules.
ELEMENT SYMBOL: A one- or twoletter abbreviation for the name of an element. These may be a single capitalized letter (O for oxygen), or a capitalized letter followed by a lowercase one (Ne for neon). Sometimes the second letter is not the second letter of the element name (for example, Pt for platinum). In addition, the symbol may refer to an original Greek or Latin name, rather than the name used now, is the case with Au (aurum) for gold.
MONATOMIC:
A term describing an ele-
ment that exists as single atoms. This in contrast to diatomic elements. NEUTRON:
A subatomic particle that
has no electric charge. Neutrons are found at the nucleus of an atom, alongside protons. NUCLEUS: The center of an atom, a
region where protons and neutrons are located, and around which electrons spin. PERIODIC TABLE OF ELEMENTS: A
chart that shows the elements arranged in
An atom that has lost or gained one or more electrons, and thus has a net electric charge.
order of atomic number, along with ele-
ISOTOPES: Atoms that have an equal
element. Vertical columns within the peri-
number of protons, and hence are of the same element, but differ in their number of neutrons.
odic table indicate groups or “families”
MASS NUMBER: The sum of protons
PROTON:
and neutrons in an atom’s nucleus. Where an isotope is represented, the mass number is placed above the atomic number to the left of the element symbol.
in an atom. Protons and neutrons, which
MOLECULE: A group of atoms, usu-ally
greater than that of an electron. The num-
but not always representing more than one element, joined in a structure.
ber of protons in the nucleus of an atom is
ION:
minum (baking powder) is sometimes used in the leavening process; or even in cheeses, as an aid to melting when heated. The relatively high concentrations of aluminum in these products, as well as fluorine in drinking water, has raised concerns among some scientists. Generally speaking, an element is healthy for the human body in proportion to its presence in the body. With trace elements and others that are found in smaller quantities, however, it is some-
S C I E N C E O F E V E R Y D AY T H I N G S
ment symbol and the average atomic mass (in atomic mass units) for that particular
of elements with similar chemical characteristics. A positively charged particle
together form the nucleus around which electrons spin, have approximately the same mass—a mass that is many times
the atomic number of an element.
times possible and even advisable to increase the presence of those elements by taking dietary supplements. Hence a typical multivitamin contains calcium, iron, iodine, magnesium, zinc, selenium, copper, chromium, manganese, molybdenum, boron, and vanadium. For most of these, recommended daily allowances (RDA) have been established by the federal government. Usually, people do not take
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sodium as a supplement, though—Americans already get more than their RDA of sodium through salt, which is overly abundant in the American diet. WHERE TO LEARN MORE Challoner, Jack. The Visual Dictionary of Chemistry. New York: DK Publishing, 1996. “Classification of Elements and Compounds” (Web site). (May 14, 2001).
126
(May 14, 2001). “Elements, Compounds, and Mixtures” (Web site). (May 14, 2001). Knapp, Brian J. Elements. Illustrated by David Woodroffe and David Hardy. Danbury, CT: Grolier Educational, 1996. “Matter—Elements, Compounds, and Mixtures” (Web site). (May 14, 2001). Oxlade, Chris. Elements and Compounds. Chicago, IL: Heinemann Library, 2001.
“Elements and Compounds” (Web site). (May 14, 2001).
Stwertka, Albert. A Guide to the Elements. New York: Oxford University Press, 1998.
“Elements, Compounds, and Mixtures.” Purdue University Department of Chemistry. (Web site).
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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Periodic Table of Elements
P E R I O D I C TA B L E OF ELEMENTS
CONCEPT In virtually every chemistry classroom on the planet, there is a chart known as the periodic table of elements. At first glance, it looks like a mere series of boxes, with letters and numbers in them, arranged according to some kind of code not immediately clear to the observer. The boxes would form a rectangle, 18 across and 7 deep, but there are gaps in the rectangle, particularly along the top. To further complicate matters, two rows of boxes are shown along the bottom, separated from one another and from the rest of the table. Even when one begins to appreciate all the information contained in these boxes, the periodic table might appear to be a mere chart, rather than what it really is: one of the most sophisticated and usable means ever designed for representing complex interactions between the building blocks of matter.
HOW IT WORKS Introduction to the Periodic Table As a testament to its durability, the periodic table—created in 1869—is still in use today. Along the way, it has incorporated modifications involving subatomic properties unknown to the man who designed it, Russian chemist Dmitri Ivanovitch Mendeleev (1834-1907). Yet Mendeleev’s original model, which we will discuss shortly, was essentially sound, inasmuch as it was based on the knowledge available to chemists at the time. In 1869, the electromagnetic force fundamental to chemical interactions had only recent-
S C I E N C E O F E V E R Y D AY T H I N G S
ly been identified; the modern idea of the atom was less than 70 years old; and another three decades were to elapse before scientists began uncovering the substructure of atoms that causes them to behave as they do. Despite these limitations in the knowledge available to Mendeleev, his original table was sound enough that it has never had to be discarded, but merely clarified and modified, in the years since he developed it. The rows of the periodic table of elements are called periods, and the columns are known as groups. Each box in the table represents an element by its chemical symbol, along with its atomic number and its average atomic mass in atomic mass units. Already a great deal has been said, and a number of terms need to be explained. These explanations will require the length of this essay, beginning with a little historical background, because chemists’ understanding of the periodic table—and of the elements and atoms it represents—has evolved considerably since 1869.
Elements and Atoms An element is a substance that cannot be broken down chemically into another substance. An atom is the smallest particle of an element that retains all the chemical and physical properties of the element, and elements contain only one kind of atom. The scientific concepts of both elements and atoms came to us from the ancient Greeks, who had a rather erroneous notion of the element and—for their time, at least—a highly advanced idea of the atom. Unfortunately, atomic theory died away in later centuries, while the mistaken notion of four “elements” (earth, air, fire, and water) survived
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In A New System of Chemical Philosophy (1808), Dalton put forward the idea that nature is composed of tiny particles, and in so doing he adopted the Greek word atomos to describe these basic units. Drawing on Proust’s law of constant composition, Dalton recognized that the structure of atoms in a particular element or compound is uniform, but maintained that compounds are made up of compound “atoms.” In fact, these compound atoms are really molecules, or groups of two or more atoms bonded to one another, a distinction clarified by Italian physicist Amedeo Avogadro (1776-1856).
Periodic Table of Elements
DMITRI MENDELEEV. (Bettmann/Corbis. Reproduced by permission.)
virtually until the seventeenth century, an era that witnessed the birth of modern science. Yet the ancients did know of substances later classified as elements, even if they did not understand them as such. Among these were gold, tin, copper, silver, lead, and mercury. These, in fact, are such an old part of human history that their discoverers are unknown. The first individual credited with discovering an element was German chemist Hennig Brand (c. 1630-c. 1692), who discovered phosphorus in 1674. MATURING CONCEPTS OF ATOMS, ELEMENTS, AND MOLECULES. The work of English physicist and
chemist Robert Boyle (1627-1691) greatly advanced scientific understanding of the elements. Boyle maintained that no substance was an element if it could be broken down into other substances: thus air, for instance, was not an element. Boyle’s studies led to the identification of numerous elements in the years that followed, and his work influenced French chemists Antoine Lavoisier (1743-1794) and Joseph-Louis Proust (1754-1826), both of whom helped define an element in the modern sense. These men in turn influenced English chemist John Dalton (1766-1844), who reintroduced atomic theory to the language of science.
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Dalton’s and Avogadro’s contemporary, Swedish chemist Jons Berzelius (1779-1848), developed a system of comparing the mass of various atoms in relation to the lightest one, hydrogen. Berzelius also introduced the system of chemical symbols—H for hydrogen, O for oxygen, and so on—in use today. Thus, by the middle of the nineteenth century, scientists understood vastly more about elements and atoms than they had just a few decades before, and the need for a system of organizing elements became increasingly clear. By mid-century, a number of chemists had attempted to create just such an organizational system, and though Mendeleev’s was not the first, it proved the most useful.
Mendeleev Constructs His Table By the time Mendeleev constructed his periodic table in 1869, there were 63 known elements. At that point, he was working as a chemistry professor at the University of St. Petersburg, where he had become acutely aware of the need for a way of classifying the elements to make their relationships more understandable to his students. He therefore assembled a set of 63 cards, one for each element, on which he wrote a number of identifying characteristics for each. Along with the element symbol, discussed below, he included the atomic mass for the atoms of each. In Mendeleev’s time, atomic mass was understood simply to be the collective mass of a unit of atoms—a unit developed by Avogadro, known as the mole—divided by Avogadro’s number, the number of atoms or molecules in a mole. With the later discovery of subatomic particles, which in turn made possible the discovery of isotopes, figures for atomic mass were clarified, as will also be discussed.
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Periodic Table of Elements
Main–Group Elements
Main–Group Elements
Atomic number Symbol N ame
1
IA 1 1
H
2
3 Li
1.00794
Period
5
6
2
radon
4 Be
13
11 22.989768 12 Na Mg
5
Transition Metals
magnesium
19
20
39.0983
3
4
5
6
7
III B
IV B
VB
VI B
VII B
21 44.955910 22
40.078
47.88
23
50.9415
24
51.9961
25
8
54.9305
26
10
VIII B
55.847
10.811
27 58.93320 28
58.69
11
12
IB
II B
29
63.546
30
65.39
15
IV A 6
12.011
14.00674
F
Ne
oxygen
fluorine
neon
15
16
17
18
28.0855
30.973762
Si
P
S
Cl
Ar
silicon
phosphorus
sulfur
chlorine
argon
31
69.723
32
72.61
33
74.92159
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Ga
Ge
As
vanadium
chromium
manganese
iron
cobalt
nickel
copper
zinc
gallium
germanium
arsenic
37
38
42
43
50
51
88.90585
40
91.224
41
92.90638
95.94
(98)
Y
Zr
Nb
Mo
zirconium
niobium
molybdenum technetium
71
72
73
55 132.90543 56 Cs Ba 87
137.327
67-70
*
barium (223)
88
Fr
Ra
francium
radium
(226)
89-102
†
174.967
178.49
180.9479
74
Tc 183.85
75
186.207
44
101.07
45 102.90550 46
106.42
47
107.8682
48
112.411
49
114.82
118.710
121.75
Rh
Pd
Ag
Cd
In
Sn
Sb
rhodium
palladium
silver
cadmium
indium
tin
antimony
77
78
79 196.96654 80
192.22
195.08
200.59
81
204.3833
82
207.2
78.96
35
79.904
36 Kr krypton
52
53 126.90447 54 Xe I
127.60
tellurium
83 208.98037 84
iodine (209)
85
(210)
86
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
Tl
Pb
Bi
Po
At
Rn
hafnium
tantalum
tungsten
rhenium
osmium
iridium
platinum
gold
mercury
thallium
lead
bismuth
polonium
astatine
radon
(262)
104
(261)
105
Lr
Rf
rutherfordium dubnium
(262) 106
Db
(263)
107
(264)
108
(265)
109
(268)
110
(269)
111
(272)
112
114
(277)
Sg
Bh
Hs
Mt
Uun
Uuu
Uub
seaborgium
bohrium
hassium
meitnerium
ununnilium
unununium
ununbiium
116
(289)
Uuq ununquadium
131.29
xenon
Lu
lawrencium
83.80
Br bromine
lutetium
103
39.948
selenium
Te
Ru 190.2
34 Se
ruthenium
76
35.4527
Al
titanium
yttrium
32.066
20.1797
aluminum
Ti
39
helium
O
scandium 87.62
He 10
nitrogen
Sc
strontium
18.9984032
N
calcium
Sr
VII A 9
C
Ca 85.4678
15.9994
carbon
K
rubidium
17
VI A 8
B
potassium
Rb
16
VA 7
4.002602
boron
13 26.981539 14
9
24.3050
sodium
14
III A
9.012182
beryllium
cesium
7
18
VIII A
Rn
2 6.941
lithium
4
Atomic weight
(222)
II A
hydrogen
3
86
118
(289)
(222)
(293)
Uuh
Uuo
ununhexium
ununoctium
Inner–Transition Metals
*Lanthanides
57 La
138.9055
lanthanum
89
† Actinides
THE
PERIODIC TABLE
(227)
58
140.115
59 140.90765 60 Pr
cerium
praseodymium neodymium
90
232.0381
91
Nd (231)
Ac
Th
Pa
actinium
thorium
protactinium
(IUPAC
144.24
Ce
92
238.0289
U uranium
61
(145)
62
150.36
63
151.965
64
157.25
65 158.92534 66
162.50
67 164.93032 68
Pm
Sm
Eu
Gd
Tb
Dy
Ho
promethium
samarium
europium
gadolinium
terbium
dysprosium
holmium
93
(237)
94
(244)
95
(243)
96
(247)
97
(247)
98
(251)
Np
Pu
Am
Cm
Bk
Cf
neptunium
plutonium
americium
curium
berkelium
californium
99
167.26
Er (252)
Es einsteinium
erbium
100
(257)
69 168.93421 70
173.04
Tm
Yb
thulium
ytterbium
101
(258)
102
(259)
Fm
Md
fermium
mendelevium nobelium
No
SYSTEM)
In addition, Mendeleev also included figures for specific gravity—the ratio between the density of an element and the density of water—as well as other known chemical characteristics of an element. Today, these items are typically no longer included on the periodic table, partly for considerations of space, but partly because chemists’ much greater understanding of the properties of atoms makes it unnecessary to clutter the table with so much detail. Again, however, in Mendeleev’s time there was no way of knowing about these factors. As far as chemists knew in 1869, an atom was an indivisible little pellet of matter that could not be characterized by terms any more detailed than its mass and the ways it interacted with atoms of other elements. Mendeleev therefore ar-
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ranged his cards in order of atomic mass, then grouped elements that showed similar chemical properties. CONFIDENT PREDICTIONS. As Mendeleev observed, every eighth element on the chart exhibits similar characteristics, and thus, he established columns whereby element number x was placed above element number x + 8—for instance, helium (2) above neon (10). The patterns he observed were so regular that for any “hole” in his table, he predicted that an element to fill that space would be discovered.
Indeed, Mendeleev was so confident in the basic soundness of his organizational system that in some instances, he changed the figures for the atomic mass of certain elements because he was convinced they belonged elsewhere on the table.
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Later discoveries of isotopes, which in some cases affected the average atomic mass considerably, confirmed his suppositions. Likewise the undiscovered elements he named “eka-aluminum,” “eka-boron,” and “eka-silicon” were later identified as gallium, scandium, and germanium, respectively.
REAL-LIFE APPLICAT ION S Subatomic Structures Clarify the Periodic Table Over a period of 35 years, between the discovery of the electron in 1897 and the discovery of the neutron in 1932, chemists’ and physicists’ understanding of atomic structure changed completely. The man who identified the electron was English physicist J. J. Thomson (1856-1940). The electron is a negatively charged particle that contributes little to an atom’s mass; however, it has a great deal to do with the energy an atom possesses. Thomson’s discovery made it apparent that something else had to account for atomic mass, as well as the positive electric charge offsetting the negative charge of the electron. Thomson’s student Ernest Rutherford (1871-1937)—for whom, incidentally, rutherfordium (104 on the periodic table) is named— identified that “something else.” In a series of experiments, he discovered that the atom has a nucleus, a center around which electrons move, and that the nucleus contains positively charged particles called protons. Protons have a mass 1,836 times as great as that of an electron, and thus, this seemed to account for the total atomic mass. ISOTOPES AND ATOMIC MASS.
Later, working with English chemist Frederick Soddy (1877-1956), Rutherford discovered that when an atom emitted certain types of particles, its atomic mass changed. Rutherford and Soddy named these atoms of differing mass isotopes, though at that point—because the neutron had yet to be discovered—they did not know exactly what change had caused the change in mass. Certain types of isotopes, Soddy and Rutherford went on to conclude, had a tendency to decay by emitting particles or gamma rays, moving (sometimes over a great period of time) toward stabilization. In the process, these radioactive iso-
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topes changed into other isotopes of the same element—and sometimes even to isotopes of other elements. Soddy concluded that atomic mass, as measured by Berzelius, was actually an average of the mass figures for all isotopes within that element. This explained a problem with Mendeleev’s periodic table, in which there seemed to be irregularities in the increase of atomic mass from element to element. The answer to these variations in mass, it turned out, related to the number of isotopes associated with a given element: the greater the number of isotopes, the more these affected the overall measure of the element’s mass. A CLEARER DEFINITION OF ATOMIC NUMBER. Just a few years after
Rutherford and Soddy discovered isotopes, Welsh physicist Henry Moseley (1887-1915) uncovered a mathematical relationship between the amount of energy a given element emitted and its atomic number. Up to this point, the periodic table had assigned atomic number in order of mass, beginning with the lightest element, hydrogen. Using atomic mass and other characteristics as his guides, Mendeleev had been able to predict the discovery of new elements, but such predictions had remained problematic. Thanks to Moseley’s work, it became possible to predict the existence of undiscovered elements with much greater accuracy. As Moseley discovered, the atomic number corresponds to the number of positive charges in the nucleus. Thus carbon, for instance, has an atomic number of 6 not because there are five lighter elements—though this is also true—but because it has six protons in its nucleus. The ordering by atomic number happens to correspond to the ordering by atomic mass, but atomic number provides a much more precise means of distinguishing elements. For one thing, atomic number is always a whole integer—1 for hydrogen, for instance, or 17 for chlorine, or 92 for uranium. Figures for mass, on the other hand, are almost always rendered with whole numbers and decimal fractions (for example, 1.008 for hydrogen). If atoms have no electric charge, meaning that they have the same number of protons as electrons, then why do chemists not say that atomic number represents the number of protons or electrons? The reason is that electrons can easily be lost or gained by atoms to form ions,
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which have an electric charge. However, protons are very hard to remove.
mass take carbon-12, an isotope found in all living things, as their reference point.
NEUTRONS AND ATOMIC MASS.
It is inconvenient, to say the least, to measure the mass of a single carbon-12 atom, or indeed of any other atom. Instead, chemists use a large number of atoms, a value known as Avogadro’s number, which in general is the number of atoms in a mole (abbreviated mol). Avogadro’s number is defined as 6.02214199 • 1023, with an uncertainty of 4.7 • 1016. In other words, the number of particles in a mole could vary by as much as 47,000,000,000,000,000 on either side of the value for Avogadro’s number. This might seem like a lot, but in fact it is equal to only about 80 parts per billion.
By 1932, scientists had come a long way toward understanding the structure of the atom. Not only had the electron, nucleus, and proton been discovered, but the complex model of electron configuration (described later in this essay) had begun to evolve. Yet, one nagging question remained: the mass of the protons in the nucleus simply could not account for the entire mass of the atom. Neither did the electrons make a significant contribution to mass. Suppose a proton was “worth” $1,836, while an electron had a value of only $1. In the “bank account” for deuterium, an isotope of hydrogen, there is $3,676, which poses a serious discrepancy in accounting. Because deuterium is a form of hydrogen, it has one proton as well as one electron, but that only accounts for $1,837. Where does deuterium get the other $1,839? These numbers are not chosen at random, as we shall see. The answer to the problem of atomic mass came when English physicist James Chadwick (1891-1974) identified the neutron, a particle with no electric charge, residing in the nucleus alongside the protons. Whereas the proton has a mass 1,836 times as large as that of the electron, the neutron’s mass is slightly larger—1,839 times that of an electron. This made it possible to clarify the values of atomic mass, which up to that time had been problematic, because a mole of atoms representing one element is likely to contain numerous isotopes.
Periodic Table of Elements
When 1 is divided by Avogadro’s number, the result is 1.66 • 10–24—the value, in grams, of 1 amu. However, according to the 1960 agreement, 1 amu is officially 1/12 the mass of a carbon-12 atom, whose exact value (re-tested in 1998), is 1.6653873 ⫻ 10–24 g. Carbon-12, sometimes represented as (12/6)C, contains six protons and six neutrons, so the value of 1 amu thus obtained is, in effect, an average of the mass for a proton and neutron. Though atoms differ, subatomic particles do not. There is no such thing, for instance, as a “hydrogen proton”—otherwise, these subatomic particles, and not atoms, would constitute the basic units of an element. Given the unvarying mass of subatomic particles, combined with the fact that the neutron only weighs 0.16% more than a proton, the established value of 1 amu provides a convenient means of comparing mass. This is particularly useful in light of the large numbers of isotopes—and hence of varying figures for mass—that many elements have.
Average Atomic Mass Today, the periodic table lists, along with chemical symbol and atomic number, the average atomic mass of each element. As its name suggests, the average atomic mass provides the average value of mass—in atomic mass units (amu)—for a large sample of atoms. According to Berzelius’s system for measuring atomic mass, 1 amu should be equal to the mass of a hydrogen atom, even though that mass had yet to be measured, since hydrogen almost never appears alone in nature. Today, in accordance with a 1960 agreement among members of the international scientific community, measurements of atomic
S C I E N C E O F E V E R Y D AY T H I N G S
ATOMIC MASS UNITS AND THE PERIODIC TABLE. The periodic table as it
is used today includes figures in atomic mass units for the average mass of each atom. As it turns out, Berzelius was not so far off in his use of hydrogen as a standard, since its mass is almost exactly 1 amu—but not quite. The value is actually 1.008 amu, reflecting the presence of slightly heavier deuterium isotopes in the average sample of hydrogen Figures increase from hydrogen along the periodic table, though not by a regular pattern. Sometimes the increase from one element to the next is by just over 1 amu, and in other cases, the
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increase is by more than 3 amu. This only serves to prove that atomic number, rather than atomic mass, is a more straightforward means of ordering the elements. Mass figures for many elements that tend to appear in the form of radioactive isotopes are usually shown in parentheses. This is particularly true for elements with very, very high atomic numbers (above 92), because samples of these elements do not stay around long enough to be measured. Some have a half-life—the period in which half the isotopes decay to a stable form— of just a few minutes, and for others, the half-life is a fraction of a second. Therefore, atomic mass figures represent the mass of the longest-lived isotope.
are liquids at normal temperature: mercury, a metal, and the nonmetal halogen bromine. It should be noted that the metal gallium becomes liquid at just 85.6°F (29.76°C); below that temperature, however, it— like the elements other than those named in this paragraph—is a solid.
Chemical Names and Symbols For the sake of space and convenience, elements are listed on the periodic table by chemical symbol or element symbol—a one-or two-letter abbreviation for the name of the element according to the system first developed by Berzelius. These symbols, which are standardized and unvarying for any particular element, greatly aid the chemist in writing out chemical formulas, which could otherwise be quite cumbersome.
Elements As of 2001, there were 112 known elements, of which about 90 occur naturally on Earth. Uranium, with an atomic number of 92, was the last naturally occurring element discovered: hence some sources list 92 natural elements. Other sources, however, subtract those elements with a lower atomic number than uranium that were first created in laboratories rather than discovered in nature. In any case, all elements with atomic numbers higher than 92 are synthetic, meaning that they were created in laboratories. Of these 20 elements—all of which have appeared only in the form of radioactive isotopes with short half-lives—the last three have yet to receive permanent names. In addition, three other elements—designated by atomic numbers 114, 116, and 118, respectively—are still on the drawing board, as it were, and do not yet even have temporary names. The number of elements thus continues to grow, but these “new” elements have little to do with the daily lives of ordinary people. Indeed, this is true even for some of the naturally occurring elements: for example, few people who are not chemically trained would be able to identify yttrium, which has an atomic number of 39. Though an element can exist theoretically as a gas, liquid, or a solid, in fact, the vast majority of elements are solids. Only 11 elements exist in the gaseous state at a normal temperature of about 77°F (25°C). These are the six noble gases; fluorine and chlorine from the halogen family; as well as hydrogen, nitrogen, and oxygen. Just two
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Many of the chemical symbols are simple one-letter designations: H for hydrogen, O for oxygen, and F for fluorine. Others are two-letter abbreviations, such as He for helium, Ne for neon, and Si for silicon. Note that the first letter is always capitalized, and the second is always lowercase. In many cases, the two-letter symbols indicate the first and second letters of the element’s name, but this is not nearly always the case. Cadmium, for example, is abbreviated Cd, while platinum is Pt. Many of the one-letter symbols indicate elements discovered early in history. For instance, carbon is represented by C, and later “C” elements took two-letter designations: Ce for cerium, Cr for chromium, and so on. Likewise, krypton had to take the symbol Kr because potassium had already been assigned K. The association of potassium with K brings up one of the aspects of chemical symbols most confusing to students just beginning to learn about the periodic table: why K and not P? The latter had in fact already been taken by phosphorus, but then why not Po, assigned many years later instead to polonium? CHEMICAL SYMBOLS BASED IN OTHER LANGUAGES. In fact, potassi-
um’s symbol is one of the more unusual examples of a chemical symbol, taken from an ancient or non-European language. Soon after its discovery in the early nineteenth century, the element was named kalium, apparently after the Arabic qali or “alkali.” Hence, though it is known as potassium today, the old symbol still stands.
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The use of Arabic in naming potassium is unusual in the sense that “strange” chemical symbols usually refer to Latin and Greek names. Latin names include aurum, or “shining dawn” for gold, symbolized as Au; or ferrum, the Latin word for iron, designated Fe. Likewise, lead (Pb) and sodium (Na) are represented by letters from their Latin names, plumbum and natrium, respectively. Some chemical elements are named for Greek or German words describing properties of the element. Consider, for instance, the halogens, collectively named for a Greek term meaning “salt producing.” Chloros, in Greek, describes a sickly yellow color, and was assigned to chlorine; the name of bromine comes from a Greek word meaning “stink”; and that of iodine is a form of a Greek term meaning “violet-colored.” Astatine, last-discovered of the halogens and the rarest of all natural elements, is so radioactive that it was given a name meaning “unstable.” Another Greek-based example outside the halogen family is phosphorus, or “I bring light”—appropriate enough, in view of its phosphorescent properties. NAMES OF LATER ELEMENTS.
The names of several elements with high atomic numbers—specifically, the lanthanides, the transuranium elements of the actinide series, and some of the later transition metals—have a number of interesting characteristics. Several reflect the places where they were originally discovered or created: for example, germanium, americium, and californium. Other elements are named for famous or not-so-famous scientists. Most people could recognize einsteinium as being named after Albert Einstein (1879-1955), but the origin of the name gadolinium—Finnish chemist Johan Gadolin (1760-1852)—is harder for the average person to identify. Then of course there is element 101, named mendelevium in honor of the man who created the periodic table. Two elements are named after women: curium after French physicist and chemist Marie Curie (1867-1934), and meitnerium after Austrian physicist Lise Meitner (1878-1968). Curie, the first scientist to receive two Nobel Prizes—in both physics and chemistry—herself discovered two elements, radium and polonium. In keeping with the trend of naming transuranium elements after places, she commemorated the land of her birth, Poland, in the name of polonium. One of Curie’s students, French physicist Marguerite
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Perey (1909-1975), also discovered an element and named it after her own homeland: francium.
Periodic Table of Elements
Meitnerium, the last element to receive a name, was created in 1982 at the Gesellschaft für Schwerionenforschung, or GSI, in Darmstadt, Germany, one of the world’s three leading centers of research involving transuranium elements. The other two are the Joint Institute for Nuclear Research in Dubna, Russia, and the University of California at Berkeley, for which berkelium is named.
OF
THE IUPAC AND THE NAMING ELEMENTS. One of the researchers
involved with creating berkelium was American nuclear chemist Glenn T. Seaborg (1912-1999), who discovered plutonium and several other transuranium elements. In light of his many contributions, the scientists who created element 106 at Dubna in 1974 proposed that it be named seaborgium, and duly submitted the name to the International Union of Pure and Applied Chemistry (IUPAC). Founded in 1919, the IUPAC is, as its name suggests, an international body, and it oversees a number of matters relating to the periodic table: the naming of elements, the assignment of chemical symbols to new elements, and the certification of a particular research team as the discoverers of that element. For many years, the IUPAC refused to recognize the name seaborgium, maintaining that an element could not be named after a living person. The dispute over the element’s name was not resolved until the 1990s, but finally the IUPAC approved the name, and today seaborgium is included on the international body’s official list. Elements 110 through 112 had yet to be named in 2001, and hence were still designated by the three-letter symbols Uun, Uuu, and Uub respectively. These are not names, but alphabetic representations of numbers: un for 1, nil for 0, and bium for 2. Thus, the names are rendered as ununnilium, unununium, and ununbium; the undiscovered elements 114, 116, and 118 are respectively known as ununquadium, ununhexium, and ununoctium.
Layout of the Periodic Table TWO SYSTEMS FOR LABELING GROUPS. Having discussed the three items of
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information contained in the boxes of the periodic table—atomic number, chemical symbol/ name, and average atomic mass—it is now possible to step back from the chart and look at its overall layout. To reiterate what was stated in the introduction to the periodic table above, the table is arranged in rows called periods, and columns known as groups. The deeper meaning of the periods and groups, however—that is, the way that chemists now understand them in light of what they know about electron configurations—will require some explanation. All current versions of the periodic table show seven rows—in other words, seven periods—as well as 18 columns. However, the means by which columns are assigned group numbers varies somewhat. According to the system used in North America, only eight groups are numbered. These are the two “tall” columns on the left side of the “dip” in the chart, as well as the six “tall” columns to the right of it. The “dip,” which spans 10 columns in periods 4 through 7, is the region in which the transition metals are listed. The North American system assigns no group numbers to these, or to the two rows set aside at the bottom, representing the lanthanide and actinide series of transition metals. As for the columns that the North American system does number, this numbering may appear in one of four forms: either by Roman numerals; Roman numerals with the letter A (for example, IIIA); Hindu-Arabic numbers (for example, 3); or Hindu-Arabic numerals with the letter A. Throughout this book, the North American system of assigning Hindu-Arabic numerals without the letter A has been used. However, an attempt has been made in some places to include the group designation approved by the IUPAC, which is used by scientists in Europe and most parts of the world outside of North America. (Some scientists in North America are also adopting the IUPAC system.) The IUPAC numbers all columns on the chart, so that instead of eight groups, there are 18. The table below provides a means of comparing the North American and IUPAC systems. Columns are designated in terms of the element family or families, followed in parentheses by the atomic numbers of the elements that appear at the top and bottom of that column. The first number following the colon is the number in the North American system (as described above, a
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Hindu-Arabic numerical without an “A”), and the second is the number in the IUPAC system. Element
North
Family
American
IUPAC
1
1
2
2
Hydrogen and alkali metals (1, 87) Alkaline metals (4, 88) Transition metals (21,89)
3
Transition metals (22,104)
4
Transition metals (23,105)
5
Transition metals (24,106)
6
Transition metals (25,107)
7
Transition metals (26,108)
8
Transition metals (27,109)
9
Transition metals (28,110)
10
Transition metals (29,111)
11
Transition metals (30,112)
12
Nonmetals and metals (5,81) Nonmetals, metalloids, and metal (6,82)
3
13
4
14
5
15
Nonmetals, metalloids, and metal (7,83) Nonmetals, metalloids,
6
16
Halogens (9,85)
7
17
Noble gases (2,86)
8
18
(8,84)
Lanthanides (58,71)
No number group assigned in either system
Actinides (90,103)
No number group assigned in either system
Valence Electrons, Periods, and Groups The merits of the IUPAC system are easy enough to see: just as there are 18 columns, the IUPAC lists 18 groups. Yet the North American system is more useful than it might seem: the group number in the North American system indicates the number of valence electrons, the electrons that are involved in chemical bonding. Valence electrons also occupy the highest energy level in the atom—which might be thought of as the orbit farthest from the nucleus, though in fact the reality is more complex. A more detailed, though certainly far from comprehensive, discussion of electrons and energy levels, as well as the history behind these discoveries, appears in the Electrons essay. In what follows, the basics of electron configuration will be presented with the specific aim of making it clear exactly why elements appear in particular columns of the periodic table.
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PRINCIPAL ENERGY LEVELS AND PERIODS. At one time, scientists
thought that electrons moved around a nucleus in regular orbits, like planets around the Sun. In fact the paths of an electron are much more complicated, and can only be loosely defined in terms of orbitals, a set of probabilities regarding the positions that an electron is likely to occupy as it moves around the nucleus. The pattern of orbitals is determined by the principal energy level of the atom, which indicates a distance that an electron may move away from the nucleus. Principal energy level is designated by a whole-number integer, beginning with 1 and moving upward: the higher the number, the further the electron is from the nucleus, and hence the greater the energy in the atom. Each principal energy level is divided into sublevels corresponding to the number n of the principal energy level: thus, principal energy level 1 has one sublevel, principal energy level 2 has two, and so on. The relationship between principal energy level and period is relatively easy to demonstrate: the number n of a period on the periodic table is the same as the number of the highest principal energy level for the atoms on that row—that is, the principal energy level occupied by its valence electrons. Thus, elements on period 4 have a highest principal energy level of 4, whereas the valence electrons of elements on period 7 are at principal energy level 7. Note the conclusion that this allows us to draw: the further down the periodic table an element is positioned, the greater the energy in a single atom of that element. Not surprisingly, most of the elements used in nuclear power come from period 7, which includes the actinides. VALENCE ELECTRON CONFIGURATIONS AND GROUPS. Now to a
more involved subject, whereby group number is related to valence electron configuration. As mentioned earlier, the principal energy levels are divided into sublevels, which are equal in number to the principal energy level number: principal energy level 1 has one sublevel, level 2 has two sublevels, and so on. As one might expect, with an increase in principal energy levels and sublevels, there are increases in the complexity of the orbitals. The four types of orbital patterns are designated as s, p,d, and f. Two electrons can move in an s orbital pattern or shell, six in a p, 10 in a d,
S C I E N C E O F E V E R Y D AY T H I N G S
and 14 in an f orbital pattern or shell. This says nothing about the number of electrons that are actually in a particular atom; rather, the higher the principal energy level and the larger the number of sublevels, the greater the number of ways that the electrons can move. It does happen to be the case, however, that with higher atomic numbers—which means more electrons to offset the protons—the higher the energy level, the larger the number of orbitals for those electrons.
Periodic Table of Elements
Let us now consider a few examples of valence shell configurations. Hydrogen, with the simplest of all atomic structures, has just one electron on principal energy level 1, so in effect its valence electron is also a core electron. The valence configuration for hydrogen is thus written as 1s1. Moving straight down the periodic table to francium (atomic number 87), which is in the same column as hydrogen, one finds that it has a valence electron configuration of 7s1. Thus, although francium is vastly more complex and energy-filled than hydrogen, the two elements have the same valence-shell configuration; only the number of the principal energy level is different. Now look at two elements in Group 3 (Group 13 in the IUPAC system): boron and thallium, which respectively occupy the top and bottom of the column, with atomic numbers of 5 and 81. Boron has a valence-shell configuration of 2s22p1. This means its valence shell is at principal energy level 2, where there are two electrons in an s orbital pattern, and 2 in a p orbital pattern. Thallium, though it is on period 6, nonetheless has the same valence-shell configuration: 6s26p1. Notice something about the total of the superscript figures for any element in Group 3 of the North American system: it is three. The same is true in the other columns numbered on North American charts, in which the total number of electrons equals the group number. Thus in Group 7, the valence shell configuration is ns2np5, where n is the principal energy level. There is only one exception to this: helium, in Group 8 (the noble gases), has a valence shell configuration of 1s2. Were it not for the fact that it clearly fits with the noble gases due to shared properties, helium would be placed next to hydrogen at the top of Group 2, where all the atoms have a valence-shell configuration of ns2.
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Obviously the group numbers in the IUPAC system do not correspond to the number of valence electrons, because the IUPAC chart includes numbers for the columns of transition metals, which are not numbered in the North American system. In any case, in both systems the columns contain elements that all have the same number of electrons in their valence shells. Thus the term “group” can finally be defined in accordance with modern chemists’ understanding, which incorporates electron configurations of which Mendeleev was unaware. All the members of a group have the same number of valence electrons in the same orbital patterns, though at different energy levels. (Once again, helium is the lone exception.)
Some Challenges of the Periodic Table The groups that are numbered in the North American system are referred to as “representative” elements, because they follow a clearly established pattern of adding valence shell electrons. By contrast, the 40 elements listed in the “dip” at the middle of the chart—the transition elements— do not follow such a pattern. This is why the North American system does not list them by group number, and also why neither system lists two “branches” of the transition-metal family, the lanthanides and actinides. IRREGULAR
PATTERNS.
Even within the representative elements, there are some challenges as far as electron configuration. For the first 18 elements—1 (hydrogen) to 18 (argon)—there is a regular pattern of orbital filling. Beginning with helium (2) onward, all of principal level 1 is filled; then, beginning with beryllium (4), sublevel 2s begins to fill. Sublevel 2p—and hence principal level 2 as a whole—becomes filled at neon (10).
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indeed, the transition elements are defined by the fact that they fill the d orbitals rather than the p orbitals, as was the pattern up to that point. After the first period of transition metals ends with zinc (30), the next representative element—gallium (31)—resumes the filling of the p orbital rather than the d. And so it goes, all along the four periods in which transition metals break up the steady order of electron configurations. As for the lanthanide and actinide series of transitions metals, they follow an even more unusual pattern, which is why they are set apart even from the transition metals. These are the only groups of elements that involve the highly complex f sublevels. In the lanthanide series, the seven 4f orbital shells are filled, while the actinide series reflects the filling of the seven 5f orbital shells. Why these irregularities? One reason is that as the principal energy level increases, the energy levels themselves become closer—i.e., there is less difference between the energy levels. The atom is thus like a bus that fills up: when there are just a few people on board, those few people (analogous to electrons) have plenty of room, but as more people get on, the bus becomes increasingly more crowded, and passengers jostle against one another. In the atom, due to differences in energy levels, the 4s orbital actually has a lower energy than the 3d, and therefore begins to fill first. This is also true for the 6s and 4f orbitals. CHANGES IN ATOMIC SIZE. The
subject of element families is a matter unto itself, and therefore a separate essay in this book has been devoted to it. The reader is encouraged to consult the Families of Elements essay, which discusses aspects of electron configuration as well as the properties of various element families.
After argon, as one moves to the element occupying the nineteenth position on the periodic table—potassium—the rules change. Argon, in Group 8 of the North American system, has a valence shell of 3s23p6, and by the pattern established with the first 18 elements, potassium should begin filling principal level 3d. Instead, it “skips” 3d and moves on to 4s. The element following argon, calcium, adds a second electron to the 4s sublevel.
One last thing should be mentioned about the periodic table: the curious fact that the sizes of atoms decreases as one moves from left to right across a row or period, even though the sizes increase as one moves from top to bottom along a group. The increase of atomic size in a group, as a function of increasing atomic number, is easy enough to explain. The higher the atomic number, the higher the principal energy level, and the greater the distance from the nucleus to the furthest probability range for the electron.
After calcium, as the transition metals begin with scandium (21), the pattern again changes:
On the other hand, the decrease in size across a period is a bit more challenging to com-
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Periodic Table of Elements
KEY TERMS ATOM:
The smallest particle of an ele-
GROUPS:
Columns on the periodic
ment that retains all the chemical and
table of elements. These are ordered
physical properties of the element.
according to the numbers of valence elec-
ATOMIC
MASS
UNIT:
An SI unit
(abbreviated amu), equal to 1.66 • 10-24 g, for measuring the mass of atoms. ATOMIC
NUMBER:
The number of
trons in the outer shells of the atoms for the elements represented. HALF-LIFE: The length of time it takes a
substance to diminish to one-half its initial
protons in the nucleus of an atom. Since
amount.
this number is different for each element,
ION:
elements are listed on the periodic table of
gained one or more electrons, thus acquir-
elements in order of atomic number.
ing a net electric charge.
AVERAGE ATOMIC MASS: A figure
ISOTOPES: Atoms that have an equal
used by chemists to specify the mass—in
number of protons, and hence are of the
atomic mass units—of the average atom in
same element, but differ in their number of
a large sample.
neutrons. This results in a difference of
An atom or atoms that has lost or
A figure,
mass. Isotopes may be either stable or
named after Italian physicist Amedeo Avo-
unstable. The latter type, known as
gadro (1776-1856), equal to 6.022137 x
radioisotopes, are radioactive.
AVOGADRO’S
NUMBER:
1023. Avogadro’s number indicates the number of atoms or molecules in a mole.
MOLE:
The SI fundamental unit for
“amount of substance.” A mole is, general-
CHEMICAL SYMBOL: A one- or two-
ly speaking, Avogadro’s number of atoms,
letter abbreviation for the name of an
molecules, or other elementary particles;
element.
however, in the more precise SI definition,
COMPOUND:
A substance made of two
a mole is equal to the number of carbon
or more elements that have bonded chem-
atoms in 12.01 g of carbon.
ically. These atoms are usually, but not
MOLECULE: A group of atoms, usually
always, joined in molecules.
but not always representing more than one
ELECTRON: A negatively charged parti-
element, joined by chemical bonds. Com-
cle in an atom. The configurations of
pounds are typically made of up mole-
valence electrons define specific groups on
cules.
the periodic table of elements, while the principal energy levels of those valence electrons define periods on the table.
NEUTRON:
A subatomic particle that
has no electric charge. Neutrons, together with protons, account for the majority of
ELEMENT: A substance made up of only
average atomic mass. When atoms have the
one kind of atom, which cannot be chemi-
same number of protons—and hence are
cally broken into other substances.
the same element—but differ in their
ELEMENT SYMBOL: Another term for
number of neutrons, they are called
chemical symbol.
isotopes.
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Periodic Table of Elements
KEY TERMS NUCLEUS: The center of an atom, a
ber integer, beginning with 1 and moving
region where protons and neutrons are
upward. The higher the principal energy
located. The nucleus accounts for the vast
level, the greater the energy in the atom,
majority of the average atomic mass.
and the more complex the pattern of
ORBITAL:
A pattern of probabilities
orbitals.
regarding the regions that an electron can
PROTON:
occupy within an atom in a particular
in an atom. The number of protons in the
energy state. The higher the principal ener-
nucleus of an atom is the atomic number
gy level, the more complex the pattern of
of an element.
orbitals.
A positively charged particle
RADIOACTIVITY:
A term describing a
A
phenomenon whereby certain isotopes
chart that shows the elements arranged in
known as radioisotopes are subject to a
order of atomic number, along with chem-
form of decay brought about by the emis-
ical symbol and the average atomic mass
sion of high-energy particles. “Decay” does
(in atomic mass units) for that particular
not mean that the isotope “rots”; rather, it
element.
decays to form another isotope— either of
PERIODS: Rows of the periodic table of
the same element or another—until even-
elements. These represent successive prin-
tually it becomes stable. This stabilizing
cipal energy levels for the valence electrons
process may take a few seconds, or many
in the atoms of the elements involved.
years.
PRINCIPAL ENERGY LEVEL: A value
VALENCE
indicating the distance that an electron
that occupy the highest energy levels in an
may move away from the nucleus of an
atom. These are the electrons involved in
atom. This is designated by a whole-num-
chemical bonding.
PERIODIC TABLE OF ELEMENTS:
prehend; however, it just takes a little explaining. As one moves along a period from left to right, there is a corresponding increase in the number of protons within the nucleus. This means a stronger positive charge pulling the electrons inward. Therefore, the “cloud” of electrons is drawn ever closer toward the increasingly powerful charge at the center of the atom, and the size of the atom decreases because the electrons cannot move as far away from the nucleus.
138
CONTINUED
ELECTRONS:
Electrons
“Elementistory” (Web site). (May 22, 2001). International Union of Pure and Applied Chemistry (Web site). (May 22, 2001). Knapp, Brian J. and David Woodroffe. The Periodic Table. Danbury, CT: Grolier Educational, 1998. Oxlade, Chris. Elements and Compounds. Chicago: Heinemann Library, 2001. “A Periodic Table of the Elements” Los Alamos National Laboratory (Web site). (May 22, 2001).
WHERE TO LEARN MORE
“The Pictorial Periodic Table” (Web site). (May 22, 2001).
Challoner, Jack. The Visual Dictionary of Chemistry. New York: DK Publishing, 1996.
Stwertka, Albert. A Guide to the Elements. New York: Oxford University Press, 1998.
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“Visual Elements” (Web site). (May 22, 2001).
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WebElements (Web site).
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FA M I L I E S O F E L E M E N T S Families of Elements
CONCEPT The term “family” is used to describe elements that share certain characteristics—not only in terms of observable behavior, but also with regard to atomic structure. All noble gases, for instance, tend to be highly nonreactive: only a few of them combine with other elements, and then only with fluorine, the most reactive of all substances. Fluorine is a member of another family, the halogens, which have so many shared characteristics that they are grouped together, despite the fact that two are gases, two are solids, and one—bromine—is one of only two elements that appears at room temperature as a solid. Despite these apparent differences, common electron configurations identify the halogens as a family. Families on the periodic table include, in addition to noble gases and halogens, the alkali metals, alkaline earth metals, transition metals, lanthanides, and actinides. The nonmetals form a loosely defined cross-family grouping, as do the metalloids.
HOW IT WORKS The Basics of the Periodic Table Created in 1869, and modified several times since then, the periodic table of the elements developed by Russian chemist Dmitri Ivanovitch Mendeleev (1834-1907) provides a highly useful means of organizing the elements. Certainly other organizational systems exist, but Mendeleev’s table is the most widely used—and with good reason. For one thing, it makes it possible to see at a glance families of elements, many
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of which either belong to the same group (column) or the same period (row) on the table. The periodic table is examined in depth within the essay devoted to that subject, and among the specifics discussed in that essay are the differing systems used for periodic-table charts in North America and the rest of the world. In particular, the North American system numbers only eight groups, leaving 10 columns unnumbered, whereas the other system— approved by the International Union of Pure and Applied Chemistry (IUPAC)—numbers all 18 columns. Both versions of the periodic table show seven periods. The groups numbered in the North American system are the two “tall” columns on the left side of the “dip” in the chart, as well as the six “tall” columns to the right of it. Group 1 in this system consists of hydrogen and the alkali metals; Group 2, the alkaline earth metals; groups 3 through 6, an assortment of metals, nonmetals, and metalloids; Group 7, halogens; and Group 8, noble gases. The “dip,” which spans 10 columns in periods 4 through 7, is the region in which the transition metals are listed. The North American system assigns no group numbers to these, or to the two rows set aside at the bottom, representing the lanthanide and actinide series of transition metals. The IUPAC system, on the other hand, offers the obvious convenience of providing a number for each column. (Note that, like its North American counterpart, the IUPAC chart provides no column numbers for the lanthanides or actinides.) Furthermore, the IUPAC has behind it the authority of an international body, founded in 1919, which oversees a number of matters
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Families of Elements
SIZE
REPRESENTATION OF THE ATOMIC RADII OF THE MAIN-GROUP ELEMENTS.
relating to the periodic table: the naming of elements, the assignment of chemical symbols to new elements, and the certification of a particular individual or research team as the discoverers of that element. For these reasons, the IUPAC system is coming into favor among North American chemists as well.
part, is that most American schools still use this system; furthermore, there is a reasoning behind the assignment of numbers to only eight groups, as will be discussed. Where necessary or appropriate, however, group numbers in the IUPAC system will be provided as well.
Despite the international acceptance of the IUPAC system, as well as its merits in terms of convenience, the North American system is generally the one used in this book. The reason, in
Principal Energy Levels
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Group numbers in the North American system indicate the number of valence electrons, or the electrons that are involved in chemical bonding.
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Valence electrons also occupy the highest energy level in the atom—which might be thought of as the orbit farthest from the nucleus, though in fact the term “orbit” is misleading when applied to the ways an electron moves. Electrons do not move around the nucleus of an atom in regular orbits, like planets around the Sun; rather, their paths can only be loosely defined in terms of orbitals, a pattern of probabilities regarding the areas through which an electron is likely to move. The pattern of orbitals is determined by the principal energy level of the atom, which indicates the distance an electron may move away from the nucleus. Principal energy level is designated by a whole-number integer, beginning with 1 and moving upward to 7: the higher the number, the further the electron is from the nucleus, and hence the greater the energy in the atom. The relationship between principal energy level and period is relatively easy to demonstrate. The number n of a period on the periodic table is the same as the number of the highest principal energy level for the atoms on that row—that is, the principal energy level occupied by its valence electrons. Thus, elements on period 1 have a highest principal energy level of 1, and so on.
Valence Electron Configurations When discussing families of elements, however, the periods or rows on the periodic table are not as important as the groups or columns. These are defined by the valence electron configurations, a subject more complicated than principal energy levels—though the latter requires a bit more explanation in order to explain electron configurations. Each principal energy level is divided into sublevels corresponding to the number n of the principal energy level: thus, principal energy level 1 has one sublevel, principal energy level 2 has two, and so on. As one might expect, with an increase in principal energy levels and sublevels, there are increases in the complexity of the orbitals. ORBITAL PATTERNS. The four basic
types of orbital patterns are designated as s, p,d, and f. The s shape might be described as spherical, though when talking about electrons, nothing is quite so neat: orbital patterns, remember, only identify regions of probability for the elec-
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tron. In other words, in an s orbital, the total electron cloud will probably end up being more or less like a sphere. The p shape is like a figure eight around the nucleus, and the d like two figure eights meeting at the nucleus. Again, these and other orbital patterns do not indicate that the electron will necessary follow that path. What it means is that, if you could take millions of photographs of the electron during a period of a few seconds, the resulting blur of images in a p orbital would somewhat describe the shape of a figure eight. The f orbital pattern is so complex that most basic chemistry textbooks do not even attempt to explain it, and beyond f are other, even more complicated, patterns designated in alphabetical order: g, h, and so on. In the discussion that follows, we will not be concerned with these, since even for the lanthanides and the actinides, an atom at the ground state does not fill orbital patterns beyond an f. SUBLEVELS AND ORBITAL FILLING. Principal energy level 1 has only an
s sublevel; 2 has an s and a p, the latter with three possible orientations in space; 3 has an s, p, and d (five possible spatial orientations); and 4 has an s, p, d, and f (seven possible spatial orientations.) According to the Pauli exclusion principle, only two electrons can occupy a single orbital pattern—that is, the s sublevel or any one of the spatial orientations in p, d, and f—and those two electrons must be spinning in opposite directions. Thus, two electrons can move in an s orbital pattern or shell, six in a p, 10 in a d, and 14 in an f orbital pattern or shell. Valence shell configurations are therefore presented with superscript figures indicating the number of electrons in that orbital pattern—for instance, s1 for one electron in the s orbital, or d10, indicating a d orbital that has been completely filled.
REAL-LIFE A PPLICAT I O N S Representative Elements Hydrogen (atomic number 1), with the simplest of all atomic structures, has just one electron on principal energy level 1, so, in effect, its valence electron is also a core electron. The valence configuration for hydrogen is thus written as 1s1. It should be noted, as described in the Electrons
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essay, that if a hydrogen atom (or any other atom) is in an excited state, it may reach energy levels beyond its normal, or ground, state.
From the Representative Elements to the Transition Elements
Moving straight down the periodic table to francium (atomic number 87), which is in the same column as hydrogen, one finds that it has a valence electron configuration of 7s1. Thus, although francium is vastly more complex and energy-filled than hydrogen, the two elements have the same valence shell configuration; only the number of the principal energy level is different. All the elements listed below hydrogen in Group 1 are therefore classified together as alkali metals. Obviously, hydrogen—a gas—is not part of the alkali metal family, nor does it clearly belong to any other family: it is the “lone wolf ” of the periodic table.
Groups 3 through 6, along with hydrogen and the four families so far identified, constitute the 44 representative or main-group elements. In 43 of these 44, the number of valence shell electrons is the same as the group number in the North American system. (Helium, which is in Group 8 but has two valence electrons, is the lone exception.) By contrast, the 40 elements listed in the “dip” at the middle of the chart—the transition metals—follow a less easily defined pattern. This is part of the reason why the North American system does not list them by group number, and also why neither system lists the two other families within the transition elements—the lanthanides and actinides.
Now look at two elements in Group 2, with beryllium (atomic number 4) and radium (88) at the top and bottom respectively. Beryllium has a valence shell configuration of 2s2. This means its valence shell is at principal energy level 2, where there are two electrons on an s orbital pattern. Radium, though it is on period 7, nonetheless has the same valence shell configuration: 7s2. This defines the alkaline earth metals family in terms of valence shell configuration. For now, let us ignore groups 3 through 6— not to mention the columns between groups 2 and 3, unnumbered in the North American system—and skip over to Group 7. All the elements in this column, known as halogens, have valence shell configurations of ns2np5. Beyond Group 7 is Group 8, the noble gases, all but one of whom have valence shell configurations of ns2np6. The exception is helium, which has an s2 valence shell. This seems to put it with the alkaline earth metals, but of course helium is not a metal. In terms of its actual behavior, it clearly belongs to the noble gases family. The configurations of these valence shells have implications with regard to the ways in which elements bond, a subject developed at some length in the Chemical Bonding essay. Here we will consider it only in passing, to clarify the fact that electron configuration produces observable results. This is most obvious with the noble gases, which tend to resist bonding with most other elements because they already have eight electrons in their valence shell—the same number of valence electrons that most other atoms achieve only after they have bonded.
S C I E N C E O F E V E R Y D AY T H I N G S
Families of Elements
Before addressing the transition metals, however, let us consider patterns of orbital filling, which also differentiate the representative elements from the transition elements. Each successive representative element fills all the orbitals of the elements that precede it (with some exceptions that will be explained), then goes on to add one more possible electron configuration. The total number of electrons—not just valence shell electrons—is the same as the atomic number. Thus fluorine, with an atomic number of 9, has a complete configuration of 1s22s22p5. Neon, directly following it with an atomic number of 10, has a total configuration of 1s22s22p6. (Again, this is not the same as the valence shell configuration, which is contained in the last two sublevels represented: for example, 2s22p6 for neon.) The chart that follows shows the pattern by which orbitals are filled. Note that in several places, the pattern of filling becomes “out of order,” something that will be explained below. Orbital Filling by Principal Energy Level • • • • • • • • • • •
1s (2) 2s (2) 2p (6) 3s (2) 3p (6) 4s (2) 3d (10) 4p (6) 5s (2) 4d (10) 5p (6)
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6s (2) 4f (14) 5d (10) 6p (6) 7s (2) 5f (14) 6d (10)
PATTERNS OF ORBITAL FILLING. Generally, the 44 representative elements
follow a regular pattern of orbital filling, and this is particularly so for the first 18 elements. Imagine a small amphitheater, shaped like a cone, with smaller rows of seats at the front. These rows are also designated by section, with the section number being the same as the number of rows in that section. The two seats in the front row comprise a section labeled 1 or 1s, and this is completely filled after helium (atomic number 2) enters the auditorium. Now the elements start filling section 2, which contains two rows. The first row of section 2, labeled 2s, also has two seats, and after beryllium (4), it too is filled. Row 2p has 6 seats, and it is finally filled with the entrance of neon (10). Now, all of section 2 has been filled; therefore, the eleventh element, sodium, starts filling section 3 at the first of its three rows. This row is 3s—which, like all s rows, has only two seats. Thus, when element 13, aluminum, enters the theatre, it takes a seat in row 3p, and eventually argon (18), completes that six-seat row. By the pattern so far established, element 19 (potassium) should begin filling row 3d by taking the first of its 10 seats. Instead, it moves on to section 4, which has four rows, and it takes the first seat in the first of those rows, 4s. Calcium (20) follows it, filling the 4s row. But when the next element, scandium (21), comes into the theatre, it goes to row 3d, where potassium “should have” gone, if it had continued filling sections in order. Scandium is followed by nine companions (the first row of transition elements) before another representative element, gallium (31), comes into the theatre. (For reasons that will not be discussed here, chromium and copper, elements 24 and 29, respectively, have valence electrons in 4s—which puts them slightly off the transition metal pattern.) According to the “proper” order of filling seats, now that 3d (and hence all of section 3) is filled, gallium should take a seat in 4s. But those seats have already been taken by the two preced-
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ing representative elements, so gallium takes the first of six seats in 4p. After that row fills up at krypton (36), it is again “proper” for the next representative element, rubidium (37), to take a seat in 4d. Instead, just as potassium skipped 3d, rubidium skips 4d and opens up section 5 by taking the first of two seats in 5s. Just as before, the next transition element— yttrium (39)—begins filling up section 4d, and is followed by nine more transition elements until cadmium (48) fills up that section. Then, the representative elements resume with indium (49), which, like gallium, skips ahead to section 5p. And so it goes through the remainder of the periodic table, which ends with two representative elements followed by the last 10 transition metals.
Transition Metals Given the fact that it is actually the representative elements that skip the d sublevels, and the transition metals that go back and fill them, one might wonder if the names “representative” and “transition” (implying an interruption) should be reversed. However, remember the correlation between the number of valence shell electrons and group number for the representative elements. Furthermore, the transition metals are the only elements that fill the d orbitals. This brings us to the reason why the lanthanides and actinides are set apart even from the transition metals. In most versions of the periodic table, lanthanum (57) is followed by hafnium (72) in the transition metals section of the chart. Similarly, actinium (89) is followed by rutherfordium (104). The “missing” metals—lanthanides and actinides, respectively—are listed at the bottom of the chart. There are reasons for this, as well as for the names of these groups. After the 6s orbital fills with the representative element barium (56), lanthanum does what a transition metal does—it begins filling the 5d orbital. But after lanthanum, something strange happens: cerium (58) quits filling 5d, and moves to fill the 4f orbital. The filling of that orbital continues throughout the entire lanthanide series, all the way to lutetium (71). Thus, lanthanides can be defined as those metals that fill the 4f orbital; however, because lanthanum exhibits similar properties, it is usually included with the lanthanides. Sometimes the term “lan-
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Families of Elements
KEY TERMS Those transition metals
LANTHANIDES: The transition metals
that fill the 5f orbital. Because actinium—
that fill the 4forbital. Because lan-
which does not fill the 5f orbital—exhibits
thanum—which does not fill the 4f
characteristics similar to those of the
orbital—exhibits characteristics similar to
actinides, it is usually considered part of
those of the lanthanides, it is usually con-
the actinides family.
sidered part of the lanthanide family.
ACTINIDES:
ALKALI METALS:
All members, except
MAIN-GROUP
The 44
ELEMENTS:
hydrogen, of Group 1 on the periodic table
elements in Groups 1 through 8 on the
of elements, with valence electron configu-
periodic table of elements, for which the
rations of ns1.
number of valence electrons equals the group number. (The only exception is heli-
ALKALINE EARTH METALS: Group 2
um.) The main-group elements, also called
on the periodic table of elements, with
representative elements, include the fami-
valence electron configurations of ns2.
lies of alkali metals, alkali earth metals,
ELECTRON CLOUD: A term used to
halogens, and noble gases, as well as other
describe the pattern formed by orbitals.
metals, nonmetals, and metalloids.
FAMILIES OF ELEMENTS:
Related
elements, including the noble gases, halogens, alkali metals, alkaline earth metals, transition metals,lanthanides, and actinides. In addition, metals, nonmetals, and metalloids form loosely defined families. Other family designations—such as carbon family—are sometimes used. GROUND STATE:
A term describing
METALLOIDS: Elements which exhibit
characteristics of both metals and nonmetals. Metalloids are all solids, but are not lustrous or shiny, and they conduct heat and electricity moderately well. The six metalloids occupy a diagonal region between the metals and nonmetals on the right side of the periodic table. Sometimes astatine is included with the metalloids, but in this book it is treated within the
the state of an atom at its ordinary energy
context of the halogens family.
level.
METALS: A collection of 87 elements
Columns on the periodic
that includes numerous families—the
table of elements. These are ordered
alkali metals, alkaline earth metals, transi-
according to the numbers of valence elec-
tion metals, lanthanides, and actinides, as
trons in the outer shells of the atoms for
well as seven elements in groups 3 through
the elements represented.
5. Metals, which occupy the left, center, and
GROUPS:
HALOGENS: Group 7 of the periodic
table of elements, with valence electron configurations of ns2np5.
part of the right-hand side of the periodic table, are lustrous or shiny in appearance, and malleable, meaning that they can be molded into different shapes without
An atom or atoms that has lost or
breaking. They are excellent conductors of
gained one or more electrons, and thus has
heat and electricity, and tend to form posi-
a net electric charge.
tive ions by losing electrons.
ION:
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Families of Elements
KEY TERMS NOBLE GASES: Group 8 of the peri-
(in atomic mass units) for that particular
odic table of elements, all of whom (with
element.
the exception of helium) have valence electron configurations of ns2np6.
PERIODS: Rows of the periodic table of
elements. These represent successive ener-
NONMETALS: Elements that have a dull
gy levels in the atoms of the elements
appearance; are not malleable; are poor
involved.
conductors of heat and electricity; and tend to gain electrons to form negative ions. They are thus the opposite of metals in most regards, as befits their name. Aside from hydrogen, the other 18 nonmetals occupy the upper right-hand side of the periodic table, and include the noble gases, halogens, and seven elements in groups 3 through 6. ORBITAL:
PRINCIPAL ENERGY LEVEL: A value
indicating the distance that an electron may move away from the nucleus of an atom. This is designated by a whole-number integer, beginning with 1 and moving upward. The higher the principal energy level, the greater the energy in the atom, and the more complex the pattern of orbitals.
A pattern of probabilities
regarding the position of an electron for an atom in a particular energy state. The high-
REPRESENTATIVE ELEMENTS:
See
main-group elements.
er the principal energy level, the more
TRANSITION METALS: A group of 40
complex the pattern of orbitals. The four
elements, which are not assigned a group
types of orbital patterns are designated as s,
number in the North American version of
p, d, and f—each of which is more complex
the periodic table. These are the only ele-
than the one before.
ments that fill the d orbitals.
PERIODIC TABLE OF ELEMENTS:
146
CONTINUED
A
VALENCE
ELECTRONS:
Electrons
chart that shows the elements arranged in
that occupy the highest energy levels in an
order of atomic number, along with chem-
atom. These are the electrons involved in
ical symbol and the average atomic mass
chemical bonding.
thanide series” is used to distinguish the other 14 lanthanides from lanthanum itself.
Metals, Nonmetals, and Metalloids
A similar pattern occurs for the actinides. The 7s orbital fills with radium (88), after which actinium (89) begins filling the 6d orbital. Next comes thorium, first of the actinides, which begins the filling of the 5f orbital. This is completed with element 103, lawrencium. Actinides can thus be defined as those metals that fill the 5f orbital; but again, because actinium exhibits similar properties, it is usually included with the actinides.
The reader will note that for the seven families so far identified, we have generally not discussed them in terms of properties that can more easily be discerned—such as color, phase of matter, bonding characteristics, and so on. Instead, they have been examined primarily from the standpoint of orbital filling, which provides a solid chemical foundation for identifying families. Macroscopic characteristics, as well as the ways that the various elements find application in
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daily life, are discussed within essays devoted to the various groups. Note, also, that the families so far identified account for only 92 elements out of a total of 112 listed on the periodic table: hydrogen; six alkali metals; six alkaline earth metals; five halogens; six noble gases; 40 transition metals; 14 lanthanides; and 14 actinides. What about the other 20? Some discussions of element families assign these elements, all of which are in groups 3 through 6, to families of their own, which will be mentioned briefly. However, because these “families” are not recognized by all chemists, in this book the 20 elements of groups 3 through 6 are described generally as metals, nonmetals, and metalloids. METALS AND NONMETALS. Metals are lustrous or shiny in appearance, and malleable, meaning that they can be molded into different shapes without breaking. They are excellent conductors of heat and electricity, and tend to form positive ions by losing electrons. On the periodic table, metals fill the left, center, and part of the right-hand side of the chart. Thus it should not come as a surprise that most elements (87, in fact) are metals. This list includes alkali metals, alkaline earth metals, transition metals, lanthanides, and actinides, as well as seven elements in groups 3 through 6—aluminum, gallium, indium, thallium, tin, lead, and bismuth.
Nonmetals have a dull appearance; are not malleable; are poor conductors of heat and electricity; and tend to gain electrons to form negative ions. They are thus the opposite of metals in most regards, as befits their name. Nonmetals, which occupy the upper right-hand side of the periodic table, include the noble gases, halogens, and seven elements in groups 3 through 5. These nonmetal “orphans” are boron, carbon, nitrogen, oxygen, phosphorus, sulfur, and selenium. To these seven orphans could be added an eighth, from Group 1: hydrogen. As with the metals, a separate essay—with a special focus on the “orphans”—is devoted to nonmetals.
S C I E N C E O F E V E R Y D AY T H I N G S
METALLOIDS AND OTHER “FAMILY” DESIGNATIONS. Occupying
Families of Elements
a diagonal region between the metals and nonmetals are metalloids, elements which exhibit characteristics of both metals and nonmetals. They are all solids, but are not lustrous, and conduct heat and electricity moderately well. The six metalloids are silicon, germanium, arsenic, antimony, tellurium, and polonium. Astatine is sometimes identified as a seventh metalloid; however, in this book, it is treated as a member of the halogen family. Some sources list “families” rather than collections of “orphan” metals, metalloids, and nonmetals, in groups 3 through 6. These designations are not used in this book; however, they should be mentioned briefly. Group 3 is sometimes called the boron family; Group 4, the carbon family; Group 5, the nitrogen family; and Group 6, the oxygen family. Sometimes Group 5 is designated as the pnictogens, and Group 6 as the chalcogens. WHERE TO LEARN MORE Bankston, Sandy. “Explore the Periodic Table and Families of Elements” The Rice School Science Department (Web site). (May 23, 2001). Challoner, Jack. The Visual Dictionary of Chemistry. New York: DK Publishing, 1996. “Elementistory” (Web site). (May 22, 2001). “Families of Elements” (Web site). (May 23, 2001). Knapp, Brian J. and David Woodroffe. The Periodic Table. Danbury, CT: Grolier Educational, 1998. Maton, Anthea. Exploring Physical Science. Upper Saddle River, N.J.: Prentice Hall, 1997. Oxlade, Chris. Elements and Compounds. Chicago: Heinemann Library, 2001. “The Pictorial Periodic Table” (Web site). (May 22, 2001). Stwertka, Albert. A Guide to the Elements. New York: Oxford University Press, 1998. “Visual Elements” (Web site). (May 22, 2001).
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S C I E N C E O F E V E R Y D AY T H I N G S r e a l - l i f e CHEMISTRY
M E TA L S M E TA L S A L KA L I M E TA L S A L KA L I N E E A R T H M E TA L S T RA N S I T I O N M E TA L S ACTINIDES LANTHANIDES
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M E TA L S
Metals
CONCEPT A number of characteristics distinguish metals, including their shiny appearance, as well as their ability to be bent into various shapes without breaking. In addition, metals tend to be highly efficient conductors of heat and electricity. The vast majority of elements on the periodic table are metals, and most of these fall into one of five families: alkali metals; alkaline earth metals; the very large transition metals family; and the inner transition metal families, known as the lanthanides and actinides. In addition, there are seven “orphans,” or metals that do not belong to a larger family of elements: aluminum, gallium, indium, thallium, tin, lead, and bismuth. Some of these may be unfamiliar to most readers; on the other hand, a person can hardly spend a day without coming into contact with aluminum. Tin is a well-known element as well, though much of what people call “tin” is not really tin. Lead, too, is widely known, and once was widely used as well; today, however, it is known primarily for the dangers it poses to human health.
HOW IT WORKS General Properties of Metals Metals are lustrous or shiny in appearance, and malleable or ductile, meaning that they can be molded into different shapes without breaking. Despite their ductility, metals are extremely durable and have high melting and boiling points. They are excellent conductors of heat and electricity, and tend to form positive ions by losing electrons.
S C I E N C E O F E V E R Y D AY T H I N G S
The bonds that metals form with each other, or with nonmetals, are known as ionic bonds, which are the strongest type of chemical bond. Even within a metal, however, there are extremely strong bonds. Therefore, though it is easy to shape metals (that is, to slide the atoms in a metal past one another), it is very difficult to separate metal atoms. Their internal bonding is thus very strong, but nondirectional. Internal bonding in metals is described by the electron sea model, which depicts metal atoms as floating in a “sea” of valence electrons, the electrons involved in bonding. These valence electrons are highly mobile within the crystalline structure of the metal, and this mobility helps to explain metals’ high conductivity. The ease with which metal crystals allow themselves to be rearranged explains not only metals’ ductility, but also their ability to form alloys, a mixture containing one or more metals.
Abundance of Metals Metals constitute a significant portion of the elements found in Earth’s crust, waters, and atmosphere. The following list shows the most abundant metals on Earth, with their ranking among all elements in terms of abundance. Many other metals are present in smaller, though still significant, quantities. • • • • • •
3. Aluminum (7.5%) 4. Iron (4.71%) 5. Calcium (3.39%) 6. Sodium (2.63%) 7. Potassium (2.4%) 8. Magnesium (1.93%)
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Metals
ALUMINUM IS THE MOST ABUNDANT METAL ON EARTH. THIS PHOTO SHOWS THE FIRST BLOBS OF ALUMINUM ISOLATED, A FEAT PERFORMED BY CHARLES HALL IN 1886. (James L. Amos/Corbis. Reproduced by permission.)
• 10. Titanium (0.58%) • 13. Manganese (0.09%) In addition, metals are also important components of the human body. The following list shows the ranking of the most abundant metals among the elements in the body, along with the percentage that each constitutes. As with the quantities of metals on Earth, other metals are present in much smaller, but still critical, amounts. • • • • • •
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5. Calcium (1.4%) 7. Magnesium (0.50%) 8. Potassium (0.34%) 10. Sodium (0.14%) 12. Iron (0.004%) 13. Zinc (0.003%)
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EVER
Metals on the Periodic Table On the periodic table of elements, metals fill the left, center, and part of the right-hand side of the chart. The remainder of the right-hand section is taken by nonmetals, which have properties quite different from (and often opposite to) those of metals, as well as metalloids, which display characteristics both of metals and nonmetals. Nonmetallic elements are covered in essays on Nonmetals; Metalloids; Halogens; Noble Gases; and Carbon. In addition, hydrogen, the one nonmetal on the left side of the periodic table—first among the elements, in the upper left corner—is also discussed in its own essay. The total number of metals on the periodic table is 87—in other words, about 80% of all
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known elements. These include the six alkali metals, which occupy Group 1 of the periodic table, as well as the six alkaline earth metals, or Group 2. To the right of these are the 40 transition metals, whose groups are unnumbered in the North American version of the periodic table. Among the transition metals are two elements, lanthanum and actinium, often lumped in with the families of inner transition metals that exhibit similar properties. These are, respectively, the 14 lanthanides and 14 actinides. In addition, there are the seven “orphan” metals of periods 3 through 5, mentioned in the introduction to this essay, which will be discussed below.
Metals
The various families of elements are defined, not so much by external characteristics as by the configurations of valence electrons in their atoms’ shells. This subject will not be discussed in any depth here; instead, the reader is encouraged to consult essays on the specific metal families, which discuss the electron configurations of each. BEFORE THEY WERE DESTROYED BY TERRORIST ATTACKS SEPTEMBER 11, 2001, THE TWIN TOWERS OF THE WORLD TRADE CENTER IN NEW YORK CITY GLEAMED WITH A CORROSION-RESISTANT COVERING OF ALUMINUM.
ON
REAL-LIFE AP P LICATIONS Alkali Metals The members of the alkali metal family are distinguished by the fact that they have a valence electron configuration of s1 This means that they tend to bond easily with other substances. Alkali metals tend to form positive ions, or cations, with a charge of 1+. In contact with water, alkali metals form a negatively charged hydroxide ion (OH–). When alkali metals react with water, one hydrogen atom splits off from the water molecule to form hydrogen gas, while the other hydrogen atom remains bonded to the oxygen, forming hydroxide. Where the heavier members of the alkali metal family are concerned, reactions can often be so vigorous that the result is combustion or even explosion. Alkali metals also react with oxygen to produce either an oxide, peroxide, or superoxide, depending on the particular member of the alkali metal family involved. Shiny and soft enough to be cut with a knife, the alkali metals are usually white, though cesium is a yellowish white. When placed in a flame, most of these substances produce charac-
S C I E N C E O F E V E R Y D AY T H I N G S
(Bill Ross/Corbis. Reproduced by permission.)
teristic colors: lithium, for instance, glows bright red, and sodium an intense yellow. Heated potassium produces a violet color, rubidium a dark red, and cesium a light blue. This makes it possible to identify the metals by color when heated— a useful trait, since they so often tend to be bonded with other elements. The alkali metals, listed below by atomic number and chemical symbol, are: • • • • • •
3. Lithium (Li) 11. Sodium (Na) 19. Potassium (K) 37. Rubidium (Rb) 55. Cesium (Cs) 87. Francium (Fr)
Alkaline Earth Metals Occupying Group 2 of the periodic table are the alkaline earth metals, which have a valence electron configuration of s2. Like the alkali metals, the alkaline earth metals are known for their high reactivity—a tendency for bonds between atoms or molecules to be made or broken in such a way that materials are transformed. Thus they are sel-
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Metals
MOST “TIN”
ROOFS NOW CONSIST OF AN IRON OR STEEL ROOF COVERED WITH ZINC, NOT TIN. (John Hulme; Eye Ubiqui-
tous/Corbis. Reproduced by permission.)
dom found in pure form, but rather in compounds with other elements—for example, salts, a term that generally describes a compound consisting of a metal and a nonmetal. The alkaline earth metals are also like the alkali metals in that they have the properties of a base as opposed to an acid. An acid is a substance that, when dissolved in water, produces positive ions of hydrogen, designated symbolically as H+ ions. It is thus known as a proton donor. A base, on the other hand, produces negative hydroxide ions when dissolved in water. These are designated by the symbol OH-. Bases are therefore characterized as proton acceptors. The alkaline earth metals are shiny, and most are white or silvery in color. Like their “cousins” in the alkali metal family, they glow with characteristic colors when heated. Calcium glows orange, strontium a very bright red, and barium an apple green. Physically they are soft, though not as soft as the alkali metals; nor are their levels of reactivity as great as those of their neighbors in Group 1. The alkaline earth metals, listed below by atomic number and chemical symbol, are: • 4. Beryllium (Be) • 12. Magnesium (Mg)
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• • • •
20. Cadmium (Ca) 38. Strontium (Sr) 56. Barium (Ba) 88. Radium (Ra)
Transition Metals The transition metals are the only elements that fill the dorbitals. They are also the only elements that have valence electrons on two different principal energy levels. This sets them apart from the representative or main-group elements, of which the alkali metals and alkaline earth metals are a part. The transition metals also follow irregular patterns of orbital filling, which further distinguish them from the representative elements. Other than that, there is not much that differentiates the transition metals, a broad grouping that includes precious metals such as gold, silver, and platinum, as well as highly functional metals such as iron, manganese, and zinc. Many of the transition metals, particularly those on periods 4, 5, and 6, form useful alloys with one another, and with other elements. Because of their differences in valence electron configuration, however, they do not always combine in the same ways, even within an element. Iron, for
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instance, sometimes releases two electrons in chemical bonding, and at other times three. GROUPING THE TRANSITION METALS. There is no easy way to group the
transition metals, though some of these elements are traditionally categorized together. These do not constitute “families” as such, but they do provide useful ways to break down the otherwise rather daunting lineup of the transition metals. In two cases, there is at least a relationship between group number on the periodic table and the categories loosely assigned to a collection of transition metals. Thus the “coinage metals”— copper, silver, and gold—all occupy Group 9 on the IUPAC version of the periodic table. (These have traditionally been associated with one another because their resistance to oxidation, combined with their malleability and beauty, has made them useful materials for fashioning coins. Likewise the members of the “zinc group”— zinc, cadmium, and mercury—on Group 10 on the IUPAC periodic table have often been associated as a miniature unit due to common properties. Members of the “platinum group”—platinum, iridium, osmium, palladium, rhodium, and ruthenium—occupy a rectangle on the table, corresponding to periods 5 and 6, and groups 6 through 8. What actually makes them a “group,” however, is the fact that they tend to appear together in nature. Iron, nickel, and cobalt, found alongside one another on Period 4, may be grouped together because they are all magnetic to some degree. The transition metals, listed below by atomic number and chemical symbol, are: • • • • • • • • • • • • • • • •
21. Scandium (Sc) 22. Titanium (Ti) 23. Vanadium (V) 24. Chromium (Cr) 25. Manganese (Mn) 26. Iron (Fe) 27. Cobalt (Co) 28. Nickel (Ni) 29. Copper (Cu) 30. Zinc (Zn) 39. Yttrium (Y) 40. Zirconium (Zr) 41. Niobium (Nb) 42. Molybdenum (Mo) 43. Technetium (Tc) 44. Ruthenium (Ru)
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• • • • • • • • • • • • • • • • • • • • • • • •
45. Rhodium (Rh) 46. Palladium (Pd) 47. Silver (Ag) 48. Cadmium (Cd) 57. Lanthanum (La) 72. Hafnium (Hf) 73. Tantalum (Ta) 74. Tungsten (W) 75. Rhenium (Re) 76. Osmium (Os) 77. Iridium (Ir) 78. Platinum (Pt) 79. Gold (Au) 80. Mercury (Hg) 89. Actinium (Ac) 104. Rutherfordium (Rf) 105. Dubnium (Db) 106. Seaborgium (Sg) 107. Bohrium (Bh) 108. Hassium (Hs) 109. Meitnerium (Mt) 110. Ununnilium (Uun) 111. Unununium (Uuu) 112. Ununbium (Uub) The last nine, along with 11 of the actinides, are part of the list of metals known collectively as the transuranium elements—that is, elements with atomic numbers higher than 92. These have all been produced artificially, in most cases within a laboratory. Note that the last three had not been named as of 2001: the “names” by which they are known simply mean, respectively, 110, 111, and 112.
Metals
Lanthanides The lanthanides are the first of two inner transition metal groups. Note that in the list of transition metals above, lanthanum (57) is followed by hafnium (72). The “missing” group of 14 elements, normally shown at the bottom of the periodic table, is known as the lanthanides, a family which can be defined by the fact that all fill the 4f orbital. However, because lanthanum (which does not fill an f orbital) exhibits similar properties, it is usually included with the lanthanides. Bright and silvery in appearance, many of the lanthanides—though they are metals—are so soft they can be cut with a knife. They also tend to be highly reactive. Though they were once known as the “rare earth metals,” lanthanides
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only seemed rare because they were difficult to extract from compounds containing other substances—including other lanthanides. Because their properties are so similar, and because they tend to be found together in the same substances, the original isolation and identification of the lanthanides was an arduous task that took well over a century. The lanthanides (in addition to lanthanum, listed earlier with the transition metals), are: • • • • • • • • • • • • • •
58. Cerium (Ce) 59. Praseodymium (Pr) 60. Neodymium (Nd) 61. Promethium (Pm) 62. Samarium (Sm) 63. Europium (Eu) 64. Gadolinium (Gd) 65. Terbium (Tb) 66. Dysprosium (Dy) 67. Holmium (Ho) 68. Erbium (Er) 69. Thulium (Tm) 70. Ytterbium (Yb) 71. Lutetium (Lu)
Actinides Just as lanthanum is followed on the periodic table by an element with an atomic number 15 points higher, so actinium (89) is followed by rutherfordium (104). The elements in the “gap” are the other inner transition family, the actinides, which all fill the 5f orbital. These are placed below the lanthanides at the bottom of the chart, and just as lanthanum is included with the lanthanides, even though it does not fill an f orbital, so actinium is usually lumped in with the actinides due to similarities in properties. Most of the actinides tend to be unstable or radioactive, the later ones highly so. The first three members of the group (not counting actinium) occur in nature, while the other 11 are transuranium elements created artificially. In most cases, these were produced with a cyclotron or other machine for accelerating atoms, generally at the research center of the University of California at Berkeley during a period from 1940 to 1961. Einsteinium and fermium, however, were by-products of nuclear testing at Bikini Atoll in the south Pacific in 1952. The principal use of the actinides is in nuclear applications—weaponry
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or power plants—though some of them also have specialized uses as well. The actinides (in addition to actinium, listed earlier with the transition metals), are: • • • • • • • • • • • • • •
90. Thorium (Th) 91. Protactinium (Pa) 92. Uranium (U) 93. Neptunium (Np) 94. Plutonium (Pu) 95. Americium (Am) 96. Curium (Cm) 97. Berkelium (Bk) 98. Californium (Cf) 99. Einsteinium (Es) 100. Fermium (Fm) 101. Mendelevium (Md) 102. Nobelium (No) 103. Lawrencium (Lr)
“Orphan” Metals Seven other metals remain to be discussed. These are the “orphan” metals, which appear in groups 3, 4, and 5 of the North American periodic table (13, 14, and 15 of the IUPAC table), and they are called “orphans” simply because none belongs to a clearly defined family. Sometimes aluminum and the three elements below it in Group 3—gallium, indium, and thallium—are lumped together as the “aluminum family.” This is not a widely recognized distinction, but will be used here only for the purpose of giving some form of organization to the “orphan” elements. Though they do not belong to families, the “orphan” metals are nonetheless highly important. Aluminum, after all, is the most abundant of all metals on Earth, and has wide applications in daily life. Tin, too, is widely known, as is lead. Somewhat less recognizable is bismuth, but it appears in a product with which most Americans are familiar: Pepto-Bismol. The seven “orphans” are listed below, along with atomic number and chemical symbol: • • • • • • •
13. Aluminum (Al) 31. Gallium (Ga) 49. Indium (In) 50. Tin (Sn) 81. Thallium (Tl) 82. Lead (Pb) 83. Bismuth (Bi)
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Aluminum Named after alum, a salt known from ancient times and used by the Egyptians, Romans, and Greeks, aluminum is so reactive that it proved difficult to isolate. Only in 1825 did Danish physicist Hans Christian Ørsted (1777-1851) isolate an impure version of aluminum metal, using a complicated four-step process. Two years later, German chemist Friedrich Wöhler (1800-1882) obtained pure aluminum from a reaction of metallic potassium with aluminum chloride, or AlCl3. For years thereafter, aluminum continued to be so difficult to produce that it acquired the status of a precious metal. European kings displayed treasures of aluminum as though they were gold or silver, and by 1855, it was selling for about $100,000 a pound. Then in 1886, French metallurgist Paul-Louis-Toussaint Héroult (18631914) and American chemist Charles Martin Hall (1863-1914) independently developed a process that made aluminum relatively easy to extract by means of electrolysis. Thanks to what became known as the Hall-Héroult process, the price of aluminum dropped to around 30 cents a pound. America’s aluminum comes primarily from mines in Alabama, Arkansas, and Georgia, where it often appears in a clay called kaolin, used in making porcelain. Aluminum can also be found in deposits of feldspar, mica, granite, and other clays. The principal sources of aluminum outside the United States include France, Surinam, Jamaica, and parts of Africa. USES FOR ALUMINUM. Though aluminum is highly reactive, it does not corrode in moist air. Instead of forming rust the way iron does, it forms a thin, hard, invisible coating of aluminum oxide. This, along with its malleability, makes it highly useful for producing cans and other food containers. The World Trade Center Towers in New York City gleam with a corrosionresistant covering of aluminum. Likewise the element is used as a coating for mirrors: not only is it cheaper than silver, but unlike silver, it does not tarnish and turn black. Also, a thin coating of metallic aluminum gives Mylar balloons their silvery sheen.
Aluminum conducts electricity about 60% as well as copper, meaning that it is an extraordinarily good conductor, useful for transmitting electrical power. Because it is much more light-
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weight than copper and highly ductile, it is often used in high-voltage electric lines. Its conductivity also makes aluminum a favorite material for kitchen pots and pans. Unlike copper, it is not known to be toxic; however, because aluminum dissolves in strong acids, sometimes tomatoes and other acidic foods acquire a “metallic” taste when cooked in an aluminum pot.
Metals
Though it is soft in its pure form, when combined with copper, manganese, silicon, magnesium, and/or zinc, aluminum can produce strong, highly useful alloys. These find application in automobiles, airplanes, bridges, highway signs, buildings, and storage tanks. Aluminum’s high ductility also makes it the metal of choice for foil wrappings—that is, aluminum foil. Compounds containing aluminum are used in a wide range of applications, including antacids; antiperspirants (potassium aluminum sulfate tends to close up sweat-gland ducts); and water purifiers.
Other Elements in the Aluminum Group GALLIUM. When Russian chemist Dmitri Ivanovitch Mendeleev (1834-1907) created the periodic table in 1869, he predicted the existence of several missing elements on the basis of “holes” between elements on the table. Among these was what he called “eka-aluminum,” discovered in the 1870s by French chemist Paul Emile Lecoq de Boisbaudran (1838-1912). Boisbaudran named the new element gallium, after the ancient name of his homeland, Gaul.
Gallium will melt if held in the hand, and remains liquid over a large range of temperatures—from 85.6°F (29.76°C) to 3,999.2°F (2,204°C). This makes it highly useful for thermometers with a large temperature range. Used in a number of applications within the electronics industry, gallium is present in the compounds gallium arsenide and gallium phosphide, applied in lasers, solar cells, transistors, and other solidstate devices. INDIUM AND THALLIUM. As Boisbaudran would later do, German mineralogists Ferdinand Reich (1799-1882) and Hieronymus Theodor Richter (1824-1898) used a method called spectroscopy to discover one of the aluminum-group metals. Spectroscopy involves analyzing the frequencies of light (that is, the colors) emitted by an item of matter.
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However, Reich faced a problem when studying the zinc ores that he believed contained a new element: he was colorblind. Therefore he called on the help of Richter, his assistant. In 1863, they discovered an element they called indium because of the indigo blue color it emitted. Reich later tried to claim that he made the discovery alone, but Richter’s role is indisputable. Indium is used in making alloys, one of which is a combination with gallium that is liquid at room temperature. Its alloys are used in bearings, dental amalgams, and nuclear control roles. Various compounds are applied in solidstate electronics devices, and in electronics research. Two years before the discovery of indium, English physicist William Crookes (1832-1919) discovered another element using spectroscopic analysis. This was thallium, named after the Greek word thallos (“green twig”), a reference to a lime-green spectral line that told Crookes he had found a new element. Thallium is applied in electronic equipment, and the compound thallium sulfate is used for killing ants and rodents.
Three Other “Orphans” TIN. Known from ancient times, tin was combined with copper to make bronze—an alloy so significant it defines an entire stage of human technological development. Tin’s chemical symbol, Sn, refers to the name the Romans gave it: stannum. Just as tin added to copper gave bronze its strength, alloys of tin with copper and antimony created pewter, a highly useful, malleable material for pots and dinnerware popular from the thirteenth century through the early nineteenth century.
Tin is found primarily in Bolivia, Malaysia, Indonesia, Thailand, Zaire, and Nigeria—a wide geographical range. Like aluminum today, it has been widely used as a coating for other metals to retard corrosion. Hence the term “tin can,” referring to a steel can coated with tin. Also, tin has been used to coat iron or steel roofs, but because zinc is cheaper, it is now most often the coating of choice; nonetheless, these are still typically called “tin roofs.” LEAD. Due to knowledge of its toxic properties, lead is not frequently used today, but this was not always the case. The Romans, for instance, used plumbum as they called it (hence the chemical symbol Pb) as a material for making
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water pipes. This is the root of our own word plumber. (The same root explains the verb plumb or the noun plumb bob. A plumb bob is a lead weight, hung from a string, used to ensure that the walls of a structure are “plumb”—that is, perpendicular to the foundation.) Many historians believe that plumbum in the Romans’ water supply was one of the reasons behind the decline and fall of the Roman Empire. The human body can only excrete very small quantities of lead a day, and this is particularly true of children. Even in small concentrations, lead can cause elevation of blood pressure; reduction in the synthesis of hemoglobin, which carries oxygen from the lungs to the blood and organs; and decreased ability to utilize vitamin D and calcium for strengthening bones. Higher concentrations of lead can effect the central nervous system, resulting in decreased mental functioning and hearing damage. Prolonged exposure can result in a coma or even death. Before these facts became widely known in the late twentieth century, lead was applied as an ingredient in paint. In addition, it was used in water pipes, and as an anti-knock agent in gasolines. Increased awareness of the health hazards involved have led to a discontinuation of these practices. (Note that pencil “lead” is actually graphite, a form of carbon.) Lead, however, is used for absorbing radiation—for instance, as a shield against X rays. Another important use for lead today is in storage batteries. Yet another “application” of lead relates to its three stable isotopes (lead-206, -207, and -208), the end result of radioactive decay on the part of various isotopes of uranium and other radioactive elements. BISMUTH. During the Middle Ages, when a number of unscientific ideas prevailed, scholars believed that lead eventually became tin, tin eventually turned into bismuth, and bismuth developed into silver. Hence they referred to bismuth as “roof of silver.” Only in the sixteenth century did German metallurgist Georgius Agricola (George Bauer; 1494-1555) put forward the idea that bismuth was a separate element.
Bismuth appears in nature not only in its elemental form, but also in a number of compounds and ores. It is also obtained as a by-product from the smelting of gold, silver, copper, and lead. Because bismuth expands dramatically when it cools, early printers used a bismuth alloy
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Metals
KEY TERMS Those transition metals
fill the f orbitals. For this reason, they are
that fill the 5f orbital. Because actinium—
usually treated as distinct from the transi-
which does not fill the f orbital—exhibits
tion metals.
ACTINIDES:
characteristics similar to those of the actinides, it is usually considered part of the actinides family. ALKALI METALS:
ION:
An atom or group of atoms that has
lost or gained one or more electrons, and thus has a net electric charge.
All members, ex-cept
hydrogen, of Group 1 on the periodic table of elements, with valence electron configurations of ns1.
ISOTOPES: Atoms that have an equal
number of protons, and hence are of the same element, but differ in their number of neutrons. This results in a difference of
ALKALINE EARTH METALS: Group 2
mass. Isotopes may be either stable or
on the periodic table of elements, with
unstable. The latter type, known as
valence electron configurations of ALLOY:
ns2.
A mixture containing more than
radioisotopes, are radioactive. IUPAC SYSTEM: A version of the peri-
one metal.
odic table of elements, authorized by the
CONDUCTIVITY: The ability to conduct
International Union of Pure and Applied
heat or electricity. Metals are noted for
Chemistry (IUPAC), which numbers all
their high levels of conductivity.
groups on the table from 1 to 18. Thus in
CRYSTALLINE: A term describing an
internal structure in which the constituent parts have a simple and definite geometric arrangement, repeated in all directions. Metals have a crystalline structure. DUCTILE:
Capable of being bent or
molded into various shapes without breaking.
the IUPAC system, in use primarily outside of North America, both the representative or main-group elements and the transition metals are numbered. LANTHANIDES: The transition metals
that fill the 4f orbital. Because lanthanum—which does not fill the f orbital—exhibits characteristics similar to those of the lanthanides, it is usually con-
ELECTRON SEA MODEL: A widely
accepted model of internal bonding within metals, which depicts metal atoms as floating in a “sea” of valence electrons.
sidered part of the lanthanide family. METALS: A collection of 87 elements
that includes numerous families—the alkali metals, alkaline earth metals, transi-
Columns on the periodic
tion metals, lanthanides, and actinides, as
table of elements. These are ordered
well as seven elements in groups 3 through
according to the numbers of valence elec-
5 of the North American system periodic
trons in the outer shells of the atoms for
table. Metals are lustrous or shiny in
the elements represented.
appearance, and ductile. They are excellent
GROUPS:
INNER TRANSITION METALS: The
conductors of heat and electricity, and tend
lanthanides and actinides, both of which
to form positive ions by losing electrons.
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Metals
KEY TERMS
CONTINUED
NORTH AMERICAN SYSTEM: A ver-
decays to form another isotope until even-
sion of the periodic table of elements that
tually (though this may take a long time) it
only numbers groups of elements in which
becomes stable.
the number of valence electrons equals the group number. Hence the transition metals are usually not numbered in this system. ORBITAL:
A pattern of probabilities
REACTIVITY: The tendency for bonds
between atoms or molecules to be made or broken in such a way that materials are transformed.
regarding the position of an electron for an atom in a particular energy state. The high-
REPRESENTATIVE OR MAIN-GROUP
er the principal energy level, the more
ELEMENTS:
complex the pattern of orbitals.
1 through 8 on the North American ver-
PERIODIC TABLE OF ELEMENTS: A
chart that shows the elements arranged in order of atomic number, along with chem-
sion of periodic table of elements, for which the number of valence electrons equals the group number. (The only excep-
ical symbol and the average atomic mass
tion is helium.) The alkali metals and alka-
for that particular element. Elements are
line earth metals are representative ele-
arranged in groups or columns, as well as
ments; all other metals are not.
in rows or periods, according to specific
SALT:
aspects of their valence electron config-
that brings together a metal and a non-
urations.
metal. Salts are produced, along with water,
PERIODS: Rows on the periodic table of
in the reaction of an acid and a base.
elements. These represent successive principal energy levels for the valence electrons in the atoms of the elements involved. PRINCIPAL ENERGY LEVEL: A value
indicating the distance that an electron may move away from the nucleus of an atom. This is designated by a whole-number integer, beginning with 1 and moving upward. The higher the principal energy level, the greater the energy in the atom, and the more complex the pattern of
RADIOACTIVITY:
Generally, a salt is any compound
TRANSITION METALS: A group of 40
elements (counting lanthanum and actinium), which are not assigned a group number in the version of the periodic table of elements known as the North American system. These are the only elements that fill the d orbital. In addition, the transition metals—unlike the representative or maingroup elements—have their valence electrons on two different principal energy levels. Though the lanthanides and actinides
orbitals. A term describing a
phenomenon whereby certain isotopes
160
The 44 elements in Groups
are known as inner transition metals, they are usually treated separately. Electrons
known as radioisotopes are subject to a
VALENCE
form of decay brought about by the emis-
that occupy the highest principal energy
sion of high-energy particles. “Decay” does
level in an atom. These are the electrons
not mean that the isotope “rots”; rather, it
involved in chemical bonding.
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ELECTRONS:
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to make metal type. When poured into forms cut with the shapes of letters and other characters, the alloy produced symbols with clear, sharp edges.
Kerrod, Robin. Matter and Materials. Illustrated by Terry Hadler. Tarrytown, NY: Benchmark Books, 1996. “Lead Programs.” Environmental Protection Agency (Web site). (May 28, 2001).
Wood’s metal is a bismuth alloy involving cadmium, tin, and lead, which melts at a temperature of 158°F (70°C). This makes it useful for automatic sprinkler systems inside a building: when a fire breaks out, it melts the Wood’s metal seal, and turns on the sprinklers. Bismuth compounds are applied in cosmetics, paints, and dyes, and prior to the twentieth century, compounds of bismuth were widely used for treating sexually transmitted diseases. Today, antibiotics have largely taken their place, but bismuth still has one well-known medicinal application: in bismuth subsalicylate, better known by the brand name Pepto-Bismol.
WebElements (Web site). (May 22, 2001).
WHERE TO LEARN MORE
Whyman, Kathryn. Metals and Alloys. Illustrated by Louise Nevett and Simon Bishop. New York: Gloucester Press, 1988.
Aluminum Association (Web site). (May 28, 2001).
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
S C I E N C E O F E V E R Y D AY T H I N G S
Metals
Mebane, Robert C. and Thomas R. Rybolt. Metals. Illustrated by Anni Matsick. New York: Twenty-First Century Books, 1995. “Metals Industry Guide.” About.com (Web site). (May 28, 2001). “Minerals and Metals.” Natural Resources of Canada (Web site). (May 28, 2001). Oxlade, Chris. Metal. Chicago, IL: Heinemann Library, 2001. Snedden, Robert. Materials. Des Plaines, IL: Heinemann Library, 1999.
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A L K A L I M E TA L S Alkali Metals
CONCEPT Group 1 of the periodic table of elements consists of hydrogen, and below it the six alkali metals: lithium, sodium, potassium, rubidium, cesium, and francium. The last three are extremely rare, and have little to do with everyday life; on the other hand, it is hard to spend a day without encountering at least one of the first three—particularly sodium, found in table salt. Along with potassium, sodium is an important component of the human diet, and in compounds with other substances, it has an almost endless array of uses. Lithium does not have as many applications, but to many people who have received it as a medication for bipolar disorder, it is quite literally a life-saver.
HOW IT WORKS Electron Configuration of the Alkali Metals In the essay on Families of Elements, there is a lengthy discussion concerning the relationship between electron configuration and the definition of a particular collection of elements as a “family.” Here that subject will only be touched upon lightly, inasmuch as it relates to the alkali metals. All members of Group 1 on the periodic table of elements have a valence electron configuration of s1. This means that a single electron is involved in chemical bonding, and that this single electron moves through an orbital, or range of probabilities, roughly corresponding to a sphere.
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Most elements bond according to what is known as the octet rule, meaning that when two or more atoms are bonded, each has (or shares) eight valence electrons. It is for this reason that the noble gases, at the opposite side of the periodic table from the alkali metals, almost never bond with other elements: they already have eight valence electrons. The alkali metals, on the other hand, are quite likely to find “willing partners,” since they each have just one valence electron. This brings up one of the reasons why hydrogen, though it is also part of Group 1, is not included as an alkali metal. First and most obviously, it is not a metal; additionally, it bonds according to what is called the duet rule, such that it shares two electrons with another element.
Chemical and Physical Characteristics of the Alkali Metals The term “alkali” (essentially the opposite of an acid) refers to a substance that forms the negatively charged hydroxide ion (OH-) in contact with water. On their own, however, alkali metals almost always form positive ions, or cations, with a charge of +1. When alkali metals react with water, one hydrogen atom splits off from the water molecule to form hydrogen gas, while the other hydrogen atom joins the oxygen to form hydroxide. Where the heavier members of the alkali metal family are concerned, reactions can often be so vigorous that the result is combustion or even explosion. Alkali metals also react with oxygen to produce
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Alkali Metals
ONE
OF THE USES OF LITHIUM IS IN BATTERIES.
THE NISSAN HYPERMINI
IS AN ELECTRIC VEHICLE POWERED BY A
LITHIUM BATTERY. (Reuters NewMedia Inc./Corbis. Reproduced by permission.)
either an oxide, peroxide, or superoxide, depending on the particular member of the alkali metal family involved. Shiny and soft enough to be cut with a knife, the alkali metals are usually white (though cesium is more of a yellowish white). When placed in a flame, most of these substances produce characteristic colors: lithium, for instance, glows bright red, and sodium an intense yellow. Heated potassium produces a violet color, rubidium a dark red, and cesium a light blue. This makes it possible to identify the metals, when heated, by color—a useful trait, since they are so often inclined to be bonded with other elements. MELTING AND BOILING POINTS. As one moves down the rows or
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periods of the periodic table, the mass of atoms increases, as does the energy each atom possesses. Yet the amount of energy required to turn a solid alkali metal into a liquid, or to vaporize a liquid alkali metal, actually decreases with higher atomic number. In other words, the higher the atomic number, the lower the boiling and melting points. The list below lists the six alkali metals in order of atomic number, along with chemical symbol, atomic mass, melting point, and boiling point. Note that for francium, which is radioactive, the figures given are for its most stable isotope, francium-223 (223Fr)—which has a half-life of only about 21 minutes.
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Alkali Metals
ONE
1932, WITH THE DEVELOPMENT OF THE FIRST PARTISHOWN HERE ARE ITS INVENTORS, ERNEST WALTON (LEFT), ERNEST RUTHERFORD (CENTER), COCKCROFT. (Hulton-Deutsch Collection/Corbis. Reproduced by permission.)
OF THE MOST STRIKING USES OF LITHIUM OCCURRED IN
CLE ACCELERATOR. AND
JOHN
Atomic Number, Mass, and Melting and Boiling Points of the Alkali Metals: • 3. Lithium (Li), 6.941; Melting Point: 356.9°F (180.5°C); Boiling Point: 2,457°F (1,347°C) • 11. Sodium (Na), 22.99; Melting Point: 208°F (97.8°C); Boiling Point: 1,621.4°F (883°C) • 19. Potassium (K), 39.10; Melting Point: 145.9°F (63.28°C); Boiling Point: 1,398.2°F (759°C) • 37. Rubidium (Rb), 85.47; Melting Point: 102.8°F (39.31°C); Boiling Point: 1,270.4°F (688°C) • 55. Cesium (Cs), 132.9; Melting Point: 83.12°F (28.4°C); Boiling Point: 1,239.8°F (671°C) • 87. Francium (Fr), (223); Melting Point: 80.6°F (27°C); Boiling Point: 1,250.6°F (677°C)
Abundance of Alkali Metals Sodium and potassium are, respectively, the sixth and seventh most abundant elements on Earth, comprising 2.6% and 2.4% of the planet’s known elemental mass. This may not seem like much, but considering the fact that just two elements—
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oxygen and silicon—make up about 75%, and that just 16 elements make up most of the remainder, it is an impressive share. Lithium, on the other hand, is much less abundant, and therefore, figures for its part of Earth’s known elemental mass are measured in parts per million (ppm). The total lithium in Earth’s crust is about 17 ppm. Surprisingly, rubidium is more abundant, at 60 ppm; less surprisingly, cesium, with just 3 ppm, is very rare. Almost no francium is found naturally, except in very small quantities within uranium ores.
REAL-LIFE APPLICATIONS Lithium Swedish chemist Johan August Arfvedson (17921841) discovered lithium in 1817, and named it after the Greek word for “stone.” Four years later, another scientist named W. T. Brande succeeded in isolating the highly reactive metal. Most of the lithium available on Earth’s crust is bound up with aluminum and silica in minerals. Since the time of its discovery, lithium has been used in lubricants, glass, and in alloys of
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lead, aluminum, and magnesium. In glass, it acts as a strengthening agent; likewise, metal alloys that contain lithium tend to be stronger, yet less dense. In 1994, physicist Jeff Dahn of Simon Fraser University in British Columbia, Canada, developed a lithium battery. Not only was the battery cheaper to produce than the traditional variety, Dahn and his colleagues announced, but the disposal of used lithium batteries presented less danger to the environment. One of the most striking uses of lithium occurred in 1932, when English physicist John D. Cockcroft (1897-1967) and Irish physicist Ernest Walton (1903-1995) built the first particle accelerator. By bombarding lithium atoms, they produced highly energized alpha particles. This was the first nuclear reaction brought about by the use of artificially accelerated particles—in other words, without the need for radioactive materials such as uranium-235. Cockcroft’s and Walton’s experiment with lithium thus proved pivotal to the later creation of the atomic bomb. LITHIUM IN PSYCHIATRIC TREATMENT. The most important applica-
tion of lithium, however, is in treatment for the psychiatric condition once known as manic depression, today identified as bipolar disorder. Persons suffering from bipolar disorder tend toward mood swings: during some periods the patient is giddy (“manic,” or in a condition of “mania”), and during others the person is suicidal. Indeed, prior to the development of lithium as a treatment for bipolar disorder, as many as one in five patients with this condition committed suicide. Doctors do not know exactly how lithium does what it does, but it obviously works: between 70% and 80% of patients with the bipolar condition respond well to treatment, and are able to go on with their lives in such a way that their condition is no longer outwardly evident. Lithium is also administered to patients who suffer unipolar depression and some forms of schizophrenia. EARLY MEDICINAL USES OF LITHIUM. It is said that the great Greco-
Roman physician Galen ( 129-c. 199) counseled patients suffering from “mania” to bathe in, and even drink the water from, alkaline springs. If so, he was nearly 2,000 years ahead of his time. Even in the 1840s, not long after lithium was discovered, the mineral—mixed with carbonate or cit-
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rate—was touted as a cure for insomnia, gout, epilepsy, diabetes, and even cancer.
Alkali Metals
None of these alleged cures proved a success; nor did a lithium chloride treatment administered in the 1940s as a salt substitute for patients on low-sodium diets. As it turned out, when not enough sodium is present, the body experiences a buildup of sodium’s sister element, lithium. The result was poisoning, which in some cases proved fatal. CADE’S BREAKTHROUGH. Then in 1949, Australian psychiatrist John Cade discovered the value of lithium for psychiatric treatment. He approached the problem from an entirely different angle, experimenting with uric acid, which he believed to be a cause of manic behavior. In administering the acid to guinea pigs, he added lithium salts merely to keep the uric acid soluble—and was very surprised by what he discovered. The uric acid did not make the guinea pigs manic, as he had expected; instead, they became exceedingly calm.
Cade changed the focus of his research, and tested lithium treatment on ten manic patients. Again, the results were astounding: one patient who had suffered from an acute bipolar disorder (as it is now known) for five years was released from the hospital after three months of lithium treatment, and went on to lead a healthy, normal life. Encouraged by the changes he had seen in patients who received lithium, Cade published a report on his findings in the Medical Journal of Australia, but his work had little impact at the time. Nor did the idea of lithium treatment meet with an enthusiastic reception on the other side of the Pacific: in the aftermath of the failed experiments with lithium as a sodium substitute in the 1940s, stories of lithium poisoning were widespread in the United States. LITHIUM TODAY. Were it not for the efforts of Danish physician Mogens Schou, lithium might never have taken hold in the medical community. During the 1950s and 1960s, Schou campaigned tirelessly for recognition of lithium as a treatment for manic-depressive illness. Finally during the 1960s, the U.S. Food and Drug Administration began conducting trials of lithium, and approved its use in 1974. Today some 200,000 Americans receive lithium treatments.
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A non-addictive and non-sedating medication, lithium—as evidenced by the failed experiment in the 1940s—may still be dangerous in large quantities. It is absorbed quickly into the bloodstream and carried to all tissues in the brain and body before passing through the kidneys. Both lithium and sodium are excreted through the kidneys, and since sodium affects lithium excretion, it is necessary to maintain a proper quantity of sodium in the body. For this reason, patients on lithium are cautioned to avoid a low-salt diet.
Sodium Sodium compounds had been known for some time prior to 1807, when English chemist Sir Humphry Davy (1778-1829) succeeded in isolating sodium itself. The element is represented by a chemical symbol (Na), reflecting its Latin name, natrium. In its pure form, sodium has a bright, shiny surface, but in order to preserve this appearance, it must be stored in oil: sodium reacts quickly with oxygen, forming a white crust of sodium oxide. Pure sodium never occurs in nature; instead, it combines readily with other substances to form compounds, many of which are among the most widely used chemicals in industry. It is also highly soluble: thus whereas sodium and potassium occur in crystal rocks at about the same ratio, sodium is about 30 times more abundant in seawater than its sister element. OBTAINING SODIUM CHLORIDE. Though the extraction of sodium
involves the use of a special process, the metal is plentiful in the form of sodium chloride—better known as table salt. In fact, the term salt in chemistry refers generally to any combination of a metal with a nonmetal. More specifically, salts are (along with water) the product of reactions between acids and bases. Sodium chloride is so easy to obtain, and therefore so cheap, that most industries making other sodium compounds use it, simply separating out the chloride (as described below) before adding other elements. The United States is the world’s largest producer of sodium chloride, obtained primarily from brine, a term used to describe any solution of sodium chloride in water. Brine comes from seawater, subterranean wells, and desert lakes, such as the Great Salt Lake in Utah. Another source of sodium chloride is
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rock salt, created underground by the evaporation of long-buried saltwater seas. Other top sodium-chloride-producing nations include China, Germany, Great Britain, France, India, and various countries in the former Soviet Union. Salt may be cheap and plentiful for the world in general, but there are places where it is a precious commodity. One such place is the Sahara Desert, where salt caravans ply a brisk trade today, much as they have since ancient times. ISOLATING SODIUM. Modern methods for the production of sodium represent an improvement in the technique Davy used in 1807, although the basic principle is the same. Though several decades passed before electricity came into widespread public use, scientists had been studying its properties for years, and Davy applied it in a process called electrolysis.
Electrolysis is the use of an electric current to produce a chemical reaction—in this case, to separate sodium from the other element or elements with which it is combined. Davy first fused or melted a sample of sodium chloride, then electrolyzed it. Using an electrode, a device that conducts electricity and is used to emit or collect electric charge, he separated the sodium chloride in such a way that liquid sodium metal collected on the cathode, or negatively charged end. Meanwhile, the gaseous chlorine was released through the anode, or the positively charged end. The apparatus used for sodium separation today is known as the Downs cell, after its inventor, J. C. Downs. In a Downs cell, sodium chloride and calcium chloride are combined in a molten mixture in which the presence of calcium chloride lowers the melting point of the sodium chloride by more than 30%. When an electric current is passed through the mixture, sodium ions move to the cathode, where they pick up electrons to become sodium atoms. At the same time, ions of chlorine migrate to the anode, losing electrons to become chlorine atoms. Sodium is a low-density material that floats on water, and in the Downs cell, the molten sodium rises to the top, where it is drawn off. The chlorine gas is allowed to escape through a vent at the top of the anode end of the cell, and the resulting sodium metal—that is, the elemental form of sodium—is about 99.8% pure. USES FOR SODIUM CHLORIDE.
As indicated earlier, sodium chloride is by far the most widely known and commonly used sodium
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compound—and this in itself is a distinction, given the fact that so many sodium compounds are a part of daily life. Today people think of salt primarily as a seasoning to enhance the taste of food, but prior to the development of refrigeration, it was vital as a preservative because it kept microbes away from otherwise perishable food items. Salt does not merely improve the taste of food; it is an essential nutrient. Sodium compounds regulate transmission of signals through the nervous system, alter the permeability of membranes, and perform a number of other lifepreserving functions. On the other hand, too much salt can aggravate high blood pressure. Thus, since the 1970s and 1980s, food manufacturers have increasingly offered products low in sodium, a major selling point for health-conscious consumers. OTHER SODIUM COMPOUNDS.
In addition to its widespread use in consumer goods, sodium chloride is the principal source of sodium used in making other sodium compounds. These include sodium hydroxide, for manufacturing cellulose products such as film, rayon, soaps, and paper, and for refining petroleum. In its application as a cleaning solution, sodium hydroxide is known as caustic soda or lye. Another widely used sodium compound is sodium carbonate or, soda ash, applied in glassmaking, paper production, textile manufacturing, and other areas, such as the production of soaps and detergents. Sodium also can be combined with carbon to produce sodium bicarbonate, or baking soda. Sodium sulfate, sometimes known as salt cake, is used for making cardboard and kraft paper. Yet another widely used sodium compound is sodium silicate, or “water glass,” used in the production of soaps, detergents, and adhesives; in water treatment; and in bleaching and sizing of textiles. Still other sodium compounds used by industry and/or consumers include sodium borate, or borax; sodium tartrate, or sal tartar; the explosive sodium nitrate, or Chilean saltpeter; and the food additive monosodium glutamate (MSG). Perhaps ironically, there are few uses for pure metallic sodium. Once applied as an “anti-knock” additive in leaded gasoline, before those products were phased out for environmental reasons, metallic sodium is now used
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as a heat-exchange medium in nuclear reactors. But its widest application is in the production of the many other sodium compounds used around the world.
Alkali Metals
Potassium In some ways, potassium is a strange substance, as evidenced by its behavior in response to water. As everyone knows, water tends to put out a fire, and most explosives, when exposed to sufficient quantities of water, become ineffective. Potassium, on the other hand, explodes in contact with water and reacts violently with ice at temperatures as low as -148°F (-100°C). In a complete reversal of the procedures normally followed for most substances, potassium is stored in kerosene, because it might burst into flames if exposed to moist air! Many aspects of potassium mirror those already covered with regard to sodium. The two have a number of the same applications, and in certain situations, potassium is used as a sodium substitute. Like sodium, potassium is never found alone in nature; instead, it comes primarily from sylvinite and carnalite, two ores containing potassium chloride. Also, like sodium, potassium was first isolated in 1807 by Davy, using the process of electrolysis described above. A few years later, a German chemist dubbed the newly isolated element “kalium,” apparently a derivation of the Arabic qali, for “alkali”; hence the use of K as the chemical symbol for potassium. USES FOR POTASSIUM. Potassium
has another similarity with sodium; although it was not isolated until the early nineteenth century, its compounds have been in use for many centuries. The Romans, for instance, used potassium carbonate, or potash, obtained from the ashes of burned wood, to make soap. During the Middle Ages, the Chinese applied a form of saltpeter, potassium nitrate, in making gunpowder. And in colonial America, potash went into the production of soap, glass, and other products. The production of just one ton of potash required the burning of several acres’ worth of trees—a wasteful practice in more ways than one. Though there was no environmentalist movement in those days, financial concerns never go out of style. In order to save the money lost by using up vast acres of timber, American industry in the nineteenth century sought another means of making potash. The many similarities between
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IN THE SAHARA DESERT, SALT HERE, TRADERS IN MALI LOAD
CARAVANS PLY A BRISK TRADE TODAY, MUCH AS THEY HAVE SINCE ANCIENT TIMES. A CAMEL FOR A SALT CARAVAN. (Nik Wheeler/Corbis. Reproduced by permission.)
sodium and potassium provided a key, and the substitution of sodium carbonate for potassium carbonate saved millions of trees. In 1847, German chemist Justus von Liebig (1803-1873) discovered potassium in living tis-
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sues. As a result, scientists became aware of the role this alkali metal plays in sustaining life: indeed, potassium is present in virtually all living cells. In the human body, potassium—which accounts for only 0.4% of the body’s mass—is
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Alkali Metals
KEY TERMS The elements in
mass. Isotopes may be either stable or
Group 1 of the periodic table of elements,
unstable—that is, radioactive. Such is the
with the exception of hydrogen. The alkali
case with francium, a radioactive member
metals, which include lithium, sodium,
of the alkali metals family.
ALKALI
METALS:
potassium, rubidium, cesium, and francium, all have one valence electron in the s1 orbital, and are highly reactive.
ORBITAL:
A pattern of probabilities
regarding the position of an electron for an atom in a particular energy state. The six
ANODE: An electrode at the positively
alkali metals all have valence electrons in
charged end of a supply of electric current.
an s1 orbital, which describes a more or less
BRINE:
A term used to describe any
solution of sodium chloride in water.
spherical shape. PERIODIC TABLE OF ELEMENTS: A
CATHODE: An electrode at the negative-
chart that shows the elements arranged in
ly charged end of a supply of electric cur-
order of atomic number. Vertical columns
rent.
within the periodic table indicate groups The positive ion that results
or “families” of elements with similar
when an atom loses one or more electrons.
chemical characteristics; the alkali metals
All of the alkali metals tend to form +1
occupy Group 1.
CATION:
cations (pronounced KAT-ie-un).
RADIOACTIVITY:
A term describing a
ELECTRODE: A structure, often a metal
phenomenon whereby certain materials
plate or grid, that conducts electricity, and
are subject to a form of decay brought
which is used to emit or collect electric
about by the emission of high-energy par-
charge.
ticles. “Decay” in this sense does not mean
ELECTROLYSIS: The use of an electric
“rot”; instead, radioactive isotopes contin-
current to cause a chemical reaction.
ue changing into other isotopes until they
HALF-LIFE: The length of time it takes a
become stable.
substance to diminish to one-half its initial
SALT:
amount.
water, by the reaction of an acid and a base.
ION:
An atom or group of atoms that has
A compound formed, along with
Generally, salts are any compounds that
lost or gained one or more electrons, and
bring together a metal and a nonmetal.
thus has a net electric charge.
VALENCE
ISOTOPES: Atoms that have an equal
that occupy the highest energy levels in an
number of protons, and hence are of the
atom, and which are involved in chemical
same element, but differ in their number of
bonding. The alkali metals all have one
neutrons. This results in a difference of
valence electron, in the s1 orbital.
S C I E N C E O F E V E R Y D AY T H I N G S
ELECTRONS:
Electrons
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essential to the functioning of muscles. In larger quantities, however, it can be dangerous, causing a state of permanent relaxation known as potassium inhibition. Since plants depend on potassium for growth, it was only logical that potassium, in the form of potassium chloride, was eventually applied as a fertilizer. This, at least, distinguishes it from its sister element: sodium, or sodium chloride, which can kill plants if administered to the soil in large enough quantities. Another application of potassium is in the area pioneered by the Chinese about 800 years ago: the manufacture of fireworks and gunpowder from potassium nitrate. Like ammonium nitrate, made infamous by its use in the 1993 World Trade Center bombing and the Oklahoma City bombing in 1995, potassium nitrate doubles as a fertilizer.
Rubidium, Cesium, and Francium The three heaviest alkali metals are hardly household names, though one of them, cesium, does have several applications in industry. Rubidium and cesium, discovered in 1860 by German chemist R. W. Bunsen (1811-1899) and German physicist Gustav Robert Kirchhoff (1824-1887), were the first elements ever found using a spectroscope. Matter emits electromagnetic radiation along various spectral lines, which can be recorded using a spectroscope and then analyzed to discern the particular “fingerprint” of the substance in question. When Bunsen and Kirchhoff saw the bluish spectral lines emitted by one of the two elements, they named it cesium, after a Latin word meaning “sky blue.” Cesium, which is very rare, appears primarily in compounds such as pollucite. It is used today in photoelectric cells, military infrared lamps, radio tubes, and video equipment. During the 1940s, American physicist Norman F. Ramsey, Jr. (1915-) built a highly accurate atomic clock based on the natural frequencies of cesium atoms.
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Rubidium, by contrast, has far fewer applications, and those are primarily in areas of scientific research. On Earth it is found in pollucite, lepidolite, and carnallite. It is considerably more abundant than cesium, and vastly more so than francium. Indeed, it is estimated that if all the francium in Earth’s crust were combined, it would have a mass of about 25 grams. Francium was discovered in 1939 by French physicist Marguerite Perey (1909-1975), student of the famous French-Polish physicist and chemist Marie Curie (1867-1934). For about four decades, scientists had been searching for the mysterious Element 87, and while studying the decay products of an actinium isotope, actinium227, Perey discovered that one out of 100 such atoms decayed to form the undiscovered element. She named it francium, after her homeland. Though the discovery of francium solved a mystery, the element has no known uses outside of its applications in research.
WHERE TO LEARN MORE “Alkali Metals” (Web site). (May 24, 2001). “Alkali Metals” ChemicalElements.com (Web site). (May 24, 2001). “Hydrogen and the Alkali Metals.” University of Colorado Department of Physics (Web site). (May 24, 2001). Kerrod, Robin. Matter and Materials. Illustrated by Terry Hadler. Tarrytown, N.Y.: Benchmark Books, 1996. Mebane, Robert C. and Thomas R. Rybolt. Metals. Illustrated by Anni Matsick. New York: Twenty-First Century Books, 1995. Oxlade, Chris. Metal. Chicago, IL: Heinemann Library, 2001. Snedden, Robert. Materials. Des Plaines, IL: Heinemann Library, 1999. “Visual Elements: Group I—The Alkali Metals” (Web site). (May 24, 2001).
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Alkaline Earth Metals
ALK ALINE E A R T H M E TA L S
CONCEPT The six alkaline earth metals—beryllium, magnesium, calcium, strontium, barium, and radium—comprise Group 2 on the periodic table of elements. This puts them beside the alkali metals in Group 1, and as their names suggest, the two families share a number of characteristics, most notably their high reactivity. Also, like the alkali metals, or indeed any other family on the periodic table, not all members of the alkali metal family are created equally in terms of their abundance on Earth or their usefulness to human life. Magnesium and calcium have a number of uses, ranging from building and other structural applications to dietary supplements. In fact, both are significant components in the metabolism of living things—including the human body. Barium and beryllium have numerous specialized applications in areas from jewelry to medicine, while strontium is primarily used in fireworks. Radium, on the other hand, is rarely used outside of laboratories, in large part because its radioactive qualities pose a hazard to human life.
HOW IT WORKS Defining a Family The expression “families of elements” refers to groups of elements on the periodic table that share certain characteristics. These include (in addition to the alkaline earth metals and the alkali metals) the transition metals, halogens, noble gases, lanthanides, and actinides. (All of these are covered in separate essays within this book.) In addition, there are several larger categories with regard to shared traits that often cross
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family lines; thus all elements are classified either as metals, metalloids, and nonmetals. (These are also discussed in separate essays, which include reference to “orphans,” or elements that do not belong to one of the families mentioned above.) These groupings, both in terms of family and the broader divisions, relate both to external, observable characteristics, as well as to behaviors on the part of electrons in the elements’ atomic structures. For instance, metals, which comprise the vast majority of elements on the periodic table, tend to be shiny, hard, and malleable (that is, they can bend without breaking.) Many of them melt at fairly high temperatures, and virtually all of them vaporize (become gases) at high temperatures. Metals also form ionic bonds, the tightest form of chemical bonding. ELECTRON CONFIGURATIONS OF THE ALKALINE EARTH METALS.
Where families are concerned, there are certain observable properties that led chemists in the past to group the alkaline earth metals together. These properties will be discussed with regard to the alkaline earth metals, but another point should be stressed in relation to the division of elements into families. With the advances in understanding that followed the discovery of the electron in 1897, along with the development of quantum theory in the early twentieth century, chemists developed a more fundamental definition of family in terms of electron configuration. As noted, the alkaline earth metal family occupies the second group, or column, in the periodic table. All elements in a particular group, regardless of their apparent differences, have a common pattern in the configuration of their
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DURING WORLD WAR II,
MAGNESIUM WAS HEAVILY USED IN AIRCRAFT COMPONENTS. IN THIS
ERS POUR MOLTEN MAGNESIUM INTO A CAST AT THE
1941 PHOTO, WORKWRIGHT AERONAUTICAL CORPORATION. (Bettmann/Corbis. Reproduced
by permission.)
valence electrons—the electrons at the “outside” of the atom, involved in chemical bonding. (By contrast, the core electrons, which occupy lower regions of energy within the atom, play no role in the bonding of elements.) All members of the alkaline earth metal family have a valence electron configuration of s2. This means that two electrons are involved in chemical bonding, and that these electrons move through an orbital, or range of probabilities, roughly corresponding to a sphere. The s orbital pattern corresponds to the first of several sublevels within a principal energy level. Whatever the number of the principal energy level which corresponds to the period, or row,
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on the periodic table the atom has the same number of sublevels. Thus beryllium, on Period 2, has two principal energy levels, and its valence electrons are in sublevel 2s2. At the other end of the group is radium, on Period 7. Though radium is far more complex than beryllium, with seven energy levels instead of two, nonetheless it has the same valence electron configuration, only on a higher energy level: 7s2. HELIUM AND THE ALKALINE EARTH METALS. If one studies the valence
electron configurations of elements on the periodic table, one notices an amazing symmetry and order. All members of a group, though their principal energy levels differ, share characteristics in
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their valence shell patterns. Furthermore, for the eight groups numbered in the North American version of the periodic table, the group number corresponds to the number of valence electrons. There is only one exception: helium, with a valence electron configuration of 1s2, is normally placed in Group 8 with the noble gases. Based on that s2 configuration, it might seem logical to place helium atop beryllium in the alkaline earth metals family; but there are several reasons why this is not done. First of all, helium is obviously not a metal. More importantly, helium behaves in a manner quite different from that of the alkaline earth metals. Whereas helium, like the rest of the noble gases, is highly resistant to chemical reactions and bonding, alkaline earth metals are known for their high reactivity—that is, a tendency for bonds between atoms or molecules to be made or broken so that materials are transformed. (A similar relationship exists in Group 1, which includes hydrogen and the alkali metals. All have the same valence configuration, but hydrogen is never included as a member of the alkali metals family.)
Characteristics of the Alkaline Earth Metals Like the alkali metals, the alkaline earth metals have the properties of a base, as opposed to an acid. The alkaline earth metals are shiny, and most are white or silvery in color. Like their “cousins” in the alkali metal family, they glow with characteristic colors when heated. Calcium glows orange, strontium a very bright red, and barium an apple green. Physically they are soft, though not as soft as the alkali metals, many of which can be cut with a knife.
metal hydroxide, though their reactions are less pronounced than those of the alkali metals. Magnesium metal in its pure form is combustible, and when exposed to air, it burns with an intense white light, combining with the oxygen to produce magnesium oxide. Likewise calcium, strontium, and barium react with oxygen to form oxides. Due to their high levels of reactivity, the alkaline earth metals rarely appear by themselves in nature; rather, they are typically found with other elements in compound form, often as carbonates or sulfates. This, again, is another similarity with the alkali metals. But whereas the alkali metals tend to form 1+ cations (positively charged atoms), the alkaline earth metals form 2+ cations—that is, cations with a positive charge of 2. BOILING AND MELTING POINTS. One way that the alkaline earth met-
als are distinguished from the alkali metals is with regard to melting and boiling points—those temperatures, respectively, at which a solid metal turns into a liquid, and a liquid metal into a vapor. For the alkali metals, the temperatures of the boiling and melting points decrease with an increase in atomic number. The pattern is not so clear, however, for the alkaline earth metals. The highest melting and boiling points are for beryllium, which indeed has the lowest atomic number. It melts at 2,348.6°F (1,287°C), and boils at 4,789.8°F (2,471°C). These figures are much higher than for lithium, the alkali metal on the same period as beryllium, which melts at 356.9°F (180.5°C) and boils at 2,457°F (1,347°C).
Yet another similarity the alkaline earth metals have with the alkali metals is the fact that four of the them—magnesium, calcium, strontium, and barium—were either identified or isolated in the first decade of the nineteenth century by English chemist Sir Humphry Davy (1778-1829). Around the same time, Davy also isolated sodium and potassium from the alkali metal family.
Magnesium, the second alkali earth metal, melts at 1,202°F (650°C), and boils at 1,994°F (1,090°C)—significantly lower figures than for beryllium. However, the melting and boiling points are higher for calcium, third of the alkaline earth metals, with figures of 1,547.6°F (842°C) and 2,703.2°F (1,484°C) respectively. Melting and boiling temperatures steadily decrease as energy levels rise through strontium, barium, and radium, yet these temperatures are never lower than for magnesium.
REACTIVITY. The alkaline earth metals are less reactive than the alkali metals, but like the alkali metals they are much more reactive than most elements. Again like their “cousins,” they react with water to produce hydrogen gas and the
ABUNDANCE. Of the alkaline earth metals, calcium is the most abundant. It ranks fifth among elements in Earth’s crust, accounting for 3.39% of the elemental mass. It is also fifth most abundant in the human body, with a share
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MANY
ALKALINE EARTH METALS ARE USED IN THE PRODUCTION OF FIREWORKS. (Bill Ross/Corbis. Reproduced by permission.)
of 1.4%. Magnesium, which makes up 1.93% of Earth’s crust, is the eighth most abundant element on Earth. It ranks seventh in the human body, accounting for 0.50% of the body’s mass. Barium ranks seventeenth among elements in Earth’s crust, though it accounts for only 0.04% of the elemental mass. Neither it nor the other three alkali metals appear in the body in significant quantities: indeed, barium and beryllium are poisonous, and radium is so radioactive that exposure to it can be extremely harmful.
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Within Earth’s crust, strontium is present in quantities of 360 parts per million (ppm), which in fact is rather abundant compared to a number of elements. In the ocean, its presence is about 8 ppm. By contrast, the abundance of beryllium in Earth’s crust is measured in parts per billion (ppb), and is estimated at 1,900 ppb. Vastly more rare is radium, which accounts for just 0.6 parts per trillion of Earth’s crust—a fact that made its isolation by French-Polish physicist and chemist Marie Curie (1867-1934) all the more impressive.
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REAL-LIFE AP P LICATIONS Beryllium In the eighteenth century, French mineralogist René Just-Haüy (1743-1822) had observed that both emeralds and the mineral beryl had similar properties. French chemist Louis-Nicolas Vauquelin (1763-1829) in 1798 identified the element they had in common: beryllium (Be), which has an atomic number of 4 and an atomic mass of 9.01 amu. Some three decades passed before German chemist Friedrich Wöhler (18001882) and French chemist Antoine Bussy (17941882), working independently, succeeded in isolating the element. Beryllium is found primarily in emeralds and aquamarines, both precious stones that are forms of the beryllium alluminosilicate compound beryl. Though it is toxic to humans, beryllium nonetheless has an application in the health-care industry: because it lets through more x rays than does glass, beryllium is often used in x-ray tubes. Metal alloys that contain about 2% beryllium tend to be particularly strong, resistant to wear, and stable at high temperatures. Copperberyllium alloys, for instance, are applied in hand tools for industries that use flammable solvents, since tools made of these alloys do not cause sparks when struck against one another. Alloys of beryllium and nickel are applied for specialized electrical connections, as well as for high-temperature uses.
Magnesium English botanist and physician Nehemiah Grew (1641-1712) in 1695 discovered magnesium sulfate in the springs near the English town of Epsom, Surrey. This compound, called “Epsom salts” ever since, has long been noted for its medicinal value. Epsom salts are used for treating eclampsia, a condition that causes seizures in pregnant women. The compound is also a powerful laxative, and is sometimes used to rid the body of poisons—such as magnesium’s sister element, barium. For some time, scientists confused the oxide compound magnesia with lime or calcium carbonate, which actually involves another alkaline earth metal. In 1754, Scottish chemist and physi-
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cist Joseph Black (1728-1799) wrote “Experiments Upon Magnesia, Alba, Quick-Lime, and Some Other Alkaline Substances,” an important work in which he distinguished between magnesia and lime. Davy in 1808 declared magnesia the oxide of a new element, which he dubbed magnesium, but some 20 years passed before Bussy succeeded in isolating the element.
Alkaline Earth Metals
Magnesium (Mg) has an atomic number of 12, and an atomic mass of 24.31 amu. It is found primarily in minerals such as dolomite and magnesite, both of which are carbonates; and in carnallite, a chloride. Magnesium silicates include asbestos, soapstone or talc, and mica. Not all forms of asbestos contain magnesium, but the fact that many do only serves to show the ways that chemical reactions can change the properties an element possesses in isolation. AN IMPORTANT COMPONENT OF HEALTH. Whereas magnesium is flam-
mable, asbestos was once used in large quantities as a flame retardant. And whereas asbestos has been largely removed from public buildings throughout the United States due to reports linking asbestos exposure with cancer, magnesium is an important component in the health of living organisms. It plays a critical role in chlorophyll, the green pigment in plants that captures energy from sunlight, and for this reason, it is also used in fertilizers. In the human body, magnesium ions (charged atoms) aid in the digestive process, and many people take mineral supplements containing magnesium, sometimes in combination with calcium. There is also its use as a laxative, already mentioned. Epsom salts, as befits their base or alkaline quality, are exceedingly bitter—the kind of substance a person only ingests under conditions of the most dire necessity. On the other hand, milk of magnesia is a laxative with a far less unpleasant taste. MAGNESIUM GOES TO WAR. It is a hallmark of magnesium’s chemical versatility that the same element, so important in preserving life, has also been widely used in warfare. Just before World War I, Germany was a leading manufacturer of magnesium, thanks in large part to a method of electrolysis developed by German chemist R. W. Bunsen (1811-1899). When the United States went to war against Germany, American companies began producing magnesium in large quantities.
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Bunsen had discovered that powdered magnesium burns with a brilliant white flame, and in the war, magnesium was used in flares, tracer bullets, and incendiary bombs, which ignite and burn upon impact. The bright light produced by burning magnesium has also led to a number of peacetime applications—for instance, in fireworks, and for flashes used in photography. Magnesium saw service in another world war. By the time Nazi tanks rolled into Poland in 1939, the German military-industrial complex had begun using the metal for building aircraft and other forms of military equipment. America once again put its own war-production machine into operation, dramatically increasing magnesium output to a peak of nearly 184,000 tons (166,924,800 kg) in 1943. STRUCTURAL
APPLICATIONS.
Magnesium’s principal use in World War I was for its incendiary qualities, but in World War II it was primarily used as a structural metal. It is lightweight, but stronger per unit of mass than any other common structural metal. As a metal for building machines and other equipment, magnesium ranks in popularity only behind iron and aluminum (which is about 50% more dense than magnesium). The automobile industry is one area of manufacturing particularly interested in magnesium’s structural qualities. On both sides of the Atlantic, automakers are using or testing vehicle parts made of alloys of magnesium and other metals, primarily aluminum. Magnesium is easily cast into complex structures, which could mean a reduction in the number of parts needed for building a car—and hence a streamlining of the assembly process. Among the types of sports equipment employing magnesium alloys are baseball catchers’ masks, skis, racecars, and even horseshoes. Various brands of ladders, portable tools, electronic equipment, binoculars, cameras, furniture, and luggage also use parts made of this lightweight, durable metal.
Calcium Davy isolated calcium (Ca) by means of electrolysis in 1808. The element, whose name is derived from the Latin calx, or “lime,” has an atomic number of 20, and an atomic mass of 40.08. The principal sources of calcium are limestone and
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dolomite, both of which are carbonates, as well as the sulfate gypsum. In the form of limestone and gypsum, calcium has been used as a building material since ancient times, and continues to find application in that area. Lime is combined with clay to make cement, and cement is combined with sand and water to make mortar. In addition, when mixed with sand, gravel, and water, cement makes concrete. Marble—once used to build palaces and today applied primarily for decorative touches— also contains calcium. The steel, glass, paper, and metallurgical industries use slaked lime (calcium hydroxide) and quicklime, or calcium oxide. It helps remove impurities from steel, and pollutants from smokestacks, while calcium carbonate in paper provides smoothness and opacity to the finished product. When calcium carbide (CaC2) is added to water, it produces the highly flammable gas acetylene (C2H2), used in welding torches. In various compounds, calcium is used as a bleach; a material in the production of fertilizers; and as a substitute for salt as a melting agent on icy roads. The food, cosmetic, and pharmaceutical industries use calcium in antacids, toothpaste, chewing gum, and vitamins. To an even greater extent than magnesium, calcium is important to living things, and is present in leaves, bone, teeth, shells, and coral. In the human body, it helps in the clotting of blood, the contraction of muscles, and the regulation of the heartbeat. Found in green vegetables and dairy products, calcium (along with calcium supplements) is recommended for the prevention of osteoporosis. The latter, a condition involving a loss of bone density, affects elderly women in particular, and causes bones to become brittle and break easily.
Strontium Irish chemist and physician Adair Crawford (1748-1795) and Scottish chemist and surgeon William Cumberland Cruikshank (1790-1800) in 1790 discovered what Crawford called “a new species of earth” near Strontian in Scotland. A year later, English chemist Thomas Charles Hope (1766-1844) began studying the ore found by Crawford and Cruikshank, which they had dubbed strontia. In reports produced during 1792 and 1793, Hope explained that strontia could be distinguished from lime or calcium hydroxide on the
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Alkaline Earth Metals
IN
THIS
1960
PHOTO, A MOTHER TESTS HER SON’S MILK FOR SIGNS OF RADIOACTIVITY, THE RESULT OF NUCLEAR
WEAPONS TESTING DURING THE
1950S
THAT INVOLVED THE RADIOACTIVE ISOTOPE STRONTIUM-90.
THE
ISOTOPE
FELL TO EARTH IN A FINE POWDER, WHERE IT COATED THE GRASS, WAS INGESTED BY COWS, AND EVENTUALLY WOUND UP IN THE MILK THEY PRODUCED. (Bettmann/Corbis. Reproduced by permission.)
one hand, and baryta or barium hydroxide on the other, by virtue of its response to flame tests. Whereas calcium produced a red flame and barium a green one, strontia glowed a brilliant red easily distinguished from the darker red of calcium. Once again, it was Davy who isolated the new element, using electrolysis, in 1808. Subsequently dubbed strontium (Sr), its atomic number is 38, and its atomic mass 87.62. Silvery white, it oxidizes rapidly in air, forming a pale yellow oxide crust on any freshly cut surface. Though it has properties similar to those of calcium, the comparative rarity of strontium and the expense involved in extracting it offer no economic incentives for using it in place of its much more abundant sister element. Nonetheless, strontium does have a few uses, primarily because of its brilliant crimson flame. Therefore it is applied in the making of fireworks, signal flares, and tracer bullets—that is, rounds that emit a light as they fly through the air. One of the more controversial “applications” of strontium involved the radioactive isotope strontium-90, a by-product of nuclear weapons testing in the atmosphere from the late 1940s
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onward. The isotope fell to earth in a fine powder, coated the grass, was ingested by cows, and eventually wound up in the milk they produced. Because of its similarities to calcium, the isotope became incorporated into the teeth and gums of children who drank the milk, posing health concerns that helped bring an end to atmospheric testing in the early 1960s.
Barium Aspects of barium’s history are similar to those of other alkaline earth metals. During the eighteenth century, chemists were convinced that barium oxide and calcium oxide constituted the same substance, but in 1774, Swedish chemist Carl Wilhelm Scheele (1742-1786) demonstrated that barium oxide was a distinct compound. Davy isolated the element, as he did two other alkaline earth metals, by means of electrolysis, in 1808. Barium (Ba) has an atomic mass of 137.27 and an atomic number of 56. It appears primarily in ores of barite, a sulfate, and witherite, a carbonate. Barium sulfate is used as a white pigment in paints, while barium carbonate is applied in the production of optical glass, ceramics, glazed
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Alkaline Earth Metals
KEY TERMS ALKALINE EARTH METALS: Group 2
ION:
on the periodic table of elements, with
lost or gained one or more electrons, and
valence electron configurations of ns2. The
thus has a net electric charge.
six alkaline earth metals, all of which are
ISOTOPES: Atoms that have an equal
highly reactive chemically, are beryllium,
number of protons, and hence are of the
magnesium, calcium, strontium, barium,
same element, but differ in their number of
and radium.
neutrons. This results in a difference of
ALKALI
METALS:
The elements in
Group 1 of the periodic table of elements, with the exception of hydrogen. The alkali metals all have one valence electron in the s1 orbital, and are highly reactive.
An atom or group of atoms that has
mass. Isotopes may be either stable or unstable—that is, radioactive. Such is the case with the isotopes of radium, a radioactive member of the alkaline earth metals family. ORBITAL:
CATION:
The positive ion that results
when an atom loses one or more electrons.
regarding the position of an electron for an atom in a particular energy state. The six
All of the alkaline earth metals tend to
alkaline earth metals all have valence elec-
form 2+ cations (pronounced KAT-ie-
trons in an s2 orbital, which describes a
unz).
more or less spherical shape.
ELECTROLYSIS: The use of an electric
PERIODS: Rows of the periodic table of
current to cause a chemical reaction.
elements. These represent successive prin-
pottery, and specialty glassware. One of its most important uses is as a drill-bit lubricant—known as a “mud” or slurry—for oil drilling. Like a number of its sister elements, barium (in the form of barium nitrate) is used in fireworks and flares. Motor oil detergents for keeping engines clean use barium oxide and barium hydroxide. Beryllium is not the only alkaline earth metal used in making x rays, nor is magnesium the only member of the family applied as a laxative. Barium is used in enemas, and barium sulfate is used to coat the inner lining of the intestines to allow a doctor to examine a patient’s digestive system. (Though barium is poisonous, in the form of barium sulfate it is safe for ingestion because the compound does not dissolve in water or other bodily fluids.) Prior to receiving x rays, a patient may be instructed to drink a chalky barium sulfate liquid, which absorbs a great deal of the radiation emitted by the x-ray
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A pattern of probabilities
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machine. This adds contrast to the black-andwhite x-ray photo, enabling the doctor to make a more informed diagnosis.
Radium Today radium (Ra; atomic number 88; atomic mass 226 amu) has few uses outside of research; nonetheless, the story of its discovery by Marie Curie and her husband Pierre (1859-1906), a French physicist, is a compelling chapter not only in the history of chemistry, but of human endeavor in general. Inspired by the discovery of uranium’s radioactive properties by French physicist Henri Becquerel (1852-1908), Marie Curie became intrigued with the subject of radioactivity, on which she wrote her doctoral dissertation. Setting out to find other radioactive elements, she and Pierre refined a large quantity of pitchblende, an ore commonly found in uranium mines. Within a year, they had discovered
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KEY TERMS
Alkaline Earth Metals
CONTINUED
cipal energy levels in the atoms of the ele-
broken in such a way that materials are
ments involved.
transformed.
PRINCIPAL ENERGY LEVEL: A value
SALT:
indicating the distance that an electron
that brings together a metal and a non-
may move away from the nucleus of an
metal. More specifically, salts (along with
atom. This is designated by a whole-num-
water) are the product of a reaction
ber integer, beginning with 1 and moving
between an acid and a base.
upward. The higher the principal energy
SHELL:
level, the greater the energy in the atom,
same principal energy level.
and the more complex the pattern of
SUBLEVEL: A region within the princi-
orbitals.
pal energy level occupied by electrons in an
Generally speaking, a compound
A group of electrons within the
A term describing a
atom. Whatever the number n of the prin-
phenomenon whereby certain materials
cipal energy level, there are n sublevels. At
are subject to a form of decay brought
each principal energy level, the first sublev-
about by the emission of high-energy par-
el to be filled is the one corresponding to
ticles. “Decay” in this sense does not mean
the s orbital pattern—where the alkaline
“rot”; instead, radioactive isotopes contin-
earth metals all have their valence electrons.
ue changing into other isotopes until they
VALENCE
become stable.
that occupy the highest energy levels in an
REACTIVITY: The tendency for bonds
atom, and which are involved in chemical
between atoms or molecules to be made or
bonding.
RADIOACTIVITY:
the element polonium, but were convinced that another radioactive ingredient was present— though in much smaller amounts—in pitchblende. The Curies spent most of their savings to purchase a ton of ore, and began working to extract enough of the hypothesized Element 88 for a usable sample—0.35 oz (1 g). Laboring virtually without ceasing for four years, the Curies—by then weary and in financial difficulties—finally produced the necessary quantity of radium. Their fortunes were about to improve: in 1903 they shared the Nobel Prize in physics with Becquerel, and in 1911, Marie received a second Nobel, this one in chemistry, for her discoveries of polonium and radium. She is the only individual in history to win Nobels in two different scientific categories. Because the Curies failed to patent their process, however, they received no profits from
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ELECTRONS:
Electrons
the many “radium centers” that soon sprung up, touting the newly discovered element as a cure for cancer. In fact, as it turned out, the hazards associated with this highly radioactive substance outweighed any benefits. Thus radium, which at one point was used in luminous paint and on watch dials, was phased out of use. Marie Curie’s death from leukemia in 1934 resulted from her prolonged exposure to radiation from radium and other elements. WHERE TO LEARN MORE “Alkaline Earth Metals.” ChemicalElements.com (Web site). > (May 25, 2001). “The Alkaline Earth Metals” (Web site). (May 25, 2001). Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: Houghton Mifflin, 1995.
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Kerrod, Robin. Matter and Materials. Illustrated by Terry Hadler. Tarrytown, N.Y.: Benchmark Books, 1996. Mebane, Robert C. and Thomas R. Rybolt. Metals. Illustrated by Anni Matsick. New York: Twenty-First Century Books, 1995. Oxlade, Chris. Metal. Chicago, IL: Heinemann Library, 2001.
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Snedden, Robert. Materials. Des Plaines, IL: Heinemann Library, 1999. “Visual Elements: Group 1—The Alkaline Earth Metals” (Web site). (May 25, 2001).
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T R A N S I T I O N M E TA L S
CONCEPT By far the largest family of elements is the one known as the transition metals, sometimes called transition elements. These occupy the “dip” in the periodic table between the “tall” sets of columns or groups on either side. Consisting of 10 columns and four rows or periods, the transition metals are usually numbered at 40. With the inclusion of the two rows of transition metals in the lanthanide and actinide series respectively, however, they account for 68 elements—considerably more than half of the periodic table. The transition metals include some of the most widely known and commonly used elements, such as iron—which, along with fellow transition metals nickel and cobalt, is one of only three elements known to produce a magnetic field. Likewise, zinc, copper, and mercury are household words, while cadmium, tungsten, chromium, manganese, and titanium are at least familiar. Other transition metals, such as rhenium or hafnium, are virtually unknown to anyone who is not scientifically trained. The transition metals include the very newest elements, created in laboratories, and some of the oldest, known since the early days of civilization. Among these is gold, which, along with platinum and silver, is one of several precious metals in this varied family.
HOW IT WORKS Two Numbering Systems for the Periodic Table The periodic table of the elements, developed in 1869 by Russian chemist Dmitri Ivanovitch Mendeleev (1834-1907), is discussed in several places within this volume. Within the table, ele-
S C I E N C E O F E V E R Y D AY T H I N G S
ments are arranged in columns, or groups, as well as in periods, or rows. As discussed in the Periodic Table of Elements essay, two basic versions of the chart, differing primarily in their method of number groups, are in use today. The North American system numbers only eight groups—corresponding to the representative or main-group elements—leaving the 10 columns representing the transition metals unnumbered. On the other hand, the IUPAC system, approved by the International Union of Pure and Applied Chemistry (IUPAC), numbers all 18 columns. Both versions of the periodic table show seven periods. In general, this book applies the North American system, in part because it is the version used in most American classrooms. Additionally, the North American system relates group number to the number of valence electrons in the outer shell of the atom for the element represented. Hence the number of valence electrons (a subject discussed below as it relates to the transition metals) for Group 8 is also eight. Yet where the transition metals are concerned, the North American system is less convenient than the IUPAC system. ATTEMPTS TO ADJUST THE NORTH AMERICAN SYSTEM. In
addressing the transition metals, there is no easy way to apply the North American system’s correspondence between the number of valence electrons and the group number. Some versions of the North American system do, however, make an attempt. These equate the number of valence electrons in the transition metals to a group number, and distinguish these by adding a letter “B.”
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Transition Metals
SEVERAL
PRECIOUS METALS, INCLUDING GOLD, ARE AMONG THE TRANSITION METALS. (Charles O’Rear/Corbis. Reproduced
by permission.)
Thus the noble gases are placed in Group 8A or VIIIA because they are a main-group family with eight valence electrons, whereas the transition metal column beginning with iron (Group 8 in the IUPAC system) is designated 8B or VIIIB. But this adjustment to the North American system only makes things more cumbersome, because Group VIIIB also includes two other columns—ones with nine and 10 valence electrons respectively. VALUE OF THE IUPAC SYSTEM.
Obviously, then, the North American system— while it is useful in other ways, and as noted, is applied elsewhere in this book—is not as practical for discussing the transition metals. Of course, one could simply dispense with the term “group” altogether, and simply refer to the columns on the periodic table as columns. To do so, however, is to treat the table simply as a chart, rather than as a marvelously ordered means of organizing the elements. It makes much more sense to apply the IUPAC system and to treat the transition metals as belonging to groups 3 through 12. This is particularly useful in this context, because those group numbers do correspond to the numbers of valence electrons. Scandium, in group 3 (henceforth all group numbers refer to the IUPAC ver-
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sion), has three valence electrons; likewise zinc, in Group 12, has 12. Neither the IUPAC nor the North American system provide group numbers for the lanthanides and actinides, known collectively as the inner transition metals. THE TRANSITION METALS BY IUPAC GROUP NUMBER. Here, then, is
the list of the transition metals by group number, as designated in the IUPAC system. Under each group heading are listed the four elements in that group, along with the atomic number, chemical symbol, and atomic mass figures for each, in atomic mass units. Note that, because the fourth member in each group is radioactive and sometimes exists for only a few minutes or even seconds, mass figures are given merely for the most stable isotope. In addition, the last elements in groups 8, 9, and 10, as of 2001, had not received official names. For reasons that will be explained below, lanthanum and actinium, though included here, are discussed in other essays. Group 1 • • • •
21. Scandium (Sc): 44.9559 39. Yttrium (Y): 88.9059 57. Lanthanum (La): 138.9055 89. Actinium (Ac): 227.0278
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Group 2 • • • •
Transition Metals
22. Titanium (Ti): 47.9 40. Zirconium (Zr): 91.22 72. Hafnium (Hf): 178.49 104. Rutherfordium (Rf): 261 Group 3
• • • •
23. Vanadium (V): 50.9415 41. Niobium (Nb): 92.9064 73. Tantalum (Ta): 180.9479 105. Dubnium (Db): 262 Group 4
• • • •
24. Chromium (Cr): 51.996 42. Molybdenum (Mo): 95.95 74. Tungsten (W): 183.85 106. Seaborgium (Sg): 263 Group 5
• • • •
25. Manganese (Mn): 54.938 43. Technetium (Tc): 98 75. Rhenium (Re): 186.207 107. Bohrium (Bh): 262 AN
Group 6 • • • •
26. Iron (Fe): 55.847 44. Ruthenium (Ru): 101.07 76. Osmium (Os): 190.2 108. Hassium (Hs): 265 Group 7
• • • •
27. Cobalt (Co): 58.9332 45. Rhodium (Rh): 102.9055 77. Iridium (Ir): 192.22 109. Meitnerium (Mt): 266 Group 8
• • • •
28. Nickel (Ni): 58.7 46. Palladium (Pd): 106.4 78. Platinum (Pt): 195.09 110. Ununnilium (Uun): 271 Group 9
• • • •
29. Copper (Cu): 63.546 47. Silver (Ag): 107.868 79. Gold (Au): 196.9665 111. Unununium (Uuu): 272 Group 10
• • • •
30. Zinc (Zn): 65.38 48. Cadmium (Cd): 112.41 80. Mercury (Hg): 200.59 112. Ununbium (Uub): 277
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IRON ORE MINE IN
FOURTH
MOST
ACCOUNTING FOR
SOUTH AFRICA. IRON
ABUNDANT
4.71%
ELEMENT
ON
IS THE
EARTH,
OF THE ELEMENTAL MASS IN
THE PLANET ’S CRUST. (Charles O’Rear/Corbis. Reproduced by
permission.)
Electron Configurations and the Periodic Table We can now begin to explain why transition metals are distinguished from other elements, and why the inner transition metals are further separated from the transition metals. This distinction relates not to period (row), but to group (column)—which, in turn, is defined by the configuration of valence electrons, or the electrons that are involved in chemical bonding. Valence electrons occupy the highest energy level, or shell, of the atom—which might be thought of as the orbit farthest from the nucleus. However, the term “orbit” is misleading when applied to the ways that an electron moves. Electrons do not move around the nucleus of an atom in regular orbits, like planets around the Sun; rather, their paths can only be loosely defined in terms of orbitals, a pattern of probabilities indicating the regions that an electron may occupy. The shape or pattern of orbitals is determined by the principal energy level of the
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Transition Metals
THE AMERICAN
FIVE-CENT COIN, CALLED A
“NICKEL,”
IS ACTUALLY AN ALLOY OF NICKEL AND COPPER. (Layne
Kennedy/Corbis. Reproduced by permission.)
atom, which indicates a distance that an electron may move away from the nucleus. Principal energy level defines period: elements in Period 4, for instance, all have their valence electrons at principal energy level 4. The higher the number, the further the electron is from the nucleus, and hence, the greater the energy in the atom. Each principal energy level is divided into sublevels corresponding to the number n of the principal energy level: thus, principal energy level 4 has four sublevels, principal energy level 5 has five, and so on. ORBITAL PATTERNS. The four basic
types of orbital patterns are designated as s, p, d, and f. The s shape might be described as spherical, which means that in an s orbital, the total electron cloud will probably end up being more or less like a sphere. The p shape is like a figure eight around the nucleus; the d like two figure eights meeting at the nucleus; and the f orbital pattern is so complex that most basic chemistry textbooks do not even attempt to explain it. In any case, these orbital patterns do not indicate the exact path of an electron. Think of it, instead, in this way: if you could take millions of photographs of the electron during a period of a few seconds, the
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resulting blur of images in a p orbital, for instance, would somewhat describe the shape of a figure eight. Since the highest energy levels of the transition metals begin at principal energy level 4, we will dispense with a discussion of the first three energy levels. The reader is encouraged to consult the Electrons essay, as well as the essay on Families of Elements, for a more detailed discussion of the ways in which these energy levels are filled for elements on periods 1 through 3.
Orbital Filling and the Periodic Table If all elements behaved as they “should,” the pattern of orbital filling would be as follows. In a given principal energy level, first the two slots available to electrons on the s sublevel are filled, then the six slots on the p sublevel, then the 10 slots on the d sublevel. The f sublevel, which is fourth to be filled, comes into play only at principal energy level 4, and it would be filled before elements began adding valence electrons to the s sublevel on the next principal energy level. That might be the way things “should” happen, but it is not the way that they do happen. The list that follows shows the pattern by which
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orbitals are filled from sublevel 3p onward. Following each sublevel, in parentheses, is the number of “slots” available for electrons in that shell. Note that in several places, the pattern of filling defies the ideal order described in the preceding paragraph. Orbital Filling by Principal Energy Level and Sublevel from 3p Onward: • • • • • • • • • • • • • •
3p (6) 4s (2) 3d (10) 4p (6) 5s (2) 4d (10) 5p (6) 6s (2) 4f (14) 5d (10) 6p (6) 7s (2) 5f (14) 6d (10) The 44 representative elements follow a regular pattern of orbital filling through the first 18 elements. By atomic number 18, argon, 3p has been filled, and at that point element 19 (potassium) would be expected to begin filling row 3d. However, instead it begins filling 4s, to which calcium (20) adds the second and last valence electron. It is here that we come to the transition metals, distinguished by the fact that they fill the d orbitals. Note that none of the representative elements up to this point, or indeed any that follow, fill the d orbital. (The d orbital could not come into play before Period 3 anyway, because at least three sublevels—corresponding to principal energy level 3—are required in order for there to be a d orbital.) In any case, when the representative elements fill the p orbitals of a given energy level, they skip the d orbital and go on to the next principal energy level, filling the s orbitals. Filling of the d orbital on the preceding energy level only occurs with the transition metals: in other words, on period 4, transition metals fill the 3d sublevel, and so on as the period numbers increase.
Distinguishing the Transition Metals Given the fact that it is actually the representative elements that skip the d sublevels, and the transi-
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tion metals that go back and fill them, one might wonder if the names “representative” and “transition” (implying an interruption) should be reversed. But it is the transition metals that are the exception to the rule, for two reasons. First of all, as we have seen, they are the only elements that fill the d orbitals.
Transition Metals
Secondly, they are the only elements whose outer-shell electrons are on two different principal energy levels. The orbital filling patterns of transition metals can be identified thus: ns(n-1)d, where n is the number of the period on which the element is located. For instance, zinc, on period 4, has an outer shell of 4s23d10. In other words, it has two electrons on principal energy level 4, sublevel 4s—as it “should.” But it also has 10 electrons on principal energy level 3, sublevel 3d. In effect, then, the transition metals “go back” and fill in the d orbitals of the preceding period. There are further complications in the patterns of orbital filling for the transition metals, which will only be discussed in passing here as a further explanation as to why these elements are not “representative.” Most of them have two s valence electrons, but many have one, and palladium has zero. Nor do they add their d electrons in regular patterns. Moving across period 4, for instance, the number of electrons in the d orbital “should” increase in increments of 1, from 1 to 10. Instead the pattern goes like this: 1, 2, 3, 5, 5, 6, 7, 8, 10, 10. LANTHANIDES AND ACTINIDES. The lanthanides and actinides are set
apart even further from the transition metals. In most versions of the periodic table, lanthanum (57) is followed by hafnium (72) in the transition metals section of the chart. Similarly, actinium (89) is followed by rutherfordium (104). The “missing” metals—lanthanides and actinides respectively—are listed at the bottom of the chart. There are reasons for this, as well as for the names of these groups. After the 6s orbital fills with the representative element barium (56), lanthanum does what a transition metal does—it begins filling the 5d orbital. But after lanthanum, something strange happens: cerium (58) quits filling 5d, and moves to fill the 4f orbital. The filling of that orbital continues throughout the entire lanthanide series, all the way to lutetium (71). Thus lanthanides can be defined as those metals that fill the 4f orbital; however, because lanthanum
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exhibits similar properties, it is usually included with the lanthanides.
Earth’s crust, the percentages for elements outside of the top 18 tend to very small.
A similar pattern occurs for the actinides. The 7s orbital fills with radium (88), after which actinium (89) begins filling the 6d orbital. Next comes thorium, first of the actinides, which begins the filling of the 5f orbital. This is completed with element 103, lawrencium. Actinides can thus be defined as those metals that fill the 5f orbital; but again, because actinium exhibits similar properties, it is usually included with the actinides.
In the human body, iron is the 12th most abundant element, constituting 0.004% of the body’s mass. Zinc follows it, at 13th place, accounting for 0.003%. Again, these percentages may not seem particularly high, but in view of the fact that three elements—oxygen, carbon, and hydrogen—account for 93% of human elemental body mass, there is not much room for the other 10 most common elements in the body. Transition metals such as copper are present in trace quantities within the body as well.
REAL-LIFE APPLICAT ION S Survey of the Transition Metals The fact that the transition elements are all metals means that they are lustrous or shiny in appearance, and malleable, meaning that they can be molded into different shapes without breaking. They are excellent conductors of heat and electricity, and tend to form positive ions by losing electrons. Generally speaking, metals are hard, though a few of the transition metals—as well as members of other metal families—are so soft they can be cut with a knife. Like almost all metals, they tend to have fairly high melting points, and extremely high boiling points. Many of the transition metals, particularly those on periods 4, 5, and 6, form useful alloys— mixtures containing more than one metal—with one another, and with other elements. Because of their differences in electron configuration, however, they do not always combine in the same ways, even within an element. Iron, for instance, sometimes releases two electrons in chemical bonding, and at other times three. ABUNDANCE OF THE TRANSITION METALS. Iron is the fourth most
abundant element on Earth, accounting for 4.71% of the elemental mass in the planet’s crust. Titanium ranks 10th, with 0.58%, and manganese 13th, with 0.09%. Several other transition metals are comparatively abundant: even gold is much more abundant than many other elements on the periodic table. However, given the fact that only 18 elements account for 99.51% of
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DIVIDING THE TRANSITION METALS INTO GROUPS. There is no
easy way to group the transition metals, though certain of these elements are traditionally categorized together. These do not constitute “families” as such, but they do provide useful ways to break down the otherwise rather daunting 40-element lineup of the transition metals. In two cases, there is at least a relation between group number on the periodic table and the categories loosely assigned to a collection of transition metals. Thus the “coinage metals”— copper, silver, and gold—all occupy Group 9 on the periodic table. These have traditionally been associated with one another because their resistance to oxidation, combined with their malleability and beauty, has made them useful materials for fashioning coins. Likewise the members of the “zinc group”— zinc, cadmium, and mercury—occupy Group 10 on the periodic table. These, too, have often been associated as a miniature unit due to common properties. Members of the “platinum group”— platinum, iridium, osmium, palladium, rhodium, and ruthenium—occupy a rectangle on the table, corresponding to periods 5 and 6, and groups 6 through 8. What actually makes them a “group,” however, is the fact that they tend to appear together in nature. Iron, nickel, and cobalt, found alongside one another on Period 4, may be grouped together because they are all magnetic to some degree or another. This is far from the only notable characteristic about such metals, but provides a convenient means of further dividing the transition metals into smaller sections. To the left of iron on the periodic table is a rectangle corresponding to periods 4 through 6, groups 4 through 7. These 11 elements—titani-
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um, zirconium, hafnium, vanadium, niobium, tantalum, chromium, molybdenum, tungsten, manganese, and rhenium—are referred to here as “alloy metals.” This is not a traditional designation, but it is nonetheless useful for describing these metals, most of which form important alloys with iron and other elements.
ity with gold, and jewelry found in Egyptian tombs indicates the use of sophisticated techniques among the goldsmiths of Egypt as early as 2600 B.C. Likewise the Bible mentions gold in several passages. The Romans called it aurum (“shining dawn”), which explains its chemical symbol, Au.
One element was left out of the “rectangle” described in the preceding paragraph. This is technetium, which apparently does not occur in nature. It is lumped in with a final category, “rare and artificial elements.”
Early chemistry had its roots among the medieval alchemists, who sought in vain to turn plain metals into gold. Likewise the history of European conquest in the New World is filled with bitter tales of conquistadors, lured by gold, who wiped out entire nations of native peoples.
It should be stressed that there is nothing hard and fast about these categories. The “alloy metals” are not the only ones that form alloys; nickel is used in coins, though it is not called a coinage metal; and platinum could be listed with gold and silver as “precious metals.” Nonetheless, the categories used here seem to provide the most workable means of approaching the many transition metals.
Coinage Metals GOLD. Gold almost needs no introduction: virtually everyone knows of its value, and history is full of stories about people who killed or died for this precious metal. Part of its value springs from its rarity in comparison to, say iron: gold is present on Earth’s crust at a level of about 5 parts per billion (ppb). Yet as noted earlier, it is more abundant than some metals. Furthermore, due to the fact that it is highly unreactive (reactivity refers to the tendency for bonds between atoms or molecules to be made or broken in such a way that materials are transformed), it tends to be easily separated from other elements.
This helps to explain the fact that gold may well have been the first element ever discovered. No ancient metallurgist needed a laboratory in which to separate gold; indeed, because it so often keeps to itself, it is called a “noble” metal— meaning, in this context, “set apart.” Another characteristic of gold that made it valuable was its great malleability. In fact, gold is the most malleable of all metals: A single troy ounce (31.1 g) can be hammered into a sheet just 0.00025 in (0.00064 cm) thick, covering 68 ft2 (6.3 m2). Gold is one of the few metals that is not silver, gray, or white, and its beautifully distinctive color caught the eyes of metalsmiths and royalty from the beginning of civilization. Records from India dating back to 5000 B.C. suggest a familiar-
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At one time, gold was used in coins, and nations gauged the value of their currency in terms of the gold reserves they possessed. Few coins today—with special exceptions, such as the South African Krugerrand—are gold. Likewise the United States, for instance, went off the gold standard (that is, ceased to tie its currency to gold reserves) in the 1930s; nonetheless, the federal government maintains a vast supply of gold bullion at Fort Knox in Kentucky. Gold is as popular as ever for jewelry and other decorative objects, of course, but for the most part, it is too soft to have many other commercial purposes. One of the few applications for gold, a good conductor of electricity, is in some electronic components. Also, the radioactive gold-198 isotope is sometimes implanted in tissues as a means of treating forms of cancer. SILVER. Like gold, silver has been a part of human life from earliest history. Usually it is considered less valuable, though some societies have actually placed a higher value on silver because it is harder and more durable than gold. In the seventh century B.C., the Lydian civilization of Asia Minor (now Turkey) created the first coins using silver, and in the sixth century B.C., the Chinese began making silver coins. Succeeding dynasties in China continued to mint these coins, round with square holes in them, until the early twentieth century.
The Romans called silver argentum, and therefore today its chemical symbol is Ag. Its uses are much more varied than those of gold, both because of its durability and the fact that it is less expensive. Alloyed with copper, which adds strength to it, it makes sterling silver, used in coins, silverware, and jewelry. Silver nitrate compounds are used in silver plating, applied in mir-
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rors and tableware. (Most mirrors today, however, use aluminum.) Like gold, silver was once widely used for coinage, and silver coins are still more common than their gold counterparts. In 1963, however, the United States withdrew its silver certifications, paper currency exchangeable for silver. Today, silver coins are generally issued in special situations, such as to commemorate an event. A large portion of the world’s silver supply is used by photographers for developing pictures. In addition, because it is an excellent conductor of heat and electricity, silver has applications in the electronics industry; however, its expense has led many manufacturers to use copper or aluminum instead. Silver is also present, along with zinc and cadmium, in cadmium batteries. Like gold, though to a much lesser extent, it is still an important jewelry-making component. COPPER. Most people think of pennies as containing copper, but in fact the penny is the only American coin that contains no copper alloys. Because the amount of copper necessary to make a penny today costs more than $0.01, a penny is actually made of zinc with a thin copper coating. Yet copper has long been a commonly used coinage metal, and long before that, humans used it for other purposes.
Seven thousand years ago, the peoples of the Tigris-Euphrates river valleys, in what is now Iraq, were mining and using copper, and later civilizations combined copper with zinc to make bronze. Indeed, the history of prehistoric and ancient humans’ technological development is often divided according to the tools they made, the latter two of which came from transition metals: the Stone Age, the Bronze Age (c. 33001200 B.C.), and the Iron Age. Thus, by the time the Romans dubbed copper cuprum (from whence its chemical symbol, Cu, comes), copper in various forms had long been in use. Today copper is purified by a form of electrolysis, in which impurities such as iron, nickel, arsenic, and zinc are removed. Other “impurities” often present in copper ore include gold, silver, and platinum, and the separation of these from the copper pays for the large amounts of electricity used in the electrolytic process. Like the other coinage metals, copper is an extremely efficient conductor of heat and electricity, and because it is much less expensive than the other two, pure copper is widely used for
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electrical wiring. Because of its ability to conduct heat, copper is also applied in materials used for making heaters, as well as for cookware. Due to the high conductivity of copper, a heated copper pan has a uniform temperature, but copper pots must be coated with tin because too much copper in food is toxic. Copper is also like its two close relatives in that it resists corrosion, and this makes it ideal for plumbing. Its use in making coins resulted from its anti-corrosive qualities, combined with its beauty: like gold, copper has a distinctive color. This aesthetic quality led to the use of copper in decorative applications as well: many old buildings used copper roofs, and the Statue of Liberty is covered in 300 thick copper plates. Why, then, is the famous statue not coppercolored? Because copper does eventually corrode when exposed to air for long periods of time. Over time, it develops a thin layer of black copper oxide, and as the years pass, carbon dioxide in the air leads to the formation of copper carbonate, which imparts a greenish color. The human body is about 0.0004% copper, though as noted, larger quantities of copper can be toxic. Copper is found in foods such as shellfish, nuts, raisins, and dried beans. Whereas human blood has hemoglobin, a molecule with an iron atom at the center, the blood of lobsters and other large crustaceans contains hemocyanin, in which copper performs a similar function.
The Zinc Group ZINC. Together with copper, zinc appeared in another alloy that, like bronze, helped define the ancient world: brass. (The latter is mentioned in the Bible, for instance in the Book of Daniel, when King Nebuchadnezzar dreams of a statue containing brass and other substances, symbolizing various empires.) Used at least from the first millennium B.C. onward, brass appeared in coins and ornaments throughout Asia Minor. Though it is said that the Chinese purified zinc in about A.D. 1000, the Swiss alchemist Paracelsus (1493-1541) is usually credited with first describing zinc as a metal.
Bluish-white, with a lustrous sheen, zinc is found primarily in the ore sulfide sphalerite. The largest natural deposits of zinc are in Australia and the United States, and after mining, the metal is subjected to a purification and reduction
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process involving carbon. Zinc is used in galvanized steel, developed in the eighteenth century by Italian physicist Luigi Galvani (1737-1798). Just as a penny is not really copper but zinc, “tin” roofs are usually made of galvanized steel. Highly resistant to corrosion, galvanized steel finds application in everything from industrial equipment to garbage cans. Zinc oxide is applied in textiles, batteries, paints, and rubber products, while luminous zinc sulfide appears in television screens, movie screens, clock dials, and fluorescent light bulbs. Zinc phosphide is used as a rodent poison. Like several other transition metals, zinc is a part of many living things, yet it can be toxic in large quantities or specific compounds. For a human being, inhaling zinc oxide causes involuntary shaking. On the other hand, humans and many animals require zinc in their diets for the digestion of proteins. Furthermore, it is believed that zinc contributes to the healing of wounds and to the storage of insulin in the pancreas. In 1817, German chemist Friedrich Strohmeyer (1776-1835) was working as an inspector of pharmacies for the German state of Hanover. While making his rounds, he discovered that one pharmacy had a sample of zinc carbonate labeled as zinc oxide, and while inspecting the chemical in his laboratory, he discovered something unusual. If indeed it were zinc carbonate, it should turn into zinc oxide when heated, and since both compounds were white, there should be no difference in color. Instead, the mysterious compound turned a yellowish-orange. CADMIUM.
Strohmeyer continued to analyze the sample, and eventually realized that he had discovered a new element, which he named after the old Greek term for zinc carbonate, kadmeia. Indeed, cadmium typically appears in nature along with zinc or zinc compounds. Silvery white and lustrous or shiny, cadmium is soft enough to be cut with a knife, but chemically it behaves much like zinc: hence the idea of a “zinc group.” Today cadmium is used in batteries, and for electroplating of other metals to protect them against corrosion. Because the cost of cadmium is high due to the difficulty of separating it from zinc, cadmium electroplating is applied only in specialized situations. Cadmium also appears in the control rods of nuclear power plants, where
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its ready absorption of neutrons aids in controlling the rate at which nuclear fission occurs.
Transition Metals
Cadmium is highly toxic, and is believed to be the cause behind the outbreak of itai-itai (“ouch-ouch”) disease in Japan in 1955. People ingested rice oil contaminated with cadmium, and experienced a number of painful side effects associated with cadmium poisoning: nausea, vomiting, choking, diarrhea, abdominal pain, headaches, and difficulty breathing. MERCURY. One of only two elements—
along with bromine—that appears in liquid form at room temperature, mercury is both toxic and highly useful. The Romans called it hydragyrum (“liquid silver”), from whence comes its chemical symbol, Hg. Today, however, it is known by the name of the Romans’ god Mercury, the nimble and speedy messenger of the gods. Mercury comes primarily from a red ore called cinnabar, and since it often appears in shiny globules that form outcroppings from the cinnabar, it was relatively easy to discover. Several things are distinctive about mercury, including its bright silvery color. But nothing distinguishes it as much as its physical properties— not only its liquidity, but the fact that it rolls rapidly, like the fleet-footed god after which it is named. Its surface tension (the quality that causes it to bead) is six times greater than that of water, and for this reason, mercury never wets the surfaces with which it comes in contact. Mercury, of course, is widely used in thermometers, an application for which it is extremely well-suited. In particular, it expands at a uniform rate when heated, and thus a mercury thermometer (unlike earlier instruments, which used water, wine, or alcohol) can be easily calibrated. (Note that due to the toxicity of the element, mercury thermometers in schools are being replaced by other types of thermometers.) At temperatures close to absolute zero, mercury loses its resistance to the flow of electric current, and therefore it presents a promising area of research with regard to superconductivity. Even with elements present in the human body, such as zinc, there is a danger of toxicity with exposure to large quantities. Mercury, on the other hand, does not occur naturally in the human body, and is therefore extremely dangerous. Because it is difficult for the body to eliminate, even small quantities can accumulate and exert their poisonous effects, resulting in disor-
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ders of the nervous system. In fact, the phrase “mad as a hatter” refers to the symptoms of mercury poisoning suffered by hatmakers of the nineteenth century, who used a mercury compound in making hats of beaver and fur.
Magnetic Metals IRON. In its purest form, iron is relatively soft and slightly magnetic, but when hardened, it becomes much more so. As with several of the elements discovered long ago, iron has a chemical symbol (Fe) reflecting an ancient name, the Latin ferrum. But long before the Romans’ ancestors arrived in Italy, the Hittites of Asia Minor were purifying iron ore by heating it with charcoal over a hot flame.
The Hittites jealously guarded their secret, which gave them a technological advantage over enemies such as the Egyptians. But when Hittite civilization crumbled in the wake of an invasion by the mysterious “Sea Peoples” in about 1200 B.C., knowledge of ore smelting spread throughout the ancient world. Thus began the Iron Age, in which ancient technology matured greatly. (It should be noted that the Bantu peoples, in what is now Nigeria and neighboring countries, developed their own ironmaking techniques a few centuries later, apparently without benefit of contact with any civilization exposed to Hittite techniques.) Ever since ancient times, iron has been a vital part of human existence, and with the growth of industrialization during the eighteenth century, demand for iron only increased. But heating iron ore with charcoal required the cutting of trees, and by the latter part of that century, England’s forests had been so badly denuded that British ironmakers sought a new means of smelting the ore. It was then that British inventor Abraham Darby (1678?-1717) developed a method for making coke from soft coal, which was abundant throughout England. Adoption of Darby’s technique sped up the rate of industrialization in England, and thus advanced the entire Industrial Revolution soon to sweep the Western world. Symbolic of industrialism was iron in its many forms: pig iron, ore smelted in a cokeburning blast furnace; cast iron, a variety of mixtures containing carbon and/or silicon; wrought iron, which contains small amounts of various other elements, such as nickel, cobalt, copper,
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chromium, and molybdenum; and most of all steel. Steel is a mixture of iron with manganese and chromium, purified with a blast of hot air in the Bessemer converter, named after English inventor Henry Bessemer (1813-1898). Modern techniques of steelmaking improved on Bessemer’s design by using pure oxygen rather than merely hot air. The ways in which iron is used are almost too obvious (and too numerous) to mention. If iron and steel suddenly ceased to exist, there could be no skyscrapers, no wide-span bridges, no ocean liners or trains or heavy machinery or automobile frames. Furthermore, alloys of steel with other transition metals, such as tungsten and niobium, possess exceptionally great strength, and find application in everything from hand tools to nuclear reactors. Then, of course, there are magnets and electromagnets, which can only be made of iron and/or one of the other magnetic elements, cobalt and nickel. In the human body, iron is a key part of hemoglobin, the molecule in blood that transports oxygen from the lungs to the cells. If a person fails to get sufficient quantities of iron— present in foods such as red meat and spinach— the result is anemia, characterized by a loss of skin color, weakness, fainting, and heart palpitations. Plants, too, need iron, and without the appropriate amounts are likely to lose their color, weaken, and die. COBALT. Isolated in about 1735 by Swedish chemist Georg Brandt (1694-1768), cobalt was the first metal discovered since prehistoric, or at least ancient, times. The name comes from Kobald, German for “underground gnome,” and this reflects much about the early history of cobalt. In legend, the Kobalden were mischievous sprites who caused trouble for miners, and in real life, ores containing the element that came to be known as cobalt likewise caused trouble to men working in mines. Not only did these ores contain arsenic, which made miners ill, but because cobalt had no apparent value, it only interfered with their work of extracting other minerals.
Yet cobalt had been in use by artisans long before Brandt’s isolated the element. The color of certain cobalt compounds is a brilliant, shocking blue, and this made it popular for the coloring of pottery, glass, and tile. The element, which makes up less than 0.002% of Earth’s crust, is found today primarily in ores extracted from mines in
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Canada, Zaire, and Morocco. One of the most important uses of cobalt is in a highly magnetic alloy known as alnico, which also contains iron, nickel, and aluminum. Combined with tungsten and chromium, cobalt makes stellite, a very hard alloy used in drill bits. Cobalt is also applied in jet engines and turbines. NICKEL. Moderately magnetic in its pure form, nickel had an early history much like that of cobalt. English workers mining copper were often dismayed to find a metal that looked like copper, but was not, and they called it “Old Nick’s copper”—meaning that it was a trick played on them by Old Nick, or the devil. The Germans gave it a similar name: Kupfernickel, or “imp copper.”
Though nickel was not identified as a separate metal by Swedish mineralogist Axel Fredrik Cronstedt (1722-1765) until the eighteenth century, alloys of copper, silver, and nickel had been used as coins even in ancient Egypt. Today, nickel is applied, not surprisingly, in the American five-cent piece—that is, the “nickel”—made from an alloy of nickel and copper. Its anti-corrosive nature also provides a number of other applications for nickel: alloyed with steel, for instance, it makes a protective layer for other metals.
The Platinum Group PLATINUM. First identified by an Italian physician visiting the New World in the mid-sixteenth century, platinum—now recognized as a precious metal—was once considered a nuisance in the same way that nickel and cadmium were. Miners, annoyed with the fact that it got in the way when they were looking for gold, called it platina, or “little silver.” One of the reasons why platinum did not immediately catch the world’s fancy is because it is difficult to extract, and typically appears with the other metals of the “platinum group”: iridium, osmium, palladium, rhodium, and ruthenium.
Only in 1803 did English physician and chemist William Hyde Wollaston (1766-1828) develop a means of extracting platinum, and when he did, he discovered that the metal could be hammered into all kinds of shapes. Platinum proved such a success that it made Wollaston financially independent, and he retired from his medical practice at age 34 to pursue scientific research. Today, platinum is used in everything from thermometers to parts for rocket engines,
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both of which take advantage of its ability to withstand high temperatures.
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In the same year that Wollaston isolated platinum, three French chemists applied a method of extracting it with a mixture of nitric and hydrochloric acids. The process left a black powder that they were convinced was a new element, and in 1804 English chemist Smithson Tennant (1761-1815) gave it the name iridium. Iris was the Greek goddess of the rainbow, and the name reflected the element’s brilliant, multi-colored sheen. As with platinum, iridium is used today in a number of ways, particularly for equipment such as laser crystals that must withstand high temperatures. (In addition, one particular platinumiridium bar provides the standard measure of a kilogram.) IRIDIUM
AND
OSMIUM.
Tennant discovered a second element in 1804, also from the residue left over from the acid process for extracting platinum. This one had a distinctive smell when heated, so he named it osmium after osme, Greek for “odor.” In 1898, Austrian chemist Karl Auer, Baron von Welsbach (1858-1929), developed a light bulb using osmium as a filament, the material that is heated. Though osmium proved too expensive for commercial use, Auer’s creation paved the way for the use of another transition metal, tungsten, in making long-lasting filaments. Osmium, which is very hard and resistant to wear, is also used in electrical devices, fountain-pen tips, and phonograph needles. PALLADIUM, RHODIUM, AND RUTHENIUM. By the time Tennant isolated
osmium, Wollaston had found yet another element that emerged from the refining of platinum with nitric and hydrochloric acids. This was palladium, named after a recently discovered asteroid, Pallas. Soft and malleable, palladium resists tarnishing, which makes it valuable to the jewelry industry. Combined with yellow gold, it makes the alloy known as white gold. Because palladium has the unusual ability of absorbing up to 900 times its volume in hydrogen, it provides a useful means of extracting that element. Also in 1805, Wollaston discovered rhodium, which he named because it had a slightly red color. The density of rhodium is lower, and the melting point higher, than for most of the platinum group elements, and it is often used as an alloy to harden platinum. As with many elements
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in this group, it has a number of high-temperature applications. When electroplated, it is highly reflective, and this makes it useful as a material for optical instruments. The element that came to be known as ruthenium had been detected several times before 1844, when Russian chemist Carl Ernest Claus (1796-1864) finally identified it as a distinct element. Thus it was the only platinum group element in whose isolation neither Tennant nor Wollaston played a leading role. Since it had been found in Russia, the element was called ruthenium, in honor of that country’s ancient name, Ruthenia.
Alloy Metals The elements described here as “alloy metals” will be treated briefly, but the amount of space given to them here does not reflect their importance to civilization. Several of these are relatively abundant, and many—titanium, tungsten, manganese, chromium and others—are vital parts of daily life. However, due to space considerations, the treatment of these metals that follows is a regrettably abbreviated one. As suggested by the informal name given to them here, they are often applied in alloys, typically with other transition metals such as iron, or with other “alloy metals.” They are also used in a variety of compounds for a wide variety of applications.
Titanium, Zirconium, and Hafnium English clergyman and amateur scientist William Gregor (1761-1817) in 1791 noticed what he called “a new metallic substance” in a mineral called menchanite, which he found in the Menachan region of Cornwall, England. Four years later, German chemist Martin Heinrich Klaproth (1743-1817) studied menchanite and found that it contained a new element, which he named titanium after the Titans of Greek mythology. Only in 1910, however, was the element isolated. Due to its high strength-to-weight ratio, titanium is applied today in alloys used for making airplanes and spacecraft. It is also used in white paints and in a variety of other combinations, mostly in alloys containing other transition metals, as well as in compounds with nonmetals such as oxygen.
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Six years before he identified titanium, in 1789, Klaproth had found another element, which he named zirconium after the mineral zircon in which it was found. Zircon had been in use for many centuries, and another zirconiumcontaining mineral, jacinth, is mentioned in the Bible. As with titanium, there was a long period from identification to isolation, which did not occur until 1914. Zirconium alloys are used today in a number of applications, including superconducting magnets and as a construction metal in nuclear power plants. Compounds including zirconium also have a variety of uses, ranging from furnace linings to poison ivy lotion. Because it is almost always found with zirconium, hafnium—named after the ancient name of Copenhagen, Denmark—proved extremely difficult to isolate. Only in 1923 was it isolated, using x-ray analysis, and today it is applied primarily in light bulb filaments and electrodes. Sometimes it is accidentally “applied,” when zirconium is actually the desired metal, because the two are so difficult to separate. VANADIUM, TANTALUM, AND NIOBIUM. Vanadium, named after the Norse
goddess Vanadis or Freyja, was first identified in 1801, but only isolated in 1867. It is often applied in alloys with steel, and sometimes used for bonding steel and titanium. Tantalum and niobium are likewise named after figures from mythology—in this case, Greek. These two elements appear together so often that their identification as separate substances was a long process, involving numerous scientists and heated debates. For this reason, alloys involving tantalum—valued for its high melting point—usually include niobium as well. CHROMIUM, TUNGSTEN, AND MANGANESE, AND OTHER METALS. Because it displays a wide variety of col-
ors, chromium was named after the Greek word for “color.” It is used in chrome and tinted glass, and as a strengthening agent for stainless steel. Tungsten likewise strengthens steel, in large part because it has the highest melting point of any metal: 6,170°F (3,410°C). Its name comes from a Swedish word meaning “heavy stone,” and its chemical symbol (W) refers to the ore named wolframite, in which it was first discovered. Its high resistance to heat gives tungsten alloys applications in areas ranging from light bulb filaments to furnaces to missiles.
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Transition Metals
KEY TERMS Those transition metals
that fill the 5f orbital. Because actinium—
main-group elements and the transition metals are numbered.
which does not fill the 5f orbital—exhibits
LANTHANIDES: The transition metals
characteristics similar to those of the
that fill the 4f orbital. Because lanthanum—which does not fill the 4f orbital—exhibits characteristics similar to those of the lanthanides, it is usually considered part of the lanthanide family.
ACTINIDES:
actinides, it is usually considered part of the actinides family. ALLOY:
A mixture containing more than
one metal. ELECTROLYSIS: The use of an electric
current to cause a chemical reaction. ELECTRON CLOUD: A term used to
describe the pattern formed by orbitals. GROUPS:
Columns on the periodic
table of elements. These are ordered according to the numbers of valence electrons in the outer shells of the atoms for the elements represented. INNER TRANSITION METALS: The
lanthanides and actinides, both of which fill the f orbitals. For this reason, they are usually treated separately. ION:
An atom or group of atoms that has
lost or gained one or more electrons, and thus has a net electric charge. ISOTOPES: Atoms that have an equal
number of protons, and hence are of the same element, but differ in their number of neutrons. This results in a difference of mass. Isotopes may be either stable or unstable. The latter type, known as radioisotopes, are radioactive. IUPAC SYSTEM: A version of the peri-
odic table of elements, authorized by the International Union of Pure and Applied Chemistry (IUPAC), which numbers all groups on the table from 1-18. Thus in the IUPAC system, in use primarily outside of North America, both the representative or
S C I E N C E O F E V E R Y D AY T H I N G S
NORTH AMERICAN SYSTEM: A version of the periodic table of elements that only numbers groups of elements in which the number of valence electrons equals the group number. Hence the transition metals are usually not numbered in this system. Some North American charts, however, do provide group numbers for transition metals by including an “A” after the group numbers for representative or main-group elements, and “B” after those of transition metals.
A pattern of probabilities indicating the regions that may be occupied by an electron. The higher the principal energy level, the more complex the pattern of orbitals.
ORBITAL:
PERIODIC TABLE OF ELEMENTS: A
chart that shows the elements arranged in order of atomic number, along with chemical symbol and the average atomic mass (in atomic mass units) for that particular element. Elements are arranged in groups or columns, as well as in rows or periods, according to specific aspects of their valence electron configurations. PERIODS: Rows on the periodic table of
elements. These represent successive principal energy levels for the valence electrons in the atoms of the elements involved. Elements in the transition metal family occupy periods 4, 5, 6, or 7.
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Transition Metals
KEY TERMS PRINCIPAL ENERGY LEVEL: A value
elements are assigned group numbers 1, 2,
indicating the distance that an electron
and 13 through 18. (In these last six
may move away from the nucleus of an
columns on the IUPAC chart, there is no
atom. This is designated by a whole-num-
relation between the number of valence
ber integer, beginning with 1 and moving
electrons and group number.)
upward. The higher the principal energy
SHELL:
level, the greater the energy in the atom,
valence electrons at the outside of an atom.
The orbital pattern of the
and the more complex the pattern of
SUBLEVEL:
orbitals. Elements in the transition metal
pal energy level occupied by electrons in an
family have principal energy levels of 4, 5,
atom. Whatever the number n of the prin-
6, or 7.
cipal energy level, there are n sublevels. At
A region within the princi-
A term describing a
each principal energy level, the first sublev-
phenomenon whereby certain isotopes
el to be filled is the one corresponding to
known as radioisotopes are subject to a
the s orbital pattern, followed by the p and
form of decay brought about by the emis-
then the d pattern.
sion of high-energy particles. “Decay” does
TRANSITION METALS: A group of 40
not mean that the isotope “rots”; rather, it
elements, which are not assigned a group
decays to form another isotope until even-
number in the version of the periodic table
tually (though this may take a long time), it
of elements known as the North American
becomes stable.
system. These are the only elements that fill
REACTIVITY: The tendency for bonds
the dorbital. In addition, the transition
between atoms or molecules to be made or
metals—unlike the representative or main-
broken in such a way that materials are
group elements—have their valence elec-
transformed.
trons on two different principal energy lev-
REPRESENTATIVE OR MAIN-GROUP
els. Though the lanthanides and actinides
The 44 elements in Groups
are considered inner transition metals,
RADIOACTIVITY:
ELEMENTS:
1 through 8 on the periodic table of ele-
they are usually treated separately.
ments in the North American system, for
VALENCE
which the number of valence electrons
that occupy the highest principal energy
equals the group number. (The only excep-
level in an atom. These are the electrons
tion is helium.) In the IUPAC system, these
involved in chemical bonding.
Likewise manganese, first identified in the mid-eighteenth century, is extraordinarily strong. Its major use is in steelmaking. In addition, compounds such as manganese oxide are used in fertilizers. Other alloy metals include rhenium (identified only in 1925) and molybdenum. These two are often applied in alloys together, and with tungsten, for a variety of industrial purposes.
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ELECTRONS:
Electrons
Rare and Artificial Elements RARE EARTH-LIKE ELEMENTS.
Though they are not part of the lanthanide series, scandium and yttrium share many properties with those elements, once known as the “rare earths.” (In this context, “rarity” refers not so much to scarcity as to difficulty of extraction.) Furthermore, like most of the lan-
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thanides, these two elements were first discovered in Scandinavia. Their origin is reflected in the name given by Swedish chemist Lars Nilson (1840-1899) to scandium, which he discovered in 1876. As for yttrium, it came from the complex mineral known as ytterite, from whence emerged many of the lanthanides. Yttrium is used in alloys to impart strength, and has a wide if specialized array of applications. Scandium has no important uses. ARTIFICIAL ELEMENTS. Technetium, with an atomic number of 43, is unusual in that it is one of the few elements with an atomic number less than 92 that does not occur in nature. This is reflected in its name, from the Greek technetos, meaning “artificial.” The strange thing is that technetium, produced in a laboratory in 1936, does occur naturally in the universe— but it seems to be found only in the spectral lines from older stars, and not in those of younger stars such as our Sun.
The other elements in the transition metals family are referred to as “transuranium elements,” meaning that they have atomic numbers higher than that of uranium (92). These have all been created artificially; all are highly radioac-
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tive; few survive for more than a few minutes (at most); and few have applications in ordinary life.
Transition Metals
WHERE TO LEARN MORE The Copper Page (Web site). (May 26, 2001). Gold Institute (Web site). (May 26, 2001). Kerrod, Robin. Matter and Materials. Illustrated by Terry Hadler. Tarrytown, N.Y.: Benchmark Books, 1996. Mebane, Robert C. and Thomas R. Rybolt. Metals. Illustrated by Anni Matsick. New York: Twenty-First Century Books, 1995. Oxlade, Chris. Metal. Chicago, IL: Heinemann Library, 2001. “The Pictorial Periodic Table” (Web site). (May 22, 2001). Stwertka, Albert. A Guide to the Elements. New York: Oxford University Press, 1998. “Transition Metals” ChemicalElements.com (Web site). (May 26, 2001). “The Transition Metals.”University of Colorado Department of Physics (Web site). (May 26, 2001). WebElements (Web site). (May 22, 2001). Zincworld (Web site). (May 22, 2001).
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ACTINIDES Actinides
CONCEPT The actinides (sometimes called actinoids) occupy the “bottom line” of the periodic table—a row of elements normally separated from the others, placed at the foot of the chart along with the lanthanides. Both of these families exhibit unusual atomic characteristics, properties that set them apart from the normal sequence on the periodic table. But there is more that distinguishes the actinides, a group of 14 elements along with the transition metal actinium. Only four of them occur in nature, while the other 10 have been produced in laboratories. These 10 are classified, along with the nine elements to the right of actinium on Period 7 of the periodic table, as transuranium (beyond uranium) elements. Few of these elements have important applications in daily life; on the other hand, some of the lowernumber transuranium elements do have specialized uses. Likewise several of the naturally occurring actinides are used in areas ranging from medical imaging to powering spacecraft. Then there is uranium, “star” of the actinide series: for centuries it seemed virtually useless; then, in a matter of years, it became the most talked-about element on Earth.
HOW IT WORKS The Transition Metals Why are actinides and lanthanides set apart from the periodic table? This can best be explained by reference to the transition metals and their characteristics. Actinides and lanthanides are referred to as inner transition metals, because, although they belong to this larger family, they are usually considered separately—rather like grown chil-
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dren who have married and started families of their own. The qualities that distinguish the transition metals from the representative or main-group elements on the periodic table are explained in depth within the Transition Metals essay. The reader is encouraged to consult that essay, as well as the one on Families of Elements, which further places the transition metals within the larger context of the periodic table. Here these specifics will be discussed only briefly. ORBITAL PATTERNS OF THE TRANSITION METALS. The transition
metals are distinguished by their configuration of valence electrons, or the outer-shell electrons involved in chemical bonding. Together with the core electrons, which are at lower energy levels, valence electrons move in areas of probability referred to as orbitals. The pattern of orbitals is determined by the principal energy level of the atom, which indicates a distance that an electron may move away from the nucleus. Each principal energy level is divided into sublevels corresponding to the number n of the principal energy level. The actinides, which would be on Period 7 if they were included on the periodic table with the other transition metals, have seven principal energy levels. (Note that period number and principal energy level number are the same.) In the seventh principal energy level, there are seven possible sublevels. The higher the energy level, the larger the number of possible orbital patterns, and the more complex the patterns. Orbital patterns loosely define the overall shape of the electron cloud, but this does not necessarily define the paths along which the electrons move. Rather, it
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means that if you could take millions of photographs of the electron during a period of a few seconds, the resulting blur of images would describe more or less the shape of a specified orbital. The four basic types of orbital patterns are discussed in the Transition Metals essay, and will not be presented in any detail here. It is important only to know that, unlike the representative elements, transition metals fill the sublevel corresponding to the d orbitals. In addition, they are the only elements that have valence electrons on two different principal energy levels. LANTHANIDES AND ACTINIDES. The lanthanides and actinides are fur-
ther set apart even from the transition metals, due to the fact that these elements also fill the highly complex f orbitals. Thus these two families are listed by themselves. In most versions of the periodic table, lanthanum (57) is followed by hafnium (72) in the transition metals section of the chart; similarly, actinium (89) is followed by rutherfordium (104). The “missing” metals— lanthanides and actinides, respectively—are shown at the bottom of the chart. The lanthanides can be defined as those metals that fill the 4f orbital. However, because lanthanum (which does not fill the 4f orbital) exhibits similar properties, it is usually included with the lanthanides. Likewise the actinides can be defined as those metals that fill the 5f orbital; but again, because actinium exhibits similar properties, it is usually included with the actinides.
Isotopes One of the distinguishing factors in the actinide family is its great number of radioactive isotopes. Two atoms may have the same number of protons, and thus be of the same element, yet differ in their number of neutrons—neutrally charged patterns alongside the protons at the nucleus. Such atoms are called isotopes, atoms of the same element having different masses. Isotopes are represented symbolically in one of several ways. For instance, there is this format: ᎏmᎏS, where S is the chemical symbol of the elea ment, a is the atomic number (the number of protons in its nucleus), and m the mass number—the sum of protons and neutrons. For the
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isotope known as uranium-238, for instance, this 238 is shown as ᎏ9ᎏ 2 U.
Actinides
Because the atomic number of any element is established, however, isotopes are usually represented simply with the mass number thus: 238U. They may also be designated with a subscript notation indicating the number of neutrons, so that this information can be obtained at a glance without it being necessary to do the arithmetic. For the uranium isotope shown here, this is writ238 ten as ᎏ9ᎏ 2 U146.
Radioactivity The term radioactivity describes a phenomenon whereby certain materials are subject to a form of decay brought about by the emission of highenergy particles, or radiation. Types of particles emitted in radiation include: • Alpha particles, or helium nuclei; • Beta particles—either an electron or a subatomic particle called a positron; • Gamma rays or other very high-energy electromagnetic waves. Isotopes are either stable or unstable, with the unstable variety, known as radioisotopes, being subject to radioactive decay. In this context, “decay” does not mean “rot”; rather, a radioisotope decays by turning into another isotope. By continuing to emit particles, the isotope of one element may even turn into the isotope of another element. Eventually the radioisotope becomes a stable isotope, one that is not subject to radioactive decay. This is a process that may take seconds, minutes, hours, days, years—and sometimes millions or even billions of years. The rate of decay is gauged by the half-life of a radioisotope sample: in other words, the amount of time it takes for half the nuclei (plural of nucleus) in the sample to become stable. Actinides decay by a process that begins with what is known as K-capture, in which an electron of a radioactive atom is captured by the nucleus and taken into it. This is followed by the splitting, or fission, of the atom’s nucleus. This fission produces enormous amounts of energy, as well as the release of two or more neutrons, which may in turn bring about further K-capture. This is called a chain reaction.
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Actinides
GLENN T. SEABORG HOLDS A SAMPLE CONTAINING IC TABLE. (Roger Ressmeyer/Corbis. Reproduced by permission.)
ARTIFICIAL ELEMENTS BETWEEN
REAL-LIFE APPLICAT ION S The First Three Naturally Occurring Actinides In the discussion of the actinides that follows, atomic number and chemical symbol will follow the first mention of an element. Atomic mass figures are available on any periodic table, and these will not be mentioned in most cases. The atomic mass figures for actinide elements are very high, as fits their high atomic number, but for most of these, figures are usually for the most stable isotope, which may exist for only a matter of seconds. Though it gives its name to the group as a whole, actinium (Ac, 89) is not a particularly significant element. Discovered in 1902 by German chemist Friedrich Otto Giesel (1852-1927), it is found in uranium ores. Actinium is 150 times more radioactive than radium, a highly radioactive alkaline earth metal isolated around the same time by French-Polish physicist and chemist Marie Curie (1867-1934) and her husband Pierre (1859-1906). THORIUM. More significant than actinium is thorium (Th, 90), first detected in 1815 by
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94
AND
102
ON THE PERIOD-
the renowned Swedish chemist Jons Berzelius (1779-1848). Berzelius promptly named the element after the Norse god Thor, but eventually concluded that what he had believed to be a new element was actually the compound yttrium phosphate. In 1829, however, he examined another mineral and indeed found the element he believed he had discovered 14 years earlier. It 1898, Marie Curie and an English chemist named Gerhard Schmidt, working independently, announced that thorium was radioactive. Today it is believed that the enormous amounts of energy released by the radioactive decay of subterranean thorium and uranium plays a significant part in Earth’s high internal temperature. The energy stored in the planet’s thorium reserves may well be greater than all the energy available from conventional fossil and nuclear fuels combined. Thorium appears on Earth in an abundance of 15 parts per million (ppm), many times greater than the abundance of uranium. With its high energy levels, thorium has enormous potential as a nuclear fuel. When struck by neutrons, thorium-232 converts to uranium-233, one of the few known fissionable isotopes—that is, isotopes that can be split to start nuclear reactions.
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It is perhaps ironic that this element, with its potential for use in some of the most high-tech applications imaginable, is widely applied in a very low-tech fashion. In portable gas lanterns for camping and other situations without electric power, the mantle often contains oxides of thorium and cerium, which, when heated, emit a brilliant white light. Thorium is also used in the manufacture of high-quality glass, and as a catalyst in various industrial processes. PROTACTINIUM. Russian chemist Dmitri Ivanovitch Mendeleev (1834-1907), father of the periodic table, used the table’s arrangement of elements as a means of predicting the discovery of new substances: wherever he found a “hole” in the table, Mendeleev could say with assurance that a new element would eventually be found to fill it. In 1871, Mendeleev predicted the discovery of “eka-tantalum,” an element that filled the space below the transition metal tantalum. (At this point in history, just two years after Mendeleev created the periodic table, the lanthanides and actinides had not been separated from the rest of the elements on the chart.)
Forty years after Mendeleev foretold its existence, two German chemists found what they thought might be Element 91. It had a half-life of only 1.175 minutes, and, for this reason, they named it “brevium.” Then in 1918, Austrian physicist Lise Meitner (1878-1968)—who, along with Curie and French physicist Marguerite Perey (1909-1975) was one of several women involved in the discovery of radioactive elements—was working with German chemist Otto Hahn (1879-1968) when the two discovered another isotope of Element 91. This one had a much, much longer half-life: 3.25 • 104 years, or about five times as long as the entire span of human civilization. Originally named protoactinium, the name of Element 91 was changed to protactinium (Pa), whose longest-lived isotope has an atomic mass of 231. Shiny and malleable, protactinium has a melting point of 2,861.6°F (1,572°C). It is highly toxic, and so rare that no commercial uses have been found for it. Indeed, protactinium could only be produced from the decay products of uranium and radium, and thus it is one of the few elements with an atomic number less than 93 that cannot be said to occur in nature.
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Uranium Actinides URANIUM’S
EARLY
HISTORY.
Chemistry books, in fact, differ as to the number of naturally occurring elements. Some say 88, which is the most correct figure, because protactinium, along with technetium (43) and two others, cannot be said to appear naturally on Earth. Other books say 92, a less accurate figure that nonetheless reflects an indisputable fact: above uranium (U, 92) on the periodic table, there are no elements that generally occur in nature. (However, a few do occur as radioactive by-products of uranium.) But uranium is much more than just the last truly natural element, though for about a century it apparently had no greater importance. When German chemist Martin Heinrich Klaproth (1743-1817) discovered it in 1789, he named it after another recent discovery: the planet Uranus. During the next 107 years, uranium had a very quiet existence, befitting a rather dulllooking material. Though it is silvery white when freshly cut, uranium soon develops a thin coating of black uranium oxide, which turns it a flat gray. Yet glassmakers did at least manage to find a use for it—as a coating for decorative glass, to which it imparted a hazy, fluorescent yellowish green hue. Little did they know that they were using one of the most potentially dangerous substances on Earth. THE DESTRUCTIVE POWER OF URANIUM. In 1895, German physicist Wil-
helm Röntgen (1845-1923) noticed that photographic plates held near a Crookes tube—a device for analyzing electromagnetic radiation—became fogged. He dubbed the rays that had caused this x rays. A year later, in 1896, French physicist Henri Becquerel (1852-1908) left some photographic plates in a drawer with a sample of uranium, and discovered that the uranium likewise caused a fogging of the photographic plates. This meant that uranium was radioactive. With the development of nuclear fission by Hahn and German chemist Fritz Strassman in 1938, uranium suddenly became all-important because of its ability to undergo nuclear fission, accompanied by the release of huge amounts of energy. During World War II, in what was known as the Manhattan Project, a team of scientists in Los Alamos, New Mexico, developed the atomic
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Actinides
GLOVED
HANDS HOLD A GRAY LUMP OF URANIUM.
REMOVED FROM A
TITAN II MISSILE,
THIS
MATERIAL HAS BEEN REMOLDED AFTER HAVING BEEN
PART OF THE DISARMAMENT AFTER THE END OF THE
COLD WAR. (Martin Mariet-
ta; Roger Ressmeyer/Corbis. Reproduced by permission.)
bomb. The first of the two atomic bombs dropped on Japan in 1945 contained uranium, while the second contained the transuranium element plutonium.
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OTHER
USES
FOR
URANIUM.
Though nuclear weapons have fortunately not been used against human beings since 1945, uranium has remained an important component of
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nuclear energy—both in the development of bombs and in the peaceful application of nuclear power. It has other uses as well, due to the fact that it is extremely dense. Indeed, uranium has a density close to that of gold and platinum, but is much cheaper, because it is more abundant on Earth. In addition, various isotopes of uranium are a by-product of nuclear power, which separates these isotopes from the highly fissionable 235U isotope. Thus, quantities of uranium are available for use in situations where a great deal of mass is required in a small space: in counterweights for aircraft control systems, for instance, or as ballast for missile reentry vehicles. Because 238U has a very long half-life—4.47 • 109 years, or approximately the age of Earth—it is used to estimate the age of rocks and other geological features. Uranium-238 is the “parent” of a series of “daughter” isotopes that geologists find in uranium ores. Uranium-235 also produces “daughter” isotopes, including isotopes of radium, radon, and other radioactive series. Eventually, uranium isotopes turn into lead, but this can take a very long time: even 235U, which lasts for a much shorter period than 238U, has a half-life of about 700 million years. The radiation associated with various isotopes of uranium, as well as other radioactive materials, is extremely harmful. It can cause all manner of diseases and birth defects, and is potentially fatal. The tiny amounts of radiation produced by uranium in old pieces of decorative glass is probably not enough to cause any real harm, but the radioactive fallout from Hiroshima resulted in birth defects among the Japanese population during the late 1940s.
Transuranium Elements Transuranium elements are those elements with atomic numbers higher than that of uranium. None of these occur in nature, except as isotopes that develop in trace amounts in uranium ore. The first such element was neptunium (Np, 93), created in 1940 by American physicist Edwin Mattison McMillan (1907-1991) and American physical chemist Philip Hauge Abelson. The development of the cyclotron by American physicist Ernest Lawrence (1901-1958) at the University of California at Berkeley in the 1930s made possible the artificial creation of new elements. A cyclotron speeds up protons or ions
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(charged atoms) and shoots them at atoms of uranium or other elements with the aim of adding positive charges to the nucleus. In the first two decades after the use of the cyclotron to create neptunium, scientists were able to develop eight more elements, all the way up to mendelevium (Md, 101), named in honor of the man who created the periodic table.
Actinides
Most of these efforts occurred at Berkeley under the leadership of American nuclear chemist Glenn T. Seaborg (1912-1999) and American physicist Albert Ghiorso. The pace of development in transuranium elements slowed after about 1955, however, primarily due to the need for ever more powerful cyclotrons and ionaccelerating machines. In addition to Berkeley, there are two other centers for studying these high-energy elements: the Joint Institute for Nuclear Research in Dubna, Russia, and the Gesellschaft für Schwerionenforschung (GSI) in Darmstadt, Germany.
The Transuranium Actinides PLUTONIUM. Just as neptunium had been named for the next planet beyond Uranus, a second transuranium element, discovered by Seaborg and two colleagues in 1940, was named after Pluto. Among the isotopes of plutonium (Pu, 94) is plutonium-239, one of the few fissionable isotopes other than uranium-233 and uranium-235. For that reason, it was applied in the second bomb dropped on Japan.
In addition to its application in nuclear weapons, plutonium is used in nuclear power reactors, and in thermoelectric generators, which convert the heat energy it releases into electricity. Plutonium is also used as a power source in artificial heart pacemakers. Huge amounts of the element are produced each year as a by-product of nuclear power reactors. BERKELEY DISCOVERIES OF THE 1950S. Because the lanthanide ele-
ment above it on the periodic table was named europium after Europe, americium (Am, 95) was named after America. Discovered by Seaborg, Ghiorso, and two others in 1944, it was first produced in a nuclear reaction involving plutonium-239. Americium radiation is used in measuring the thickness of glass during production; in addition, the isotope americium-241 is used as an ionization source in smoke detectors, and
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Actinides
KEY TERMS ACTINIDES: Those elements that fill the
same element, but differ in their number of
5f orbital. Because actinium—which does
neutrons. This results in a difference of
not fill the 5f orbital—exhibits characteris-
mass. Isotopes may be either stable or
tics similar to those of the actinides, it is
unstable. The unstable type, known as
usually considered part of the actinides
radioisotopes, are radioactive.
family. Of the other 14 actinides, usually shown at the bottom of the periodic table, only the first three occur in nature.
LANTHANIDES: The transition metals
that fill the 4f orbital.
The number of
MASS NUMBER: The sum of protons
protons in the nucleus of an atom. Since
and neutrons in the atom’s nucleus. The
this number is different for each element,
designation
elements are listed on the periodic table of
that this particular isotope of uranium has
elements in order of atomic number.
a mass number of 238. Since uranium has
ELECTRON CLOUD: A term used to
an atomic number of 92, this means that
describe the pattern formed by orbitals.
uranium-238 has 146 neutrons in its
HALF-LIFE: The length of time it takes a
nucleus.
substance to diminish to one-half its initial
NEUTRON:
amount. For a sample of radioisotopes, the
has no electric charge. Neutrons are found
half-life is the amount of time it takes for
at the nucleus of an atom, alongside
half of the nuclei to become stable iso-
protons.
ATOMIC
NUMBER:
238U,
for uranium-238, means
A subatomic particle that
topes. Half-life can be a few seconds; on the other hand, for uranium-238, it is a matter of several billion years. INNER TRANSITION METALS: The
lanthanides and actinides, which are
region where protons and neutrons are located, and around which electrons spin. The plural of “nucleus” is nuclei.
unique in that they fill the f orbitals.
ORBITAL:
For this reason, they are usually treated
regarding the position of an electron for an
separately.
atom in a particular energy state. The high-
ISOTOPES: Atoms that have an equal
er the principal energy level, the more
number of protons, and hence are of the
complex the pattern of orbitals.
in portable devices for taking gamma-ray photographs. Above curium (Cm, 96) on the periodic table is the lanthanide gadolinium, named after Finnish chemist Johan Gadolin (1760-1852). Therefore, the discoverers of Element 96 also decided to name it after a person, Marie Curie. As with some of the other relatively low-number
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NUCLEUS: The center of an atom, a
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A region of probabilities
transuranium elements, this one is not entirely artificial: its most stable isotope, some geologists believe, may have been present in rocks many millions of years ago, but these isotopes have long since decayed. Because curium generates great amounts of energy as it decays, it is used for providing compact sources of power in remote locations on Earth and in space vehicles.
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Actinides
KEY TERMS
CONTINUED
PRINCIPAL ENERGY LEVEL: A value
RADIOISOTOPE:
indicating the distance that an electron
the decay associated with radioactivity. A
may move away from the nucleus of an
radioisotope is thus an unstable isotope.
atom. This is designated by a whole-num-
SUBLEVEL: A region within the princi-
ber integer, beginning with 1 and moving
pal energy level occupied by electrons in an
upward. The higher the principal energy
atom. Whatever the number n of the prin-
level, the greater the energy in the atom,
cipal energy level, there are n sublevels.
and the more complex the pattern of
Actinides are distinguished by the fact that
orbitals. Elements in the transition metal
their valence electrons are in a sublevel
family have principal energy levels of 4, 5,
corresponding to the 5f orbital.
6, or 7.
TRANSITION METALS: A group of 40
RADIATION:
In a general sense, radia-
tion can refer to anything that travels in a stream, whether that stream be composed of subatomic particles or electromagnetic waves. In a more specific sense, the term relates to the radiation from radioactive materials, which can be harmful to human
An isotope subject to
elements (counting lanthanum and actinium), which are the only elements that fill the d orbital. In addition, the transition metals have their valence electrons on two different principal energy levels. Though the lanthanides and actinides are considered inner transition metals, they are usually considered separately.
beings. TRANSURANIUM ELEMENTS:
Ele-
A term describing a
ments with an atomic number higher than
phenomenon whereby certain isotopes,
that of uranium (92). These have all have
known as radioisotopes, are subject to a
been produced artificially. The transurani-
form of decay brought about by the emis-
um elements include 11 actinides, as well
sion of high-energy particles. “Decay” does
as 9 transition metals.
not mean that the isotope “rots”; rather, it
VALENCE
decays to form another isotope until even-
that occupy the highest principal energy
tually (though this may take a long time) it
level in an atom. These are the electrons
becomes stable.
involved in chemical bonding.
RADIOACTIVITY:
When Seaborg, Ghiorso, and others created Element 97, berkelium (Bk), they again took the naming of lanthanides as their cue. Just as terbium, directly above it on the periodic table, had been named for the Swedish town of Ytterby, where so many lanthanides were discovered, they named the new element after the American city where so many transuranium elements had been developed. Berkelium has no known applications
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ELECTRONS:
Electrons
outside of research. The Berkeley team likewise named californium (Cf, 98) after the state where Berkeley is located. Researchers today are studying the use of californium radiation for treatment of tumors involved in various forms of cancer. THE REMAINING TRANSURANIUM ACTINIDES. The remaining transura-
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nium actinides were all named after famous people: einsteinium (Es, 99) for Albert Einstein (1879-1955); fermium (Fm, 100) after ItalianAmerican physicist Enrico Fermi (1901-1954); mendelevium after Mendeleev; nobelium (No, 102) after Swedish inventor and philanthropist Alfred Nobel (1833-1896); and lawrencium (Lr, 103) after Ernest Lawrence. Both einsteinium and fermium were byproducts of nuclear testing at Bikini Atoll in the south Pacific in 1952. For this reason, their existence was kept a secret for two years. Neither element has a known application. The same is true of mendelevium, produced by Seaborg, Ghiorso, and others with a cyclotron at Berkeley in 1955, as well as the other two transuranium actinides.
Beyond the Transuranium Actinides As noted earlier, there are nine additional transuranium elements, which properly belong to the transition metals. The first of these is rutherfordium, discovered in 1964 by the Dubna team and named after Ernest Rutherford (18711937), the British physicist who discovered the nucleus. The Dubna team named dubnium, discovered in 1967, after their city, just as berkelium had been named after the Berkeley team’s city. Both groups developed versions of Element 106 in 1974, and both agreed to name it seaborgium after Seaborg, but this resulted in a controversy that was not settled for some time. The name of bohrium, created at Dubna in 1976, honors Danish physicist Niels Bohr (1885-
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1962), who developed much of the model of electron energy levels discussed earlier in this essay. Hassium, produced at the GSI in 1984, is named for the German state of Hess. Two years earlier, the GSI team also created the last named element on the periodic table, meitnerium (109), named after Meitner. Beyond meitnerium are three elements, as yet unnamed, created at the GSI in the mid-1990s. WHERE TO LEARN MORE Cooper, Dan. Enrico Fermi and the Revolutions in Modern Physics. New York: Oxford University Press, 1999. “Exploring the Table of Isotopes” (Web site). (May 15, 2001). Kidd, J. S. and Renee A. Kidd. Quarks and Sparks: The Story of Nuclear Power. New York: Facts on File, 1999. Knapp, Brian J. Elements. Illustrated by David Woodroffe and David Hardy. Danbury, CT: Grolier Educational, 1996. “A Periodic Table of the Elements” Los Alamos National Laboratory (Web site). (May 22, 2001). Sherrow, Victoria. The Making of the Atom Bomb. San Diego, CA: Lucent Books, 2000. “Some Physics of Uranium.” The Uranium Institute (Web site). (May 27, 2001). Stwertka, Albert. A Guide to the Elements. New York: Oxford University Press, 1998. Uranium Information Center (Web site). (May 27, 2001).
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Lanthanides
LANTHANIDES
CONCEPT Along the bottom of the periodic table of elements, separated from the main body of the chart, are two rows, the first of which represents the lanthanides. Composed of lanthanum and the 14 elements of the lanthanide series, the lanthanides were once called the “rare earth” metals. In fact, they are not particularly rare: many of them appear in as much abundance as more familiar elements such as mercury. They are, however, difficult to extract, a characteristic that defines them as much as their silvery color; sometimes high levels of reactivity; and sensitivity to contamination. Though some lanthanides have limited uses, members of this group are found in everything from cigarette lighters to TV screens, and from colored glass to control rods in nuclear reactors.
HOW IT WORKS Defining the Lanthanides The lanthanide series consists of the 14 elements, with atomic numbers 58 through 71, that follow lanthanum on the periodic table of elements. These 14, along with the actinides—atomic numbers 90 through 103—are set aside from the periodic table due to similarities in properties that define each group. Specifically, the lanthanides and actinides are the only elements that fill the f-orbitals. The lanthanides and actinides are actually “branches” of the larger family known as transition metals. The latter appear in groups 3 through 12 on the IUPAC version of the periodic table, though
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they are not numbered on the North American version. The lanthanide series is usually combined with lanthanum, which has an atomic number of 57, under the general heading of lanthanides. As their name indicates, members of the lanthanide series share certain characteristics with lanthanum; hence the collective term “lanthanides.” These 15 elements, along with their chemical symbols, are: • • • • • • • • • • • • • • •
Lanthanum (La) Cerium (Ce) Praseodymium (Pr) Neodymium (Nd) Promethium (Pm) Samarium (Sm) Europium (Eu) Gadolinium (Gd) Terbium (Tb) Dysprosium (Dy) Holmium (Ho) Erbium (Er) Thulium (Tm) Ytterbium (Yb) Lutetium (Lu) Most of these are discussed individually in this essay. PROPERTIES OF LANTHANIDES. Bright and silvery in appearance,
many of the lanthanides—though they are metals—are so soft they can be cut with a knife. Lanthanum, cerium, praseodymium, neodymium, and europium are highly reactive. When exposed to oxygen, they form an oxide coating. (An oxide is a compound formed by metal with an oxygen.) To prevent this result, which tarnishes the
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Lanthanides
MISCH
METAL, WHICH INCLUDES CERIUM, IS OFTEN USED IN CIGARETTE LIGHTERS. (Massimo Listri/Corbis. Reproduced by
permission.)
metal, these five lanthanides are kept stored in mineral oil. The reactive tendencies of the other lanthanides vary: for instance, gadolinium and lutetium do not oxidize until they have been exposed to air for a very long time. Nonetheless, lanthanides tend to be rather “temperamental” as a class. If contaminated with other metals, such as calcium, they corrode easily, and if contaminated with nonmetals, such as nitrogen or oxygen, they become brittle. Contamination also alters their boiling points, which range from 1,506.2°F (819°C) for ytterbium to 3,025.4°F (1,663°C) for lutetium. Lanthanides react rapidly with hot water, or more slowly with cold water, to form hydrogen gas. As noted earlier, they also are quite reactive with oxygen, and they experience combustion readily in air. When a lanthanide reacts with another element to form a compound, it usually loses three of its outer electrons to form what are called tripositive ions, or atoms with an electric charge of +3. This is the most stable ion for lanthanides, which sometimes develop less stable +2 or +4 ions. Lanthanides tend to form ionic compounds, or compounds containing either positive or negative ions, with other substances—in particular, fluorine.
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Are They Really “Rare”? Though they were once known as the rare earth metals, lanthanides were so termed because, as we shall see, they are difficult to extract from compounds containing other substances— including other lanthanides. As for rarity, the scarcest of the lanthanides, thulium, is more abundant than either arsenic or mercury, and certainly no one thinks of those as rare substances. In terms of parts per million (ppm), thulium has a presence in Earth’s crust equivalent to 0.2 ppm. The most plentiful of the lanthanides, cerium, has an abundance of 46 ppm, greater than that of tin. If, on the other hand, rarity is understood not in terms of scarcity, but with regard to difficulty in obtaining an element in its pure form, then indeed the lanthanides are rare. Because their properties are so similar, and because they are inclined to congregate in the same substances, the original isolation and identification of the lanthanides was an arduous task that took well over a century. The progress followed a common pattern. First, a chemist identified a new lanthanide; then a few years later, another scientist came along and extracted another lanthanide from the
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sample that the first chemist had believed to be a single element. In this way, the lanthanides emerged over time, each from the one before it, rather like Russian matryoshka or “nesting” dolls. EXTRACTING
Lanthanides
LANTHANIDES.
Though most of the lanthanides were first isolated in Scandinavia, today they are found in considerably warmer latitudes: Brazil, India, Australia, South Africa, and the United States. The principal source of lanthanides is monazite, a heavy, dark sand from which about 50% of the lanthanide mass available to science and industry has been extracted. In order to separate lanthanides from other elements, they are actually combined with other substances—substances having a low solubility, or tendency to dissolve. Oxalates and fluorides are low-solubility substances favored for this purpose. Once they are separated from non-lanthanide elements, ion exchange is used to separate one lanthanide element from another. There is a pronounced decrease in the radii of lanthanide atoms as they increase in atomic number: in other words, the higher the atomic number, the smaller the radius. This decrease, known as the lanthanide contraction, aids in the process of separation by ion exchange. The lanthanides are mixed in an ionic solution, then passed down a long column containing a resin. Various lanthanide ions bond more or less tightly, depending on their relative size, with the resin. After this step, the lanthanides are washed out of the ion exchange column and into various solutions. One by one, they become fully separated, and are then mixed with acid and heated to form an oxide. The oxide is then converted to a fluoride or chloride, which can then be reduced to metallic form with the aid of calcium.
REAL-LIFE AP P LICATIONS The Historical Approach In studying the lanthanides, one can simply move along the periodic table, from lanthanum all the way to lutetium. However, in light of the difficulties involved in extracting the lanthanides, one from another, an approach along historical lines aids in understanding the unique place each lanthanide occupies in the overall family.
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SAMARIUM
IS USED IN NUCLEAR POWER PLANT CON-
TROL RODS, SUCH AS THE ONE SHOWN HERE. (Tim
Wright/Corbis. Reproduced by permission.)
The terms “lanthanide series” or even “lanthanides” did not emerge for some time—in other words, scientists did not immediately know that they were dealing with a whole group of metals. As is often the case with scientific discovery, the isolation of lanthanides followed an irregular pattern, and they did not emerge in order of atomic number. Cerium was in fact discovered long before lanthanum itself, in the latter half of the eighteenth century. There followed, a few decades later, the discovery of a mineral called ytterite, named after the town of Ytterby, Sweden, near which it was found in 1787. During the next century, most of the remaining lanthanides were extracted from ytterite, and the man most responsible for this was Swedish chemist Carl Gustav Mosander (1797-1858). Because Mosander had more to do with the identification of the lanthanides than any one individual, the middle portion of this historical overview is devoted to his findings. The recognition and isolation of lanthanides did not stop with Mosander, however; therefore another
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group of minerals is discussed in the context of the latter period of lanthanide discovery.
Early Lanthanides CERIUM. In 1751, Swedish chemist Axel Crönstedt (1722-1765) described what he thought was a new form of tungsten, which he had found at the Bastnäs Mine near Riddarhyttan, Sweden. Later, German chemist Martin Heinrich Klaproth (1743-1817) and Swedish chemist Wilhelm Hisinger (1766-1852) independently analyzed the material Crönstedt had discovered, and both concluded that this must be a new element. It was named cerium in honor of Ceres, an asteroid between Mars and Jupiter discovered in 1801. Not until 1875 was cerium actually extracted from an ore.
Among the applications for cerium is an alloy called misch metal, prepared by fusing the chlorides of cerium, lanthanum, neodymium, and praseodymium. The resulting alloy ignites at or below room temperature, and is often used as the “flint” in a cigarette lighter, because it sparks when friction from a metal wheel is applied. Cerium is also used in jet engine parts, as a catalyst in making ammonia, and as an antiknock agent in gasoline—that is, a chemical that reduces the “knocking” sounds sometimes produced in an engine by inferior grades of fuel. In cerium (IV) oxide, or CeO2, it is used to extract the color from formerly colored glass, and is also applied in enamel and ceramic coatings. GADOLINIUM. In 1794, seven years after the discovery of ytterite, Finnish chemist Johan Gadolin (1760-1852) concluded that ytterite contained a new element, which was later named gadolinite in his honor. A very similar name would be applied to an element extracted from ytterite, and the years between Gadolin’s discovery and the identification of this element spanned the period of the most fruitful activity in lanthanide identification.
During the next century, all the other lanthanides were discovered within the composition of gadolinite; then, in 1880, Swiss chemist JeanCharles Galissard de Marignac (1817-1894) found yet another element hiding in it. French chemist Paul Emile Lecoq de Boisbaudran (18381912) rediscovered the same element six years later, and proposed that it be called gadolinium.
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Silvery in color, but with a sometimes yellowish cast, gadolinium has a high tendency to oxidize in dry air. Because it is highly efficient for capturing neutrons, it could be useful in nuclear power reactors. However, two of its seven isotopes are in such low abundance that it has had little nuclear application. Used in phosphors for color television sets, among other things, gadolinium shows some promise for ultra hightech applications: at very low temperatures it becomes highly magnetic, and may function as a superconductor.
Mosander’s Lanthanides LANTHANUM. Between 1839 and 1848, Mosander was consumed with extracting various lanthanides from ytterite, which by then had come to be known as gadolinite. When he first succeeded in extracting an element, he named it lanthana, meaning “hidden.” The material, eventually referred to as lanthanum, was not prepared in pure form until 1923.
Like a number of other lanthanides, lanthanum is very soft—so soft it can be cut with a knife—and silvery-white in color. Among the most reactive of the lanthanides, it decomposes rapidly in hot water, but more slowly in cold water. Lanthanum also reacts readily with oxygen, and corrodes quickly in moist air. As with cerium, lanthanum is used in misch metal. Because lanthanum compounds bring about special optical qualities in glass, it also used for the manufacture of specialized lenses. In addition, compounds of lanthanum with fluorine or oxygen are used in making carbon-arc lamps for the motion picture industry. SAMARIUM. While analyzing an oxide formed from lanthanide in 1841, Mosander decided that he had a new element on his hands, which he called didymium. Four decades later, Boisbaudran took another look at didynium, and concluded that it was not an element; rather, it contained an element, which he named samarium after the mineral samarskite, in which it is found. Still later, Marignac was studying samarskite when he discovered what came to be known as gadolinium. But the story did not end there: even later, in 1901, French chemist EugèneAnatole Demarçay (1852-1903) found yet another element, europium, in samarskite.
Samarium is applied today in nuclear power plant control rods, in carbon-arc lamps, and in
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optical masers and lasers. In alloys with cobalt, it is used in manufacturing the most permanent electromagnets available. Samarium is also utilized in the manufacture of optical glass, and as a catalyst in the production of ethyl alcohol. ERBIUM AND TERBIUM. To return to Mosander, he was examining ytterite in 1843 when he identified three different “earths,” all of which he also named after Ytterby: yttria, erbia, and terbia. Erbium was the first to be extracted. A pure sample of its oxide was prepared in 1905 by French chemist Georges Urbain (1872-1938) and American chemist Charles James (18801928), but the pure metal itself was only extracted in 1934.
Soft and malleable, with a lustrous silvery color, erbium produces salts (which are usually combinations of a metal with a nonmetal) that are pink and rose, making it useful as a tinting agent. One of its oxides is utilized, for instance, to tint glass and porcelain with a pinkish cast. It is also applied, to a limited extent, in the nuclear power industry. Mosander also identified another element, terbium, in ytterite in 1839, and Marignac isolated it in a purer form nearly half a century later, in 1886. To repeat a common theme, it is silverygray and soft enough to be cut with a knife. When hit by an electron beam, a compound containing terbium emits a greenish color, and thus it is used as a phosphor in color television sets.
Later Isolation of Lanthanides YTTERBIUM, HOLMIUM, AND THULIUM. For many years after Mosander,
there was little progress in the discovery of lanthanides, and when it came, it was in the form of a third element, named after the town where so many of the lanthanides were discovered. In 1878, while analyzing what Mosander had called erbia, Marignac realized that it contained one or possibly two elements. A year later, Swedish chemist Lars Frederik Nilson (1840-1899) concluded that it did indeed contain two elements, which were named ytterbium and scandium. (Scandium, with an atomic number of 21, is not part of the lanthanide series.) Urbain is sometimes credited for discovering ytterbium: in 1907, he showed that the materials Nilson had studied were actually a mixture of two oxides. In any case, Urbain said that
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Lanthanides
KEY TERMS
ALLOY:
A mixture of two or more
metals. The number of protons in the nucleus of an atom. Since this number is different for each element, elements are listed on the periodic table of elements in order of atomic number. ATOMIC
NUMBER:
An atom or atoms that has lost or gained one or more electrons, and thus has a net electrical charge. ION:
A progressive decrease in the radius of lanthanide atoms as they increase in atomic number. LANTHANIDE
CONTRACTION:
LANTHANIDE SERIES: A group of 14 elements, with atomic numbers 58 through 71, that follow lanthanum on the periodic table of elements.
The lanthanide series, along with lanthanum. LANTHANIDES:
OXIDE: A compound formed by the chemical bonding of a metal with oxygen. PERIODIC TABLE OF ELEMENTS: A
chart showing the elements arranged in order of atomic number, grouping them according to common characteristics. RARE EARTH METALS: An old name for the lanthanides, reflecting the difficulty of separating them from compounds containing other lanthanides or other substances.
Groups 3 through 12 on the IUPAC or European version of the periodic table of elements. The lanthanides and actinides, which appear at the bottom of the periodic table, are “branches” of this family. TRANSITION
METALS:
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the credit should be given to Marignac, who is the most important figure in the history of lanthanides other than Mosander. As for ytterbium, it is highly malleable, like other lanthanides, but does not have any significant applications in industry. Swedish chemist Per Teodor Cleve (18401905) found in 1879 that erbia contained two more elements, which he named holmium and thulium. Thulium refers to the ancient name for Scandinavia, Thule. Rarest of all the lanthanides, thulium is highly malleable—and also highly expensive. Hence it has few commercial applications. DYSPROSIUM. Named for the Greek word dysprositos, or “hard to get at,” dysprosium was discovered by Boisbaudran. Separating ytterite in 1886, he found gallium (atomic number 31—not a lanthanide); samarium (discussed above); and dysprosium. Yet again, a mineral extracted from ytterite had been named after a previously discovered element, and, yet again, it turned out to contain several elements. The substance in question this time was holmium, which, as Boisbaudran discovered, was actually a complex mixture of terbium, erbium, holmium, and the element he had identified as dysprosium. A pure sample was not obtained until 1950.
Because dysprosium has a high affinity for neutrons, it is sometimes used in control rods for nuclear reactors, “soaking up” neutrons rather as a sponge soaks up water. Soft, with a lustrous silver color like other lanthanides, dysprosium is also applied in lasers, but otherwise it has few uses. EUROPIUM
AND
LUTETIUM.
Whereas many other lanthanides are named for regions in northern Europe, the name for europium refers to the European continent as a whole, and that of lutetium is a reference to the old Roman name for Paris. As mentioned earlier,
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Demarçay found europium in samarskite, a discovery he made in 1901. Actually, Boisbaudran had noticed what appeared to be a new element about a decade previously, but he did not pursue it, and thus the credit goes to his countryman. Most reactive of the lanthanides, europium responds both to cold water and to air. In addition, it is capable of catching fire spontaneously. Among the most efficient elements for the capture of neutrons, it is applied in the control systems of nuclear reactors. In addition, its compounds are utilized in the manufacture of phosphors for TV sets: one such compound, for instance, emits a reddish glow. Yet another europium compound is added to the glue on postage stamps, making possible the electronic scanning of stamps. Urbain, who discovered lutetium, named it after his hometown. James also identified a form of the lanthanide, but did not announce his discovery until much later. Except for some uses at a catalyst in the production of petroleum, lutetium has few industrial applications.
WHERE TO LEARN MORE Cotton, Simon. Lanthanides and Actinides. New York: Oxford University Press, 1991. Heiserman, David L. Exploring Chemical Elements and Their Compounds. Blue Ridge Summit, PA: Tab Books, 1992. “Luminescent Lanthanides” (Web site). (May 16, 2001). Snedden, Robert. Materials. Des Plaines, IL: Heinemann Library, 1999. Oxlade, Chris. Metal. Chicago: Heinemann Library, 2001. Stwertka, Albert. A Guide to the Elements. New York: Oxford University Press, 1996. Whyman, Kathryn. Metals and Alloys. Illustrated by Louise Nevett and Simon Bishop. New York: Gloucester Press, 1988.
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S C I E N C E O F E V E RY DAY T H I N G S r e a l - l i f e CHEMISTRY
N O N M E TA L S A N D M E TA L L O I D S N O N M E TA L S M E TA L L O I D S HALOGENS NOBLE GASES CARBON HYDROGEN
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Nonmetals
CONCEPT Nonmetals, as their name implies, are elements that display properties quite different from those of metals. Generally, they are poor conductors of heat and electricity, and they are not ductile: in other words, they cannot be easily reshaped. Included in this broad grouping are the six noble gases, the five halogens, and eight “orphan” elements. Two of these eight—hydrogen and carbon—are so important that separate essays are devoted to them. Two more, addressed in this essay, are absolutely essential to human life: oxygen and nitrogen. Hydrogen and helium, a nonmetal of the noble gas family, together account for about 99% of the mass of the universe, while Earth and the human body are composed primarily of oxygen, with important components of carbon, nitrogen, and hydrogen. Indeed, much of life—human, animal, and plant—can be summed up with these four elements, which together make Earth different from any other known planet. Among the other “orphan” nonmetals are phosphorus and sulfur, the “brimstone” of the Bible, as well as boron and selenium.
N O N M E TA L S
losing electrons. The vast majority of elements— 87 in all—are metals, and these occupy the left, center, and part of the right-hand side of the periodic table. With the exception of hydrogen, placed in Group 1 above the alkali metals, the nonmetals fill a triangle-shaped space in the upper right corner of the periodic table. All gaseous elements are nonmetals, a group that also includes some solids, as well as bromine, the only element other than mercury that is liquid at room temperature. In general, the nonmetals are characterized by properties opposite those of metals. They are poor conductors of heat and electricity (though carbon, a good electrical conductor, is an exception), and they tend to form negative ions by gaining electrons. They are not particularly malleable, and whereas most metals are shiny, nonmetals may be dull-colored, black (in the case of carbon in some forms or allotropes), or invisible, as is the case with most of the gaseous nonmetals.
Grouping the Nonmetals
The majority of elements on the periodic table are metals: solids (along with one liquid, mercury) which are lustrous or shiny in appearance. Metals are ductile, or malleable, meaning that they can be molded into different shapes without breaking. They are excellent conductors of heat and electricity, and tend to form positive ions by
Whereas the metals can be broken down into five families, along with seven “orphans”—elements that do not fit into a family grouping—the nonmetals are arranged in two families, as well as eight “orphans.” Hydrogen, because of its great abundance in the universe and its importance to chemical studies, is addressed in a separate essay within this book. The same is true of carbon: though not nearly as abundant as hydrogen, carbon is a common element of all living things, and therefore it is discussed in the essay on Carbons and Organic Chemistry.
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HOW IT WORKS Defining the Nonmetals
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Nonmetals
LIQUID
NITROGEN ACCOUNTS FOR ABOUT ONE-THIRD OF ALL COMMERCIAL USES OF NITROGEN.
HERE,
A MEDICAL
WORKER PUTS A SAMPLE OF BONE MARROW INTO A TANK OF LIQUID NITROGEN FOR PRESERVATION. (Leif Skoogfors/
Corbis. Reproduced by permission.)
The other six “orphan” nonmetals, which will be examined in detail later in this essay, are listed below by atomic number: • • • • • •
5. Boron (B) 7. Nitrogen (N) 8. Oxygen (O) 15. Phosphorus (P) 16. Sulfur (S) 34. Selenium (Se)
T H E N O B L E GAS E S . The noble gases, discussed in detail within an essay devoted to that subject, are listed below by atomic number:
• • • • • •
2. Helium (He) 10. Neon (Ne) 18. Argon (Ar) 36. Krypton (Kr) 54. Xenon (Xe) 86. Radon (Rn) Occupying Group 8 of the North American periodic table, the noble gases—with the exception of helium—have valence electron configurations of ns2np6. This means that they have two valence electrons (the electrons involved in chemical bonding) on the orbital designated as s, and six more on the p orbital. As for n, this des-
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ignates the energy level, a number that corresponds to the period or row that an element occupies on the periodic table. Most elements bond according to what is known as the octet rule, forming a shell composed of eight electrons. Since the noble gases already have eight electrons on their shell, they tend not to bond with other elements: hence the name “noble,” which in this context means “set apart.” Helium, on the other hand, has a valence shell of s2; however, it too is characterized by a lack of reactivity, and therefore is included in the noble gas family. Noble gases are all monatomic, meaning that they exist as individual atoms, rather than in molecules. To put it another way, their molecules are single atoms. (By contrast, atoms of oxygen, for instance, usually combine to form a diatomic molecule, designated O2.) Due to their apparent lack of reactivity, the noble gases—also known as the rare gases—were once called the inert (inactive) gases. Indeed, helium, neon, and argon have not been found to combine with other elements to form compounds. However, in 1962, English chemist Neil Bartlett (1932-) succeeded in preparing a compound of xenon with platinum and fluorine (XePtF6), thus overturning the idea that the
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AT
AN
“OXYGEN BAR,” YOU CAN RELAX BY BREATHING JAPAN. (AFP/Corbis. Reproduced by permission.)
OXYGEN.
HERE,
A WOMAN IS BREATHING FLAVORED OXYGEN
AT A BAR IN
noble gases were entirely “inert.” Since that time, numerous compounds of xenon with other elements, most notably oxygen and fluorine, have been developed. Fluorine has also been used to form simple compounds with krypton and radon. T H E H A LO G E N S . Next to the noble
gases, in Group 7, are the halogens, a family discussed in a separate essay. These are listed below, along with atomic number and chemical symbol. Note that astatine is sometimes included with the metalloids, elements that display characteristics both of metals and nonmetals. • • • • •
9. Fluorine (F) 17. Chlorine (Cl) 35. Bromine (Br) 53. Iodine (I) 85. Astatine (At) The halogens all have valence electron configurations of ns2np5: in other words, at any energy level n, they have two valence electrons in the s orbital, and 5 in the p orbital. In terms of phase of matter, the halogens are the most varied family on the periodic table. Fluorine and chlorine are gases, iodine is a solid, and bromine (as noted earlier) is one of only two elements existing at room temperature as a liquid. As for asta-
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tine, it is a solid too, but so highly radioactive it is hard to determine much about its properties. (The only other nonmetal that has a large number of radioactive isotopes is the noble gas radon, considered highly dangerous.) Though they are “next door” to the noble gases, the halogens could not be more different. Whereas their neighbors to the right are the least reactive elements on the periodic table, the halogens are the most reactive. Indeed, fluorine has the highest possible value of electronegativity, the relative ability of an atom to attract valence electrons. It is therefore one of the only elements that will bond with a noble gas. All of the halogens tend to form salts, compounds—formed, along with water, from the reaction of an acid and base—that bring together a metal and a nonmetal. Due to this tendency, the first of the family to be isolated—chlorine, in 1811—was originally named “halogen,” a combination of the Greek words halos, or salt, and gennan, “to form or generate.” In their pure form, halogens are diatomic, and in contact with other elements, they form ionic bonds, which are the strongest form of chemical bond. In the process of bonding, they become negatively charged ions, or anions.
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Abundance of the Nonmetals Nonmetals I N T H E U N I V E R S E . As is stated many times throughout this book, humans may be created equal, but the elements are not. Though 88 elements exist in nature, this certainly does not mean that each occupies a 1/88 share of the total pie. Just two elements—the nonmetals hydrogen and helium, which occupy the first two positions on the periodic table— account for 99.9% of the matter in the entire universe, yet the percentage of matter they make up on Earth is very small.
The reason for this disparity is that, whereas our own planet (as far as we know) is unique in sustaining life—requiring oxygen, carbon, nitrogen, and other elements—the vast majority of the universe is made up of stars, composed primarily of hydrogen and helium. O N E A RT H A N D I N T H E AT M O S P H E R E . Nonmetals account for a large
portion of Earth’s total known elemental mass— that is, the composition of the planet’s crust, waters, and atmosphere. Listed below are figures ranking nonmetals within the overall picture of elements on Earth. The numbers following each element’s name indicate the percentage of each within the planet’s total known elemental mass. • • • • • • • •
1. Oxygen (49.2%) 9. Hydrogen (0.87%) 11. Chlorine (0.19%) 12. Phosphorus (0.11%) 14. Carbon (0.08%) 15. Sulfur (0.06%) 17. Nitrogen (0.03%) 18. Fluorine (0.03%) Some of the figures above may seem rather small, but in fact only 18 elements account for all but 0.49% of the planet’s known elemental mass, the remainder being composed of numerous other elements in small quantities. In Earth’s atmosphere, the composition is all nonmetallic, as one might expect: • • • •
1. Nitrogen (78%) 2. Oxygen (21%) 3. Argon (0.93%) 4. Various trace gases, including water vapor, carbon dioxide, and ozone or O3 (0.07%) I N T H E H U M A N B O DY. As noted earlier, carbon is a component in all living things, and it constitutes the second-most abundant ele-
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ment in the human body. Together with oxygen and hydrogen, it accounts for 93% of the body’s mass. Listed below are the most abundant nonmetals in the human body, by ranking. • • • • • • •
1. Oxygen (65%) 2. Carbon (18%) 3. Hydrogen (10%) 4. Nitrogen (3%) 6. Phosphorus (1.0%) 9. Sulfur (0.26%) 11. Chlorine (0.14%)
REAL-LIFE A P P L I C AT I O N S Boron The first “orphan” nonmetal, by atomic number, is boron, named after the Arabic word buraq or the Persian burah. (It is thus unusual in being one of the only elements whose name is not based on a word from a European language, or— for the later elements—the name of a person or place.) It was discovered in 1808 by English chemist Sir Humphry Davy (1778-1829), a man responsible for identifying or isolating numerous elements; French physicist and chemist Joseph Gay-Lussac (1778-1850), known in part for the gas law named after him; and French chemist Louis Jacques Thénard (1777-1857). These scientists used the reaction of boric acid (H3BO3) with potassium to isolate the element. Sometimes classified as a metalloid because it is a semiconductor of electricity, boron is applied in filaments used in fiber optics research. Few of its other applications, however, have much to do with electrical conductivity. Boric or boracic acid is used as a mild antiseptic, and in North America, it is applied for the control of cockroaches, silverfish, and other pests. A compound known as borax is a water softener in washing powders, while other compounds are used to produce enamels for the coating of refrigerators and other appliances. Compounds involving boron are also present in pyrotechnic flares, because they emit a distinctive green color, and in the igniters of rockets.
Nitrogen Though most people think of air as consisting primarily of oxygen, in fact—as noted above— the greater part of the air we breathe is made up
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of nitrogen. Scottish chemist David Rutherford (1749-1819) is usually given credit for discovering the element: in 1772, he identified nitrogen as the element that remained when oxygen was removed from air. Several other scientists around the same time made a similar discovery. Because of its heavy presence in air, nitrogen is obtained primarily by cooling air to temperatures below the boiling points of its major components. Nitrogen boils (that is, turns into a gas) at a lower temperature than oxygen: -320.44°F (-195.8°C), as opposed to -297.4°F (-183°C). When air is cooled to -328°F (-200°C) and then allowed to warm slowly, the nitrogen boils first, and therefore evaporates first. The nitrogen gas is captured, cooled, and liquefied once more. Nitrogen can also be obtained from compounds such as potassium nitrate or saltpeter, found primarily in India; or sodium nitrate (Chilean saltpeter), which comes from the desert regions of Chile. To isolate nitrogen, various processes are undertaken in a laboratory—for instance, heating barium azide or sodium azide, both of which contain nitrogen. R E AC T I O N S W I T H O T H E R E L E M E N T S . Existing as diatomic molecules,
nitrogen forms very strong triple bonds, and as a result tends to be fairly unreactive at low temperatures. Thus, for instance, when a substance burns, it reacts with the oxygen in the air, but not with the nitrogen. At high temperatures, however, nitrogen combines with other elements, reacting with metals to form nitrides; with hydrogen to form ammonia; with O2 to form nitrites; and with O3 to form nitrates. Nitrogen and oxygen, in particular, react at high temperatures to form numerous compounds: nitric oxide (NO), nitrous oxide (N2O), nitrogen dioxide (NO2), dinitrogen trioxide (N2O3), and dinitrogen pentoxide (N2O5). In reaction with halogens, nitrogen forms unstable, explosive compounds such as nitrogen trifluoride (NF3), nitrogen trichloride (NCl3), and nitrogen triiodide (NI3). One thing is for sure: never mix ammonia with bleach, which involves the halogen chlorine. Together, these two produce chloramines, gases with poisonous vapors. U S E S F O R N I T R O G E N . One of the most striking scenes in a memorable film, “Terminator 2: Judgment Day” (1991), occurs near the end of the movie, when the villainous T1000 robot steps into a pool of liquid nitrogen
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and cracks to pieces. As noted, nitrogen must be at extremely low temperatures to assume liquid form. Liquid nitrogen, which accounts for about one-third of all commercial uses of the element, is applied for quick-freezing foods, and for preserving foods in transit. Liquid nitrogen also makes it possible to process materials, such as some forms of rubber, that are too pliable for machining at room temperature. These materials are first cooled in liquid nitrogen, and then become more rigid.
Nonmetals
In processing iron or steel, which forms undesirable oxides if exposed to oxygen, a blanket of nitrogen is applied to prevent this reaction. The same principle is applied in making computer chips and even in processing foods, since these items too are detrimentally affected by oxidation. Because it is far less combustible than air (magnesium is one of the few elements that burns nitrogen in combustion), nitrogen is also used to clean tanks that have carried petroleum or other combustible materials. As noted, nitrogen combines with hydrogen to form ammonia, used in fertilizers and cleaning materials. Ammonium nitrate, applied primarily as a fertilizer, is also a dangerous explosive, as shown with horrifying effect in the bombing of the Alfred P. Murrah Federal Building in Oklahoma City on April 19, 1995—a tragedy that took 168 lives. Nor is ammonium nitrate the only nitrogen-based explosive. Nitric acid is used in making trinitrotoluene (TNT), nitroglycerin, and dynamite, as well as gunpowder and smokeless powder. NITROGEN, THE ENVIRONM E N T, A N D H E A LT H . The nitrogen
cycle is the process whereby nitrogen passes from the atmosphere into living things, and ultimately back into the atmosphere. Both through the action of lightning in the sky, and of bacteria in the soil, nitrogen is converted to nitrates and nitrites—compounds of nitrogen and oxygen. These are then absorbed by plants to form plant proteins, which convert to animal proteins in the bodies of animals who eat the plants. When an animal dies, the proteins are returned to the soil, and denitrifying bacteria break down these compounds, returning elemental nitrogen to the atmosphere. Not all nitrogen in the atmosphere is healthful, however. Oxides of nitrogen, formed in the high temperatures of internal combustion
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engines, pass into the air as nitric oxide. This compound reacts readily with oxygen in the air to form nitrogen dioxide, a toxic reddish-brown gas that adds to the tan color of smog over major cities. Another health concern is posed by sodium nitrate and sodium nitrite, added to bacon, sausage, hot dogs, ham, bologna and other food products to inhibit the growth of harmful microorganisms. Many researchers believe that nitrites impair the ability of a young child’s blood to carry oxygen. Furthermore, nitrites often combine with amines, a form of organic compound, to create a variety of toxins known as nitrosoamines. Because of concerns about these dangers, scientists and health activists have called for a ban on the use of nitrites and nitrates as food additives.
Oxygen Discovered independently by Swedish chemist Carl W. Scheele (1742-1786) and English chemist Joseph Priestley (1733-1804) in the period 17731774, oxygen was named by a third scientist, French chemist Antoine Lavoisier (1743-1794). Believing (incorrectly) that all acids contained the newly discovered element, Lavoisier called it oxygen, which comes from a French word meaning “acid-former.” Like many elements, oxygen has been in use since the beginning of time. But this is quite different from saying, for instance, that iron has been in use since the early stages of human history. A person can live without iron (except for the necessary quantities in the human body), and can survive for weeks or even months without food. One can live for a few days without water (the most famous and plentiful of all oxygencontaining compounds); but one cannot survive for more than a few minutes without the oxygen in air. Oxygen appears in three allotropes (different versions of the same element, distinguished by molecular structure): monatomic oxygen (O); diatomic oxygen or O2; and triatomic oxygen (O3), better known as ozone. The diatomic form dominates the natural world, but in the upper atmosphere, ozone forms a protective layer that keeps the Sun’s harmful ultraviolet radiation from reaching Earth. Concerns that chlorofluorocarbons (CFCs) may be depleting the ozone layer by converting these triatomic molecules to
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O2 has led to a reduction in the output of CFCs by industrialized nations. O B TA I N I N G OX Y G E N . Oxygen, of
course, is literally “in the air,” mixed with larger quantities of nitrogen. Higher up in the atmosphere, it occurs as a free element. Through electrolysis,, it can be obtained from water; however, this process is prohibitively expensive for most commercial applications. Oxygen-containing compounds are also sources of oxygen for commercial use, but generally oxygen is obtained by the fractional distillation of liquid air, described above with regard to nitrogen. After the nitrogen has been separated, argon and neon (which also have lower boiling points than oxygen) also boil off, leaving behind an impure form of oxygen. This is further purified by a process of cooling, liquefying, and evaporation, which eliminates traces of noble gases such as krypton and xenon. Many millions of years ago, when Earth was first formed, there was no oxygen on the planet. The growth of oxygen on Earth coincided with the development of organisms that, as they evolved, increasingly needed oxygen. The present concentration of oxygen in the atmosphere, oceans, and the rocks of Earth’s crust was reached about 580 million years ago, and is sustained today by biological activity. When plants undergo photosynthesis, carbon dioxide and water react in the presence of chlorophyll to produce carbohydrates and oxygen. OXIDES AND OTHER COMP O U N D S . Though the bond in diatomic
oxygen is strong, once it is broken, monatomic oxygen reacts readily with other elements to form a seemingly limitless range of compounds: oxides, silicates, carbonates, phosphates, sulfates, and other more complex substances. The process known as oxidation results in the formation of numerous oxides. Sometimes oxygen and another element form several oxides, as for example in the case of nitrogen, whose five oxides are listed above. Water is an oxide; so too are carbon dioxide and carbon monoxide. When animals and plants die, the organic materials that make them up react with oxygen in the air, resulting in a complex form of oxidation known as decay—or, in common language, “rotting.” Oxygen, reacting with compounds such as hydrocarbons, produces carbon dioxide and water vapor at high temperatures. If the oxida-
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tion process is extremely rapid, and takes place at high temperatures, it is usually identified as combustion. In addition, oxygen reacts with iron and other metals to form oxides. Many of these oxides, commonly known as rust, are undesirable. Every year, millions upon millions of dollars are spent on painting metal structures, or for other precautions to protect against the formation of metallic oxides. On the other hand, metallic oxides may be produced deliberately for applications in materials such as mortar color, to enhance the appearance of a brick building. U S E S O F OX Y G E N . Aside from the obvious application of oxygen for breathing, there are four major fields that make use of this element: medicine, metallurgy, rocketry, and the field of chemistry concerned with chemical synthesis. The medical application is closest to how we normally use oxygen in our daily lives. In oxygen therapy, a patient having difficulty breathing is given doses of pure, or nearly pure, oxygen. This is used during surgical procedures, and to treat patients who have had heart attacks, as well as those suffering from various infectious or respiratory diseases.
The use of oxygen in metallurgy involves refining coke, which is almost pure carbon, to make carbon monoxide. Carbon monoxide, in turn, reduces iron oxides to pure metallic iron. Oxygen is also used in blast furnaces to convert pig iron to steel by removing excess carbon, silicon, and metallic impurities. In addition, oxygen is applied in torches for welding and cutting. In the form of liquefied oxygen, or LOX, oxygen is used in rockets and missiles. The space shuttle, for instance, carries a huge internal tank containing oxygen and hydrogen, which, when they react, give the vehicle enormous thrust. In chemical synthesis—the preparation of compounds (especially organic ones) from easily available chemicals—commercial chemists use oxygen, for instance, to loosen the bonds in hydrocarbons. If this is done too quickly, it results in combustion; but at a controlled rate, the chemical synthesis of hydrocarbons can generate products such as acetylene, ethylene, and propylene.
addition, divers carry tanks in which oxygen is mixed with helium, rather than nitrogen, to prevent the dangerous condition known as “the bends.”
Nonmetals
As early as the 1960s, smog-ridden cities such as Tokyo and Mexico City were equipped with coin-operated oxygen booths—a sort of “phone booth for the lungs.” After inserting the appropriate amount of money, a person received a dose of oxygen for inhaling. This idea, spawned by necessity, is the likely inspiration for a rather bizarre fad that took hold in the trendier cities of North America during the mid-1990s: oxygen bars. Popular in Los Angeles, New York, and Toronto, these are establishments in which patrons pay up to a dollar per minute to inhale pure or flavored oxygen. Enthusiasts have touted the health benefits of this practice, but some physicians have warned of oxygen toxicity and other dangers.
The Other “Orphan” Nonmetals P H O S P H O R U S . Some elements, such as iron or gold, were known from ancient or even prehistoric times—meaning that the identity of the discoverer is unknown. Phosphorus was the first element whose discoverer is known: German chemist Hennig Brand (c. 1630-c. 1692), who identified it in 1674.
Highly reactive with oxygen, phosphorus is used in the production of safety matches, smoke bombs, and other incendiary devices. It is also important in fertilizers, and in various industrial applications. Phosphorus forms a number of important compounds, most notably phosphates, on which animals and plants depend. Phosphorus pollution, created by the use of household detergents containing phosphates, raised environmental concerns in the 1960s and 1970s. It was feared that high phosphate levels in rivers and creeks would lead to runaway, detrimental growth of plants and algae near bodies of water, a condition known as eutrophication. These concerns led to a ban on the use of phosphates in detergents.
Oxygen can be used to produce synthetic fuels, as well as for water purification and sewage treatment. Airplanes carry oxygen supplies in case of depressurization at high altitudes; in
On its own, sulfur has no smell, but in combination with other elements, it often acquires a foul odor, which has given it an unpleasant reputation. The element’s smell, combined with its combustibility, led to the associa-
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KEY TERMS ALLOTROPES:
Different versions of the same element, distinguished by molecular structure.
gases are noted for their extreme lack of reactivity—in other words, they tend not to react to, or bond with, other elements.
A term describing an element that exists as molecules composed of two atoms. This is in contrast to monatomic elements.
Elements that have a dull appearance; are not malleable; are poor conductors of heat and electricity; and tend to gain electrons to form negative ions. They are thus opposite of metals in most regards, as befits their name. In addition to hydrogen, in Group 1 of the periodic table, the other 18 nonmetals occupy the upper right-hand side of the chart. They include the noble gases, halogens, and seven “orphan” elements: boron, carbon, nitrogen, oxygen, phosphorus, sulfur, and selenium.
DIATOMIC:
The use of an electric current to cause a chemical reaction. ELECTROLYSIS:
HALOGENS: Group 7 of the periodic table of elements, with valence electron configurations of ns2np5. In contrast to the noble gases, the halogens are known for high levels of reactivity.
An atom or group of atoms that has lost or gained one or more electrons, and thus has a net electric charge. ION:
Atoms that have an equal number of protons, and hence are of the same element, but differ in their number of neutrons. This results in a difference of mass. Isotopes may be either stable or unstable. The unstable type, known as radioisotopes, are radioactive. ISOTOPES:
Elements that are lustrous or shiny in appearance; malleable, meaning that they can be molded into different shapes without breaking; and excellent conductors of heat and electricity. Metals, which constitute the vast majority of all elements, tend to form positive ions by losing electrons. METALS:
A term describing an element that exists as single atoms. This in contrast to diatomic elements.
MONATOMIC:
Group 8 of the periodic table of elements, all of whom (with the exception of helium) have valence electron configurations of ns2np6. The noble NOBLE GASES:
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NONMETALS:
ORBITAL: A pattern of probabilities regarding the position of an electron for an atom in a particular energy state. The higher the principal energy level, the more complex the pattern of orbitals.
A term describing a phenomenon whereby certain isotopes known as radioisotopes are subject to a form of decay brought about by the emission of high-energy particles. “Decay” does not mean that the isotope “rots”; rather, it decays to form another isotope until eventually (though this may take a long time), it becomes stable. RADIOACTIVITY:
The tendency for bonds between atoms or molecules to be made or broken in such a way that materials are transformed.
REACTIVITY:
SHELL: The orbital pattern of the valence electrons at the outside of an atom.
Electrons that occupy the highest principal energy level in an atom. These are the electrons involved in chemical bonding.
VALENCE ELECTRONS:
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tion of “brimstone”—the ancient name for sulfur—with the fires of hell. Because it is not usually combined with other elements in nature, the discovery of sulfur was relatively easy. Pure, or nearly pure, sulfur is mined on the Gulf Coast of the United States, as well as in Poland and Sicily. Sulfur compounds also appear in a number of ores, such as gypsum (calcium sulfate), or magnesium sulfate, better known as Epsom salts. Applications of the aforementioned compounds are discussed in the Alkaline Earth Metals essay. In addition, sulfates are used as agricultural insecticides, and for killing algae in water supplies. Potassium aluminum sulfate, a gelatinous solid that sinks to the bottom when dropped into water, is also used in water purification. Sulfur is sometimes applied in pure form as a fungicide, or in matches, fireworks, and gunpowder. More often, however, it is found in compounds such as the sulfates or the sulfides— including sulfuric acid and the evil-smelling gas known as hydrogen sulfide. Rotten eggs and intestinal gas are two examples of hydrogen sulfide, which, though poisonous, usually poses little danger, because the smell keeps people away. Another sulfur compound is mercaptan, an ingredient in the skunk’s distinctive aroma. Tiny quantities of mercaptan are added to natural gas (which has no odor) so that dangerous gas leaks can be detected by smell. S E L E N I U M . When Swedish chemist Jons Berzelius (1779-1848) first discovered selenium in 1817, in deposits at the bottom of a tank in a sulfuric acid factory, he thought it was tellurium, a metalloid discovered in 1800. A few months later, he reconsidered the evidence, and realized he had found a new element. Because tellurium, which lies just below selenium on the periodic table, had been named for the Earth (tellus in Latin), he named his new discovery after the Greek word for the Moon, selene.
Found primarily in impurities from sulfide ores, selenium is often obtained commercially as
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a by-product of the refining of copper by electrolysis. It occurs in at least three allotropic forms, variously black and red in color. Plants and animals, including humans, need small amounts of selenium to survive, but larger quantities can be toxic. This was demonstrated in the late 1970s, when waterfowl in the area of Kesterson Reservoir in northern California began turning up with birth defects. The cause was later traced to the dumping of selenium from agricultural wastes and industrial plants.
Nonmetals
Because selenium is photovoltaic (able to convert light directly into electricity) and photoconductive (meaning that its resistance to the flow of electric current decreases in the presence of light), it has applications in photocells, exposure meters, and solar cells. It is also used for the conversion of alternating current to direct current, and is applied as a semiconductor in electronic and solid-state appliances. Photocopiers use selenium in toners, and compounds containing selenium are used to tint glass red, orange, or pink. WHERE TO LEARN MORE Beatty, Richard. Phosphorus. New York: Benchmark Books, 2001. Blashfield, Jean F. Nitrogen. Austin, TX: Raintree SteckVaughn, 1999. Fitzgerald, Karen. The Story of Oxygen. New York: F. Watts, 1996. “Group Trends: Selected Nonmetals” (Web site). (May 29, 2001). Knapp, Brian J. Elements. Illustrated by David Woodroffe and David Hardy. Danbury, CT: Grolier Educational, 1996. “Nonmetals” Rutgers University Department of Chemistry (Web site). (May 29, 2001). “Nonmetals, Semimetals, and Their Compounds” (Web site). (May 29, 2001). WebElements (Web site). (May 22, 2001).
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M E TA L L O I D S Metalloids
CONCEPT The term “metalloid” may sound like a reference to a heavy-metal music fan, but in fact it describes a small collection of elements on the right-hand side of the periodic table. Forming a diagonal between boron and astatine, which lies four rows down and four columns to the right of boron, the metalloids are six elements that display qualities of both metals and nonmetals. (Some classifications include boron and astatine as well, but in this book, they are treated as a nonmetal and a halogen respectively.) Of these six—silicon, germanium, arsenic, antimony, tellurium, and polonium—only a few are household names. People know that arsenic is poison, and they have some general sense that silicon is important in surgical implants. But most people do not know that silicon, also the principal material in sand and glass, is the second-most plentiful element on Earth. Without silicon, from which computer chips are made, our computerbased society simply could not exist.
HOW IT WORKS Families and “Orphans” Most elements fit into some sort of “family” grouping: the alkali metals, the alkaline earth metals, transition metals, lanthanides, actinides, halogens, and noble gases. These seven families, five metallic and two nonmetallic, account for 91 of 112 elements on the periodic table. The “orphan” elements, or those not readily classifiable within a family, occupy groups 3 through 6 on the North American version of the
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periodic table, which only numbers the “tall” columns. Twenty elements, occupying a rectangle that stretches across four groups or columns, and five periods or rows, are “orphans.” (This is in addition to hydrogen, on Period 1, Group 1.) These are best classified, not by family, but by crossfamily characteristics that unite large groups of elements. These cross-family groupings can be likened to nations: on one level, a person identifies with his or her family (“I’m a Smith”); but on another level, a person has a national identity (“I’m an American.”) Likewise gold, for instance, is both a member of the transition metals family, and of the larger metals grouping. The “orphan” elements, because they have no family, are best identified with characteristics that unite a large body of elements. (For this reason, the “orphan” metals are discussed in the Metals essay, and the “orphan” nonmetals in the Nonmetals essay.)
Between Metals and Nonmetals Of the twenty “orphan” elements in groups 3 through 6, seven are metals and seven nonmetals. Between them runs a diagonal, comprising the six metalloids. (As noted earlier, boron is sometimes considered a metalloid, but in this book, it is discussed in the Nonmetals essay, while astatine—also sometimes grouped with the metalloids—is treated in the Halogens essay.) What is a metalloid? The best way to answer that question is by evaluating the differences between a metal and a nonmetal. On the periodic table, metals fill the left, center, and part of the right-hand side of the
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WITHOUT SILICON, FROM WHICH COMPUTER CHIPS ARE MADE, OUR COMPUTER-BASED SOCIETY SIMPLY COULD NOT HERE, A WORKER HOLDS A SILICON WAFER WITH INTEGRATED CIRCUITS. (Charles O’Rear/Corbis. Reproduced by
EXIST.
permission.)
chart, as well as the two rows—corresponding to the lanthanides and actinides—placed separately at the bottom. Thus it should not come as a surprise that most elements (87, in fact) are metals. Metals are lustrous or shiny in appearance, and ductile, meaning that they can be molded into different shapes without breaking. They are excellent conductors of heat and electricity, and tend to form positive ions by losing electrons. Nonmetals, which occupy the upper righthand side of the periodic table, include the noble gases, halogens, and the seven “orphan” elements alluded to above. With the addition of hydrogen (which, as noted, is covered in a separate essay), they comprise 19 elements. Whereas all metals
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are solids, except for mercury—a liquid at room temperature—the nonmetals are a collection of gases, solids, and one other liquid, bromine. (Not surprisingly, all gaseous elements are nonmetals.) As their name suggests, nonmetals are opposite to metals in most regards: dull in appearance, they are not particularly ductile or malleable. With the exception of carbon, they are poor conductors of heat and electricity, and tend to gain electrons to form negative ions.
Survey of the Metalloids The metalloids can thus be defined as those elements which exhibit characteristics of both metals and nonmetals. They are all solids, but not
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wise known from ancient times, and both attracted the attention of alchemists—medieval mystics, in many regards the forerunners of chemists, who believed it was possible to change plain metals into gold.
Metalloids
Traces of the alchemical mindset remained a part of European science as late as the mid-eighteenth century, a tendency exemplified by the fact that tellurium, discovered around that time, was believed to be “unripe gold.” On the other hand, the discovery of germanium more than a century later—following predictions of its existence based on the periodic table—reflected a much greater degree of scientific rigor. Finally, the isolation of polonium, known for its radioactivity, was evidence of an even more advanced stage of development in chemistry and science as a whole.
POLONIUM WAS FIRST ISOLATED BY MARIE AND PIERRE CURIE. MARIE CURIE NAMED THE ELEMENT IN HONOR OF HER HOMELAND, POLAND.
lustrous, and conduct heat and electricity moderately well. The six metalloids treated here are listed below, with the atomic number and chemical symbol of each. • • • • • •
14. Silicon (Si) 32. Germanium (Ge) 33. Arsenic (As) 51. Antimony (Sb) 52. Tellurium (Te) 84. Polonium (Po) Silicon is the second most abundant element on Earth, comprising 25.7% of the planet’s known elemental mass. Together with oxygen, it accounts for nearly three-quarters of the known total. (The planet’s core is probably composed largely of iron, with significant deposits of uranium and other metals between the crust and the core, but geologists can only make educated guesses as to the elemental composition beneath the crust.) THE
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M E TA L LO I D S
IN
HISTO-
REAL-LIFE A P P L I C AT I O N S Silicon Swedish chemist Jons Berzelius (1779-1848) discovered silicon in 1823, but humans had been using the element—in the form of compounds known as silicates—for thousands of years. Indeed, silicon may have been one of the first elements formed, many millions of years before life appeared on this planet. Geologists believe that the Earth was once composed primarily of molten iron, oxygen, silicon, and aluminum, still the predominant elements in the planet’s crust. Because iron has a greater atomic mass, it settled toward the center, while the more lightweight elements rose to the surface. Silicon is found in everything from the Sun and other stars, as well as meteorites, to plants and animal bones. Many hundreds of minerals on Earth contain silicon and oxygen in various forms: for instance, silicon and oxygen form silica (SiO2), commonly known as sand. This sand is mixed with lime and soda (sodium carbonate), as well other substances, to make glass. The purest varieties of silica form quartz, known for its clear crystals, while impure quartz forms crystals of semiprecious gems such as amethyst, opal, and agate.
RY. By far the most important of the metalloids, silicon has been in use as a compound for centuries, but was only isolated in the early nineteenth century. Arsenic and antimony were like-
bon on the periodic table, and the elements in
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that group (which includes germanium, selenium, and lead) are sometimes called the “carbon family.” Like carbon, silicon forms a huge array of compounds, because it has four electrons to share in chemical bonding, and thus can form long strings of atoms. Because silicon atoms are much larger than carbon atoms, however, not as many other atoms can get close to silicon. Thus the number of possible compounds involving silicon—though still quite impressive—is less than the many millions of carbon-based compounds Often silicon is combined with oxygen in long chains that use the oxygen atoms as separators. Because oxygen has a valence of two, meaning that it can bond to two other atoms at a time, it bonds easily between two other silicon atoms. The silicon, meanwhile, has two other electrons to use in bonding, so it typically attaches to two more, non-bridging, oxygen atoms. Compounds of this type are known as silicates, and most of the rocks and clay on Earth—with the exception of lime, which is calcium oxide—are silicates made up of combinations of silicon, oxygen, and various metals such as aluminum, iron, sodium, and potassium. Silicones are another variety of compound involving silicon atoms strung together by bridging oxygen atoms. Instead of attaching to two other, non-bridging oxygen atoms, as in a silicate, the silicon atoms in a silicone attach to organic groups—that is, molecules containing carbon. Because silicones often resemble organic compounds such as oils, greases, and rubber, silicone oils are frequently used in place of organic petroleum as a lubricant because they can withstand greater variations in temperature. Silicone rubbers are used in everything from bouncing balls to space vehicles. And because the body tolerates the introduction of silicone implants better than it does organic ones, silicones are used in surgical implants as well. THE MANY OTHER USES OF S I L I C O N . Silicones are also present in elec-
trical insulators, rust preventives, fabric softeners, hair sprays, hand creams, furniture and automobile polishes, paints, adhesives (including bathtub sealers), and chewing gum. Yet even this list does not exhaust the many applications of elemental silicon, as opposed to silicone.
with as many as half a million microscopic and intricately connected electronic circuits. These chips manipulate voltages using binary codes, for which 1 means “voltage on” and 0 means “voltage off.” By means of these pulses, silicon chips perform multitudes of calculations in seconds—calculations that would take humans hours or months or even years.
Metalloids
A porous form of silica, known as silica gel, absorbs water vapor from the air, and is often packed alongside moisture-sensitive products such as electronics components, in order to keep them dry. Silicon carbine, an extremely hard crystalline material manufactured by fusing sand with coke (almost pure carbon) at high temperatures, has applications as an abrasive.
Arsenic Silicon is unquestionably the “star” of the metalloids, but several other elements in this broad grouping have been known since ancient times. Among these is arsenic, well-known from many a detective novel. Highly poisonous, it is often a fixture of such stories: in a typical plot, a greedy nephew drops some arsenic into the tea of an elderly aunt who has left money to him in her will, and it is up to the detective/hero/heroine to uncover the details behind this dastardly scheme. The use of arsenic as a prop in such tales had already become something of a cliché by 1941, when “Arsenic and Old Lace,” a play by Joseph Kesselring that satirized an old-fashioned “whodunit,” made its debut on Broadway. Known since ancient times, arsenic is named after the Greek word arsenikon, meaning “yellow orpiment.” (Orpiment is arsenic trisulfide, or As2S3.) But the Greeks were not the only peoples in antiquity who knew of arsenic and its toxic properties: the Egyptians and Chinese were likewise familiar with it. Alchemists took an interest in arsenic, and one of them, Albertus Magnus (1193-1280)—a German physician who contributed significantly to the rebirth of interest in science during the late Middle Ages—probably isolated the element from arsenic trisulfide in about 1250.
Due to its semi-metallic qualities, silicon is used as a semiconductor of electricity. Computer chips are tiny slices of ultra-pure silicon, etched
Arsenic is more than just a prop in a detective story. (And in fact it is not a very effective poison for a murderer who hopes to get away with his crime: traces of arsenic remain in the body of a murder victim—even in the person’s hair—for years after death.) Today, arsenic is
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used for purposes such as bronzing, and for hardening and improving the sphericity (roundness) of lead shot in shotgun shells. In solid-state devices such as transistors, arsenic or antimony is used for the purposes of “doping.” This may sound like another version of the whodunit-style poisoning described above, but actually doping involves the alteration of chemical properties by deliberately introducing impurities. Through the doping of silicon, its electrical conductivity is improved.
Antimony In ancient times, antimony was known by the Latin name stibium; hence its chemical symbol of Sb. The word, which can be deciphered as “a metal that does not occur by itself,” has roots much older than the Roman civilization, however. Many centuries before the rise of the Romans, the biblical prophet Jeremiah railed against women’s use of “stibic stone” to paint their faces. In fact, stibic stone is antimony (III) sulfide, or Sb2S3, a black mineral which has long been used as an eyeliner. During the Middle Ages, alchemists studied antimony and its compounds, but the first scientist to distinguish between the compounds and the element itself was French chemist Jean-Baptiste Buquet, in 1771. During the early modern era, antimony was used in making bells, tools, and type for printing presses, because its addition to an alloy strengthened the other metals. Today, antimony is added to lead in storage batteries to make the lead harder and stronger. It is still used in metal type, as well as bullets and cable sheathing. Antimony was a component in early varieties of matches, but by 1855, the less volatile phosphorus had replaced it. In altered form, however, antimony still appears in some matches. Oxides and sulfides of antimony are also applied in paints, ceramics, fireworks, pharmaceuticals, and other products. These are also utilized for dyeing cloth and fireproofing materials. In addition, as noted above with regard to arsenic, antimony is applied for the doping of silicon and other materials in semiconductors, particularly those that use infrared detectors.
Tellurium
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century, he did so in alchemical terms, referring to it as “unripe gold.” This reflected the belief, still lingering from the Middle Ages, that metals “grow” to higher states. At least part of his confusion is understandable, since the element did appear in minerals that also contained gold. A few years later, Baron Franz Joseph Müller von Reichenstein, an Austrian mining inspector in Transylvania, analyzed the substance, which he concluded was bismuth sulfide. Later he changed his mind, then subjected the material to a series of tests over a period of many years, until finally he sent a sample to the distinguished German chemist, Martin Heinrich Klaproth (1743-1817). Klaproth concluded that it was indeed a new element, and suggested the Latin word tellus, for “earth,” as a name. Grayish-white and lustrous, tellurium looks like a metal, but it is much more brittle than most metallic elements. Furthermore, it is a semiconductor, which further separates it from the typically conductive metals. Its semiconductive properties have led to applications in building electronic components. Added to copper and stainless steel, tellurium improves the machinability of those metals; in addition, tellurium compounds are used for the coloring of glass, porcelain, enamel, and ceramics.
Germanium and Polonium Germanium. Both named after European countries, germanium and polonium were identified much later than the other metalloids. In 1871, two years after he created his famous periodic table, Russian chemist Dmitri Ivanovitch Mendeleev (1834-1907) predicted the existence of an element he called “eka-silicon.” This turned out to be germanium, which sits directly beneath silicon on the periodic table, and which was discovered in 1886 by German chemist Clemens Alexander Winkler (1838-1904). Germanium is principally used as a doping agent in making transistor elements. It is also used as a phosphor in fluorescent lamps. In addition, germanium and germanium oxide, transparent to the infrared portion of the electromagnetic spectrum, are present in infrared spectroscopes and infrared detectors.
When Hungarian chemist Joseph Ramacsaházy first described tellurium in the mid-eighteenth
P O LO N I U M . While the applications of germanium are limited compared to those of, say, silicon, polonium is useful primarily as a source
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Metalloids
KEY TERMS ION:
An atom or group of atoms that
has lost or gained one or more electrons,
and tend to form positive ions by losing electrons.
and thus has a net electric charge.
Elements that have a
NONMETALS:
Atoms that have an equal
dull appearance; are not malleable; are
number of protons, and hence are of the
poor conductors of heat and electricity;
same element, but differ in their number of
and tend to gain electrons to form negative
neutrons. This results in a difference of
ions. They are thus the opposite of metals
mass. Isotopes may be either stable or
in most regards, as befits their name.
ISOTOPES:
unstable. The latter type, known as radioisotopes, are radioactive.
NORTH AMERICAN SYSTEM:
A ver-
sion of the periodic table of elements that
Elements which exhibit
only numbers groups of elements in which
characteristics of both metals and non-
the number of valence electrons equals the
metals. Metalloids are all solids, but are not
group number—that is, the two “tall”
lustrous or shiny, and they conduct heat
columns to the left of the transition metals,
and electricity moderately well. The six
as well as the six “tall” columns to the right.
METALLOIDS:
metalloids occupy a diagonal region
“ORPHAN”:
between the metals and nonmetals on the
belong to any clearly defined family of ele-
right side of the periodic table. Sometimes
ments. The metalloids are all “orphans.”
An element that does not
boron and astatine are included with the metalloids, but in this volume, they are treated as an “orphan” nonmetal and a halogen, respectively.
RADIOACTIVITY:
A term describing a
phenomenon whereby certain isotopes known as radioisotopes are subject to a form of decay brought about by the emis-
Elements that are lustrous, or
sion of high-energy particles. “Decay” does
shiny in appearance, and malleable, mean-
not mean that the isotope “rots”; rather, it
ing that they can be molded into different
decays to form another isotope until even-
shapes without breaking. They are excel-
tually (though this may take a long time) it
lent conductors of heat and electricity,
becomes stable.
METALS:
of neutrons in atomic laboratories—hardly something with which a person comes in contact during the course of an ordinary day. Yet the isolation of polonium by Polish-French physicist and chemist Marie Curie (1867-1934), along with her husband Pierre (1859-1906), a French physicist, was a prelude to one of the greatest stories in the history of chemistry. Setting out to find radioactive elements other than uranium, the Curies refined a large quantity of pitchblende, an ore commonly found
in uranium mines. Within a year, they had discovered polonium, which Marie named after her homeland. Polonium is about 100 times as radioactive as uranium, but the Curies were certain that yet another element lay in the pitchblende, and they devoted the next four years to the exhausting process of isolating it. The story of radium, its isolation, and the great price Marie Curie paid for working with radioactive materials is discussed in the essay on Alkaline Earth Metals.
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WHERE TO LEARN MORE “The Arsenic Website Project.” Harvard University Department of Physics (Web site). (May 30, 2001). Knapp, Brian J. Elements. Illustrated by David Woodroffe and David Hardy. Danbury, CT: Grolier Educational, 1996.
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“Metalloids.” ChemicalElements.com (Web site). (May 30, 2001). “Metalloids” (Web site). (May 30, 2001). Pflaum, Rosalynd. Marie Curie and Her Daughter Irène. Minneapolis, MN: Lerner Publications, 1993. Thomas, Jens. Silicon. New York: Benchmark Books, 2001.
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HALOGENS
Halogens
CONCEPT Table salt, bleach, fluoride in toothpaste, chlorine in swimming pools—what do all of these have in common? Add halogen lamps to the list, and the answer becomes more clear: all involve one or more of the halogens, which form Group 7 of the periodic table of elements. Known collectively by a term derived from a Greek word meaning “saltproducing,” the halogen family consists of five elements: fluorine, chlorine, bromine, iodine, and astatine. The first four of these are widely used, often in combination; the last, on the other hand, is a highly radioactive and extremely rare substance. The applications of halogens are many and varied, including some that are dangerous, controversial, and deadly.
HOW IT WORKS The Halogens on the Periodic Table As noted, the halogens form Group 7 of the periodic table of elements. They are listed below, along with chemical symbol and atomic number: • • • • •
place. Many chemists outside the United States refer to these as 18 different groups of elements; however, within the United States, a somewhat different system is used. In many American versions of the chart, there are only eight groups, sometimes designated with Roman numerals. The 40 transition metals in the center are not designated by group number, nor are the lanthanides and actinides, which are set apart at the bottom of the periodic table. The remaining eight columns are the only ones assigned group numbers. In many ways, this is less useful than the system of 18 group numbers; however, it does have one advantage. E L E C T R O N C O N F I G U RAT I O N S A N D B O N D I N G . In the eight-group sys-
tem, group number designates the number of valence electrons. The valence electrons, which occupy the highest energy levels of an atom, are the electrons that bond one element to another. These are often referred to as the “outer shell” of an atom, though the actual structure is much more complex. In any case, electron configuration is one of the ways halogens can be defined: all have seven valence electrons.
Fluorine (F) 9 Chlorine (Cl): 17 Bromine (Br): 35 Iodine (I): 53 Astatine (At): 85 On the periodic table, as displayed in chemistry labs around the world, the number of columns and rows does not vary, since these configurations are the result of specific and interrelated properties among the elements. There are always 18 columns; however, the way in which these are labeled differs somewhat from place to
Because the rows in the periodic table indicate increasing energy levels, energy levels rise as one moves up the list of halogens. Fluorine, on row 2, has a valence-shell configuration of 2s22p5; while that of chlorine is 3s23p5. Note that only the energy level changes, but not the electron configuration at the highest energy level. The same goes for bromine (4s24p5), iodine (4s24p5), and astatine (5s25p5).
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All members of the halogen family have the same valence-shell electron configurations, and thus tend to bond in much the same way. As we
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Halogens
SALT,
LIKE THE MOUND SHOWN HERE, IS A SAFE AND COMMON SUBSTANCE THAT CONTAINS CHLORINE. (Charles
O’Rear/Corbis. Reproduced by permission.)
shall see, they are inclined to form bonds more readily than most other substances, and indeed fluorine is the most reactive of all elements. Thus it is ironic that they are “next door” to the Group 8 noble gases, the least reactive among the elements. The reason for this, as discussed in the Chemical Bonding essay, is that most elements bond in such a way that they develop a valence shell of eight electrons; the noble gases are already there, so they do not bond, except in some cases—and then principally with fluorine.
Characteristics of the Halogens In terms of the phase of matter in which they are normally found, the halogens are a varied group. Fluorine and chlorine are gases, iodine is a solid, and bromine is one of only two elements that exists at room temperature as a liquid. As for astatine, it is a solid too, but so highly radioactive that it is hard to know much about its properties.
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figurations. One of the first things scientists noticed about these five elements is the fact that they tend to form salts. In everyday terminology, “salt” refers only to a few variations on the same thing—table salt, sea salt, and the like. In chemistry, however, the meaning is much broader: a salt is defined as the result of bonding between an acid and a base. Many salts are formed by the bonding of a metal and a nonmetal. The halogens are all nonmetals, and tend to form salts with metals, as in the example of sodium chloride (NaCl), a bond between chlorine, a halogen, and the metal sodium. The result, of course, is what people commonly call “salt.” Due to its tendency to form salts, the first of the halogens to be isolated— chlorine, in 1811—was originally named “halogen.” This is a combination of the Greek words halos, or salt, and gennan, “to form or generate.”
Despite these differences, the halogens have much in common, and not just with regard to their seven valence electrons. Indeed, they were identified as a group possessing similar characteristics long before chemists had any way of knowing about electrons, let alone electron con-
In their pure form, halogens are diatomic, meaning that they exist as molecules with two atoms: F2, Cl2, and so on. When bonding with metals, they form ionic bonds, which are the strongest form of chemical bond. In the process, halogens become negatively charged ions, or anions. These are represented by the symbols F-, Cl-, Br-, and I-, as well as the names fluoride, chloride, bromide, and iodide. All of the halogens
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are highly reactive, and will combine directly with almost all elements.
Halogens
Due to this high level of reactivity, the halogens are almost never found in pure form; rather, they have to be extracted. Extraction of halogens is doubly problematic, because they are dangerous. Exposure to large quantities can be harmful or fatal, and for this reason halogens have been used as poisons to deter unwanted plants and insects—and, in one of the most horrifying chapters of twentieth century military history, as a weapon in World War I.
REAL-LIFE A P P L I C AT I O N S Chlorine Chlorine is a highly poisonous gas, greenishyellow in color, with a sharp smell that induces choking in humans. Yet, it can combine with other elements to form compounds safe for human consumption. Most notable among these compounds is salt, which has been used as a food preservative since at least 3000 B.C. Salt, of course, occurs in nature. By contrast, the first chlorine compound made by humans was probably hydrochloric acid, created by dissolving hydrogen chloride gas in water. The first scientist to work with hydrochloric acid was Persian physician and alchemist Rhazes (ar-Razi; c. 864-c. 935), one of the most outstanding scientific minds of the medieval period. Alchemists, who in some ways were the precursors of true chemists, believed that base metals such as iron could be turned into gold. Of course this is not possible, but alchemists in about 1200 did at least succeed in dissolving gold using a mixture of hydrochloric and nitric acids known as aqua regia. The first modern scientist to work with chlorine was Swedish chemist Carl W. Scheele (1742-1786), who also discovered a number of other elements and compounds, including barium, manganese, oxygen, ammonia, and glycerin. However, Scheele, who isolated it in 1774, thought that chlorine was a compound; only in 1811 did English chemist Sir Humphry Davy (1778-1829) identify it as an element. Another chemist had suggested the name “halogen” for the alleged compound, but Davy suggested that it
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THIS
WORKER
REFRIGERATOR.
IS
REMOVING
CFCS
FREON
FROM
AN
OLD
LIKE FREON MAY BE RESPONSI-
BLE FOR THE DEPLETION OF THE OZONE LAYER. (James A.
Sugar/Corbis. Reproduced by permission.)
be called chlorine instead, after the Greek word chloros, which indicates a sickly yellow color. U S E S O F C H LO R I N E . The dangers involved with chlorine have made it an effective substance to use against stains, plants, animals— and even human beings. Chlorine gas is highly irritating to the mucous membranes of the nose, mouth, and lungs, and it can be detected in air at a concentration of only 3 parts per million (ppm).
The concentrations of chlorine used against troops on both sides in World War I (beginning in 1915) was, of course, much higher. Thanks to the use of chlorine gas and other antipersonnel agents, one of the most chilling images to emerge from that conflict was of soldiers succumbing to poisonous gas. Yet just as it is harmful to humans, chlorine can be harmful to microbes, thus preserving human life. As early as 1801, it had been used in solutions as a disinfectant; in 1831, its use in hospitals made it effective as a weapon against a cholera epidemic that swept across Europe. Another well-known use of chlorine is as a bleaching agent. Until 1785, when chlorine was
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first put to use as a bleach, the only way to get stains and unwanted colors out of textiles or paper was to expose them to sunlight, not always an effective method. By contrast, chlorine, still used as a bleach today, can be highly effective—a good reason not to use regular old-fashioned bleach on anything other than white clothing. (Since the 1980s, makers of bleaches have developed all-color versions to brighten and take out stains from clothing of other colors.)
Fluorine
Calcium hydrocholoride (CaOCl), both a bleaching powder and a disinfectant used in swimming pools, combines both the disinfectant and bleaching properties of chlorine. This and the others discussed here are just some of many, many compounds formed with the highly reactive element chlorine. Particularly notable—and controversial—are compounds involving chlorine and carbon.
French chemist Edmond Fremy (1814-1894) very nearly succeeded in isolating fluorine, and though he failed to do so, he inspired his student Henri Moissan (1852-1907) to continue the project. One of the problems involved in isolating this highly reactive element was the fact that it tends to “attack” any container in which it is placed: most metals, for instance, will burst into flames in the presence of fluorine. Like the others before him, Moissan set about to isolate fluorine from hydrogen fluoride by means of electrolysis—the use of an electric current to cause a chemical reaction—but in doing so, he used a platinum-iridium alloy that resisted attacks by fluorine. In 1906, he received the Nobel Prize for his work, and his technique is still used today in modified form.
CHLORINE AND ORGANIC C O M P O U N D S . Chlorine bonds well with
organic substances, or those containing carbon. In a number of instances, chlorine becomes part of an organic polymer such as PVC (polyvinyl chloride), used for making synthetic pipe. Chlorine polymers are also applied in making synthetic rubber, or neoprene. Due to its resistance to heat, oxidation, and oils, neoprene is used in a number of automobile parts. The bonding of chlorine with substances containing carbon has become increasingly controversial because of concerns over health and the environment, and in some cases chlorinecarbon compounds have been outlawed. Such was the fate of DDT, a pesticide soluble in fats and oils rather than in water. When it was discovered that DDT was carcinogenic, or cancercausing, in humans and animals, its use in the United States was outlawed. Other, less well-known, chlorine-related insecticides have likewise been banned due to their potential for harm to human life and the environment. Among these are chlorine-containing materials once used for dry cleaning. Also notable is the role of chlorine in chlorofluorocarbons (CFCs), which have been used in refrigerants such as Freon, and in propellants for aerosol sprays. CFCs tend to evaporate easily, and concerns over their effect on Earth’s atmosphere have led to the phasing out of their use.
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Fluorine has the distinction of being the most reactive of all the elements, with the highest electronegativity value on the periodic table. Because of this, it proved extremely difficult to isolate. Davy first identified it as an element, but was poisoned while trying unsuccessfully to decompose hydrogen fluoride. Two other chemists were also later poisoned in similar attempts, and one of them died as a result.
P R O P E RT I E S A N D U S E S O F F LU O R I N E . A pale green gas of low density,
fluorine can combine with all elements except some of the noble gases. Even water will burn in the presence of this highly reactive substance. Fluorine is also highly toxic, and can cause severe burns on contact, yet it also exists in harmless compounds, primarily in the mineral known as fluorspar, or calcium fluoride. The latter gives off a fluorescent light (fluorescence is the term for a type of light not accompanied by heat), and fluorine was named for the mineral that is one of its principal “hosts”. Beginning in the 1600s, hydrofluoric acid was used for etching glass, and is still used for that purpose today in the manufacture of products such as light bulbs. The oil industry uses it as a catalyst—a substance that speeds along a chemical reaction—to increase the octane number in gasoline. Fluorine is also used in a polymer commonly known as Teflon, which provides a nonstick surface for frying pans and other cookingrelated products. Just as chlorine saw service in World War I, fluorine was enlisted in World War II to create a
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weapon far more terrifying than poison gas: the atomic bomb. Scientists working on the Manhattan Project, the United States’ effort to develop the bombs dropped on Japan in 1945, needed large quantities of the uranium-235 isotope. This they obtained in large part by diffusion of the compound uranium hexafluoride, which consists of molecules containing one uranium atom and six fluorine anions. F L U O R I D AT I O N
OF
W AT E R .
Long before World War II, health officials in the United States noticed that communities having high concentration of fluoride in their drinking water tended to suffer a much lower incidence of tooth decay. In some areas the concentration of fluoride in the water supply was high enough that it stained people’s teeth; still, at the turn of the century—an era when dental hygiene as we know it today was still in its infancy—the prevention of tooth decay was an attractive prospect. Perhaps, officials surmised, it would be possible to introduce smaller concentrations of fluoride into community drinking water, with a resulting improvement in overall dental health. After World War II, a number of municipalities around the United States undertook the fluoridation of their water supplies, using concentrations as low as 1 ppm. Within a few years, fluoridation became a hotly debated topic, with proponents pointing to the potential health benefits and opponents arguing from the standpoint of issues not directly involved in science. It was an invasion of personal liberty, they said, for governments to force citizens to drink water which had been supplemented with a foreign substance. During the 1950s, in fact, fluoridation became associated in some circles with Communism—just another manifestation of a government trying to control its citizens. In later years, ironically, antifluoridation efforts became associated with groups on the political left rather than the right. By then, the argument no longer revolved around the issue of government power; instead the concern was for the health risks involved in introducing a substance lethal in large doses.
tist and announced “Look, Ma! No cavities!” Within a few years, virtually all brands of toothpaste used fluoride; however, the use of fluoride in drinking water remained controversial.
Halogens
As late as 1993, in fact, the issue of fluoridation remained heated enough to spawn a study by the U.S. National Research Council. The council found some improvement in dental health, but not as large as had been claimed by early proponents of fluoridation. Furthermore, this improvement could be explained by reference to a number of other factors, including fluoride in toothpastes and a generally heightened awareness of dental health among the U.S. populace. CHLOROFLUOROCARBONS.
Another controversial application of fluorine is its use, along with chlorine and carbon, in chlorofluorocarbons. As noted above, CFCs have been used in refrigerants and propellants; another application is as a blowing agent for polyurethane foam. This continued for several decades, but in the 1980s, environmentalists became concerned over depletion of the ozone layer high in Earth’s atmosphere. Unlike ordinary oxygen (O2), ozone or O3 is capable of absorbing ultraviolet radiation from the Sun, which would otherwise be harmful to human life. It is believed that CFCs catalyze the conversion of ozone to oxygen, and that this may explain the “ozone hole,” which is particularly noticeable over the Antarctic in September and October. As a result, a number of countries signed an agreement in 1996 to eliminate the manufacture of halocarbons, or substances containing halogens and carbon. Manufacturers in countries that signed this agreement, known as the Montreal Protocol, have developed CFC substitutes, most notably hydrochlorofluorocarbons (HCFCs), CFC-like compounds also containing hydrogen atoms.
Fluoride had meanwhile gained application in toothpastes. Colgate took the lead, introducing “stannous fluoride” in 1955. Three years later, the company launched a memorable advertising campaign with commercials in which a little girl showed her mother a “report card” from the den-
The ozone-layer question is far from settled, however. Critics argue that in fact the depletion of the ozone layer over Antarctica is a natural occurrence, which may explain why it only occurs at certain times of year. This may also explain why it happens primarily in Antarctica, far from any place where humans have been using CFCs. (Ozone depletion is far less significant in the Arctic, which is much closer to the population centers of the industrialized world.)
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In any case, natural sources, such as volcano eruptions, continue to add halogen compounds to the atmosphere.
Bromine Bromine is a foul-smelling reddish-brown liquid whose name is derived from a Greek word meaning “stink.” With a boiling point much lower than that of water—137.84°F (58.8°C)—it readily transforms into a gas. Like other halogens, its vapors are highly irritating to the eyes and throat. It is found primarily in deposits of brine, a solution of salt and water. Among the most significant brine deposits are in Israel’s Dead Sea, as well as in Arkansas and Michigan. Credit for the isolation of bromine is usually given to French chemist Antoine-Jérôme Balard (1802-1876), though in fact German chemist Carl Löwig (1803-1890) actually isolated it first, in 1825. However, Balard, who published his results a year later, provided a much more detailed explanation of bromine’s properties. The first use of bromine actually predated both men by several millennia. To make their famous purple dyes, the Phoenicians used murex mollusks, which contained bromine. (Like the names of the halogens, the word “Phoenicians” is derived from Greek—in this case, a word meaning “red” or “purple,” which referred to their dyes.) Today bromine is also used in dyes, and other modern uses include applications in pesticides, disinfectants, medicines, and flame retardants. At one time, a compound containing bromine was widely used by the petroleum industry as an additive for gasoline containing lead. Ethylene dibromide reacts with the lead released by gasoline to form lead bromide (PbBr2), referred to as a “scavenger,” because it tends to clean the emissions of lead-containing gasoline. However, leaded gasoline was phased out during the late 1970s and early 1980s; as a result, demand for ethylene dibromide dropped considerably. H A L O G E N L A M P S . The name “halogen” is probably familiar to most people because of the term “halogen lamp.” Used for automobile headlights, spotlights, and floodlights, the halogen lamp is much more effective than ordinary incandescent light. Incandescent “heat-producing” light was first developed in the 1870s and improved during the early part of the
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twentieth century with the replacement of carbon by tungsten as the principal material in the filament, the area that is heated. Tungsten proved much more durable than carbon when heated, but it has a number of problems when combined with the gases in an incandescent bulb. As the light bulb continues to burn for a period of time, the tungsten filament begins to thin and will eventually break. At the same time, tungsten begins to accumulate on the surface of the bulb, dimming its light. However, by adding bromine and other halogens to the bulb’s gas filling—thus making a halogen lamp— these problems are alleviated. As tungsten evaporates from the filament, it combines with the halogen to form a gaseous compound that circulates within the bulb. Instead of depositing on the surface of the bulb, the compound remains a gas until it comes into contact with the filament and breaks down. It is then redeposited on the filament, and the halogen gas is free to combine with newly evaporated tungsten. Though a halogen bulb does eventually break down, it lasts much longer than an ordinary incandescent bulb and burns with a much brighter light. Also, because of the decreased tungsten deposits on the surface, it does not begin to dim as it nears the end of its life.
Iodine First isolated in 1811 from ashes of seaweed, iodine has a name derived from the Greek word meaning “violet-colored”—a reference to the fact it forms dark purple crystals. During the 1800s, iodine was obtained commercially from mines in Chile, but during the twentieth century wells of brine in Japan, Oklahoma, and Michigan have proven a better source. Among the best-known properties of iodine is its importance in the human diet. The thyroid gland produces a growth-regulating hormone that contains iodine, and lack of iodine can cause a goiter, a swelling around the neck. Table salt does not naturally contain iodine; however, sodium chloride sold in stores usually contains about 0.01% sodium iodide, added by the manufacturer. Iodine was once used in the development of photography: during the early days of photographic technology, the daguerreotype process used silver plates sensitized with iodine vapors.
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Halogens
KEY TERMS The negative ion that results
element is never called, for instance, the
A form of chemical bonding that results from attractions between ions with opposite electrical charges.
chlorine anion. Rather, an anion involving
ISOTOPES:
ANION:
when an atom gains one or more electrons. An anion (pronounced “AN-ie-un”) of an
IONIC BONDING:
The number of
Atoms that have an equal number of protons, and hence are of the same element, but differ in their number of neutrons. This results in a difference of mass. Isotopes may be either stable or unstable—that is, radioactive.
protons in the nucleus of an atom. Since
PERIODIC TABLE OF ELEMENTS:
this number is different for each element,
A chart that shows the elements arranged in order of atomic number. Vertical columns within the periodic table indicate groups or “families” of elements with similar chemical characteristics.
a single element is named by adding the suffix -ide to the name of the original element—in this case, “chloride.” Other rules apply for more complex anions. ATOMIC NUMBER:
elements are listed on the periodic table of elements in order of atomic number. CHEMICAL SYMBOL:
A one-or two-
letter abbreviation for the name of an element. DIATOMIC:
A term describing an ele-
ment that exists as molecules composed of two atoms. All of the halogens are diatomic. ELECTROLYSIS:
The use of an elec-
trical current to cause a chemical reaction. HALF-LIFE:
The length of time it takes
a substance to diminish to one-half its initial amount. HALOGENS:
Group 7 of the periodic
table of elements, including fluorine, chlorine, bromine, iodine, and astatine. The halogens are diatomic, and tend to form salts; hence their name, which comes from two Greek terms meaning “salt-forming.” ION:
A large molecule containing many small units that hook together. POLYMER:
An atom that has lost or gained
one or more electrons, and thus has a net electric charge.
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A term describing a phenomenon whereby certain materials are subject to a form of decay brought about by the emission of high-energy particles. “Decay” in this sense does not mean “rot”; instead, radioactive isotopes continue to emit particles, changing into isotopes of other elements, until they become stable.
RADIOACTIVITY:
A compound formed by the reaction of an acid with a base. Salts are usually formed by the joining of a metal and a nonmetal.
SALT:
Electrons that occupy the highest energy levels in an atom, and are involved in chemical bonding. The halogens all have seven valence electrons.
VALENCE ELECTRONS:
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Iodine compounds are used today in chemical analysis and in synthesis of organic compounds.
Astatine Just as fluorine has the distinction of being the most reactive, astatine is the rarest of all the elements. Long after its existence was predicted, chemists still had no luck finding it in nature, and it was only created in 1940 by bombarding bismuth with alpha particles (positively charged helium nuclei). The newly isolated element was given a Greek name meaning “unstable.” Indeed, none of astatine’s 20 known isotopes is stable, and the longest-lived has a half-life of only 8.3 hours. This has only added to the difficulties involved in learning about this strange element, and therefore it is difficult to say what applications, if any, astatine may have. The most promising area involves the use of astatine to treat a condition known as hyperthyroidism, related to an overly active thyroid gland.
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WHERE TO LEARN MORE “The Chemistry of the Halogens.” Purdue University Department of Chemistry (Web site). (May 20, 2001). “Halogens.” Chemical Elements.com (Web site). (May 20, 2001). “Halogens.” Corrosion Source (Web site). (May 20, 2001). “Halogens” (Web site). (May 20, 2001). “The Halogens” (Web site). (May 20, 2001). Knapp, Brian J. Chlorine, Fluorine, Bromine, and Iodine. Henley-on-Thames, England: Atlantic Europe, 1996. Oxlade, Chris. Elements and Compounds. Chicago: Heinemann Library, 2001. Stwertka, Albert. A Guide to the Elements. New York: Oxford University Press, 1998. “Visual Elements: Group VII—The Halogens” (Web site). (May 20, 2001).
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Noble Gases
NOBLE GASES
CONCEPT Along the extreme right-hand column of the periodic table of elements is a group known as the noble gases: helium, neon, argon, krypton, xenon, and radon. Also known as the rare gases, they once were called inert gases, because scientists believed them incapable of reacting with other elements. Rare though they are, these gases are a part of everyday life, as evidenced by the helium in balloons, the neon in signs—and the harmful radon in some American homes.
HOW IT WORKS Defining the Noble Gases The periodic table of elements is ordered by the number of protons in the nucleus of an atom for a given element (the atomic number), yet the chart is also arranged in such a way that elements with similar characteristics are grouped together. Such is the case with Group 8, which is sometimes called Group 18, a collection of non-metals known as the noble gases. The six noble gases are helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn). Their atomic numbers are, respectively, 2, 10, 18, 36, 54, and 86. Several characteristics, aside from their placement on the periodic table, define the noble gases. Obviously, all are gases, meaning that they only form liquids or solids at extremely low temperatures—temperatures that, on Earth at least, are usually only achieved in a laboratory. They are colorless, odorless, and tasteless, as well as monatomic—meaning that they exist as individual atoms, rather than in molecules. (By contrast,
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atoms of oxygen—another gas, though not among this group—usually combine to form a molecule, O2.)
Low Reactivity There is a reason why noble gas atoms tend not to combine: one of the defining characteristics of the noble gas “family” is their lack of chemical reactivity. Rather than reacting to, or bonding with, other elements, the noble gases tend to remain apart—hence the name “noble,” implying someone or something that is set apart from the crowd, as it were. Due to their apparent lack of reactivity, the noble gases—also known as the rare gases—were once known as the inert gases. Indeed, helium, neon, and argon have not been found to combine with other elements to form compounds. However, in 1962 English chemist Neil Bartlett (1932-) succeeded in preparing a compound of xenon with platinum and fluorine (XePtF6), thus overturning the idea that the noble gases were entirely “inert.” Since that time, numerous compounds of xenon with other elements, most notably oxygen and fluorine, have been developed. Fluorine has also been used to form simple compounds with krypton and radon. Nonetheless, low reactivity—instead of no reactivity, as had formerly been thought—characterizes the rare gases. One of the factors governing the reactivity of an element is its electron configuration, and the electrons of the noble gases are arranged in such a way as to discourage bonding with other elements.
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Noble Gases
A
SCIENTIST USING THE POTASSIUM-ARGON DATING PROCESS TO DETERMINE THE AGE OF MATERIALS. (Dean
Conger/Corbis. Reproduced by permission.)
REAL-LIFE A P P L I C AT I O N S Isolation of the Noble Gases H E L I U M . Helium is an unusual element in many respects—not least because it is the only element to have first been identified in the Solar System before it was discovered on Earth. This is significant, because the elements on Earth are the same as those found in space: thus, it is more than just an attempt at sounding poetic when scientists say that humans, as well as the world around them, are made from “the stuff of stars.”
In 1868, a French astronomer named Pierre Janssen (1824-1907) was in India to observe a total solar eclipse. To aid him in his observations, he used a spectroscope, an instrument for analyzing the spectrum of light emitted by an object. What Janssen’s spectroscope showed was surprising: a yellow line in the spectrum, never seen before, which seemed to indicate the presence of a previously undiscovered element. Janssen called it “helium” after the Greek god Helios, or Apollo, whom the ancients associated with the Sun.
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had a worldwide reputation for his work in analyzing light waves. Lockyer, too, believed that what Janssen had seen was a new element, and a few months later, he observed the same unusual spectral lines. At that time, the spectroscope was still a new invention, and many members of the worldwide scientific community doubted its usefulness, and therefore, in spite of Lockyer’s reputation, they questioned the existence of this “new” element. Yet during their lifetimes, Janssen and Lockyer were proven correct. NEON, ARGON, KRYPTON, A N D X E N O N . They had to wait a quarter
century, however. In 1893, English chemist Sir William Ramsay (1852-1916) became intrigued by the presence of a mysterious gas bubble left over when nitrogen from the atmosphere was combined with oxygen. This was a phenomenon that had also been noted by English physicist Henry Cavendish (1731-1810) more than a century before, but Cavendish could offer no explanation. Ramsay, on the other hand, had the benefit of observations made by English physicist John William Strutt, Lord Rayleigh (1842-1919).
Janssen shared his findings with English astronomer Sir Joseph Lockyer (1836-1920), who
Up to that time, scientists believed that air consisted only of oxygen, carbon dioxide, and water vapor. However, Rayleigh had noticed that when nitrogen was extracted from air after a
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process of removing those other components, it had a slightly higher density than nitrogen prepared from a chemical reaction. In light of his own observations, Ramsay concluded that whereas nitrogen obtained from chemical reactions was pure, the nitrogen extracted from air contained trace amounts of an unknown gas.
Noble Gases
Ramsay was wrong in only one respect: hidden with the nitrogen was not one gas, but five. In order to isolate these gases, Ramsay and Rayleigh subjected air to a combination of high pressure and low temperature, allowing the various gases to boil off at different temperatures. One of the gases was helium—the first confirmation that the element existed on Earth—but the other four gases were previously unknown. The Greek roots of the names given to the four gases reflected scientists’ wonder at discovering these hard-to-find elements: neos (new), argos (inactive), kryptos (hidden), and xenon (stranger). RA D O N . Inspired by the studies of Polish-French physicist and chemist Marie Curie (1867-1934) regarding the element radium and the phenomenon of radioactivity (she discovered the element, and coined the latter term), German physicist Friedrich Dorn (1848-1916) became fascinated with radium. Studying the element, he discovered that it emitted a radioactive gas, which he dubbed “radium emanation.” Eventually, however, he realized that what was being produced was a new element. This was the first clear proof that one element could become another through the process of radioactive decay.
Ramsay, who along with Rayleigh had received the Nobel Prize in 1904 for his work on the noble gases, was able to map the new element’s spectral lines and determine its density and atomic mass. A few years later, in 1918, another scientist named C. Schmidt gave it the name “radon.” Due to its behavior and the configuration of its electrons, chemists classified radon among what they continued to call the “inert gases” for another half-century—until Bartlett’s preparation of xenon compounds in 1962.
LAS VEGAS
HAS
NUMEROUS
EXAMPLES
OF
SIGNS
ILLUMINATED BY NEON. (Dave Bartruff/Corbis. Reproduced by
permission.)
released into the air long ago as a by-product of decay on the part of radioactive materials in the Earth’s crust. Within the atmosphere, argon is the most “abundant”—in comparative terms, given the fact that the “rare gases” are, by definition, rare. Nitrogen makes up about 78% of Earth’s atmosphere and oxygen 21%, meaning that these two elements constitute fully 99% of the air above the Earth. Argon ranks a distant third, with 0.93%. The remaining 0.07% is made up on water vapor, carbon dioxide, ozone (O3), and traces of the noble gases. These are present in such small quantities that the figures for them are not typically presented as percentages, but rather in terms of parts per million (ppm). The concentrations of neon, helium, krypton, and xenon in the atmosphere are 18, 5, 1, and 0.09 ppm respectively.
I N T H E AT M O S P H E R E . Though the rare gases are found in minerals and meteorites on Earth, their greatest presence is in the planet’s atmosphere. It is believed that they were
I N T H E S O I L . Radon in the atmosphere is virtually negligible, which is a fortunate thing, in light of its radioactive qualities. Few Americans, in fact, even knew of its existence until 1988, when the United States Environmental Protection Agency (EPA) released a report estimating that some ten million American homes had potentially harmful radon levels. This
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Presence of the Rare Gases on Earth
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A RESEARCHER WORKS WITH LIQUID HELIUM AS PART OF AN EXPERIMENT ON COSMIC BACKGROUND RADIATION. CLOSE TO ABSOLUTE ZERO, HELIUM TRANSFORMS INTO A HIGHLY UNUSUAL LIQUID THAT HAS NO MEASURABLE RESISTANCE TO FLOW. (Roger Ressmeyer/Corbis. Reproduced by permission.)
set off a scare, and during the late 1980s and 1990s, sales of home radon detectors boomed. Meanwhile, the federal government increased concerns with additional reports, advising people to seal their basements and ventilate their homes if radon exceeded certain levels. A number of scientists have disputed the government’s claims, yet some regions of the United States appear to be at relatively high risk due to the presence of radon in the soil. The element seems to be most plentiful in soils containing high concentrations of uranium. If radon is present in a home that has been weather-sealed to improve the efficiency of heating and cooling systems, it is indeed potentially dangerous to the residents. Chinese scientists in the 1960s made an interesting discovery regarding radon and its application to seismography, or the area of the earth sciences devoted to studying and predicting earthquakes. Radon levels in groundwater, the Chinese reports showed, rise considerably just before an earthquake. Since then, the Chinese have monitored radon concentrations in water, and used this data to predict earthquakes.
Many of the noble gases are extracted by liquefying air—that is, by reducing it to temperatures at which it assumes the properties of a liquid rather than a gas. By controlling temperatures in the liquefied air, it is possible to reach the boiling point for a particular noble gas and thereby extract it, much as was done when these gases were first isolated in the 1890s. T H E U N I Q U E S I T UAT I O N O F H E L I U M . Helium is remarkable, in that it
Radon, in fact, is not the only rare gas that can be
only liquefies at a temperature of -457.6°F (-272°C), just above absolute zero. Absolute zero is the temperature at which the motion of atoms or molecules comes to a virtual stop, but the motion of helium atoms never completely ceases. In order to liquefy it, in fact, even at those low
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E X T RAC T I N G
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obtained as the result of radioactive decay: in 1903, Ramsay and British chemist Frederick Soddy (1877-1956) showed that the breakdown of either uranium or radium results in the production of helium atoms (beta particles). A few years later, English physicist Ernest Rutherford (1871-1937) demonstrated that radiation carrying a positive electrical charge (alpha rays) was actually a stream of helium atoms stripped of an electron.
RA R E
GASES.
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temperatures, it must be subjected to pressures many times that exerted by Earth’s atmosphere.
volcanic layers above and below fossil and artifact remains in east Africa.
Given these facts, it is difficult to extract helium from air. More often, it is obtained from natural gas wells, where it is present in relatively large concentrations—between 1% and 7% of the natural gas. The majority of the Earth’s helium supply belongs to the United States, where the greatest abundance of helium-supplying wells are in Texas, Oklahoma, and Kansas. During World War II, the United States took advantage of this supply of relatively inexpensive helium to provide buoyancy for a fleet of airships used for reconnaissance.
Krypton has a number of specialized applications—for instance, it is mixed with argon and used in the manufacture of windows with a high level of thermal efficiency. Used in lasers, it is often mixed with a halogen such as fluorine. In addition, it is also sometimes used in halogen sealed-beam headlights. Many fans of Superman, no doubt, were disappointed at some point in their lives to discover that there is no such thing as “kryptonite,” the fictional element that caused the Man of Steel to lose his legendary strength. Yet krypton—the real thing—has applications that are literally out of this world. In the development of fuel for space exploration, krypton is in competition with its sister element, xenon. Xenon offers better performance, but costs about ten times more to produce; thus krypton has become more attractive as a fuel for space flight.
There is one place with an abundant supply of helium, but there are no plans for a mining expedition any time soon. That place is the Sun, where the nuclear fusion of hydrogen atoms creates helium. Indeed, helium seems to be the most plentiful element of all, after hydrogen, constituting 23% of the total mass of the universe. Why, then, is it so difficult to obtain on Earth? Most likely because it is so light in comparison to air; it simply floats off into space.
Applications for the Noble Gases RA D O N , A R G O N , K RY P T O N , A N D X E N O N . Though radon is known pri-
marily for the hazards it poses to human life and well-being, it has useful applications. As noted above, its presence in groundwater appears to provide a possible means of predicting earthquakes. In addition, it is used for detecting leaks, measuring flow rates, and inspecting metal welds. One interesting use of argon and, in particular, the stable isotope argon-40, is in dating techniques used by geologists, paleontologists, and other scientists studying the distant past. When volcanic rocks are subjected to extremely high temperatures, they release argon, and as the rocks cool, argon-40 accumulates. Because argon-40 is formed by the radioactive decay of a potassium isotope, potassium-40, the amount of argon-40 that forms is proportional to the rate of decay for potassium-40. The latter has a half-life of 1.3 billion years, meaning that it takes 1.3 billion years for half the potassium-40 originally present to be converted to argon-40. Using argon-40, paleontologists have been able to estimate the age of
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Noble Gases
In addition to its potential as a space fuel, xenon is used in arc lamps for motion-picture film projection, in high-pressure ultraviolet radiation lamps, and in specialized flashbulbs used by photographers. One particular isotope of xenon is utilized for tracing the movement of sands along a coastline. Xenon is also applied in high-energy physics for detecting nuclear radiation in bubble chambers. Furthermore, neuroscientists are experimenting with the use of xenon in diagnostic procedures to clarify x-ray images of the human brain. N E O N . Neon, of course, is best-known for its application in neon signs, which produce an eye-catching glow when lit up at night. French chemist Georges Claude (1870-1960), intrigued by Ramsay’s discovery of neon, conducted experiments that led to the development of the neon light in 1910. That first neon light was simply a glass tube filled with neon gas, which glowed a bright red when charged with electricity.
Claude eventually discovered that mixing other gases with neon produced different colors of light. He also experimented with variations in the shapes of glass tubes to create letters and pictures. By the 1920s, neon light had come into vogue, and it is still popular today. Modern neon lamps are typically made of plastic rather than glass, and the range of colors is much greater than in Claude’s day: not only the gas filling, but the coating inside the tube, is varied, resulting in a variety of colors from across the spectrum.
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Though the neon sign is its best-known application, neon is used for many other things. Neon glow lamps are often used to indicate on/off settings on electronic instrument panels, and lightweight neon lamps are found on machines ranging from computers to voltage regulators. In fact, the first practical color television, produced in 1928, used a neon tube to produce the red color in the receiver. Green came from mercury, but the blue light in that early color TV came from another noble gas, helium. H E L I U M . Helium, of course, is widely known for its use in balloons—both for large airships and for the balloons that have provided joy and fun to many a small child. Though helium is much more expensive than hydrogen as a means of providing buoyancy to airships, hydrogen is extremely flammable, and after the infamous explosion of the airship Hindenburg in 1937, helium became the preferred medium for airships. As noted earlier, the United States military made extensive use of helium-filled airships during the World War II.
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Among the most fascinating applications of helium relate to its extraordinarily low freezing point. Helium has played a significant role in the low-temperature science known as cryogenics, and has found application in research concerning superconductivity: the use of very low temperatures to develop materials that conduct electrical power with vastly greater efficiency than ordinary conductors. Close to absolute zero, helium transforms into a highly unusual liquid unlike any known substance, in that it has no measurable resistance to flow. This means that it could carry an electrical current hundreds of times more efficiently than a copper wire.
WHERE TO LEARN MORE “The Chemistry of the Rare Gases” (Web site). (May 13, 2001). “Homework: Science: Chemistry: Gases” Channelone.com (Web site). (May 12, 2001). Knapp, Brian J.; David Woodroffe; David A. Hardy. Elements. Danbury, CT: Grolier Educational, 2000.
The use of helium for buoyancy is one of the most prominent applications of this noble gas, but far from the only one. In fact, not only have people used helium to go up in balloons, but divers use helium for going down beneath the surface of the ocean. In that situation, of course, helium is not used for providing buoyancy, but as a means of protecting against the diving-related condition known as “the bends,” which occurs when nitrogen in the blood bubbles as the diver rises to the surface. Helium is mixed with oxygen in diver’s air tanks because it does not dissolve in the blood as easily as nitrogen.
Taylor, Ron. Facts on Radon and Asbestos. Illustrated by Ian Moores. New York: F. Watts, 1990.
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Mebane, Robert C. and Thomas R. Rybolt. Air and Other Gases. Illustrations by Anni Matsick. New York: Twenty-First Century Books, 1995. “Noble Gases”Xrefer.com (Web site). (May 13, 2001). Rare Gases. Praxair (Web site). (May 13, 2001). Stwertka, Albert. Superconductors: The Irresistible Future. New York: F. Watts, 1991.
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CARBON
Carbon
CONCEPT The phrase “carbon-based life forms,” often used in science-fiction books and movies by aliens to describe the creatures of Earth, is something of a cliché. It is also a redundancy when applied to creatures on Earth, the only planet known to support life: all living things contain carbon. Carbon is also in plenty of things that were once living, which makes it useful for dating the remains of past settlements on Earth. Of even greater usefulness is petroleum, a substance containing carbon-based forms that died long ago, became fossilized, and ultimately changed chemically into fuels. Then again, not all materials containing carbon were once living creatures; yet because carbon is a common denominator to all living things on Earth, the branch of study known as organic chemistry is devoted to the study of compounds containing carbon. Among the most important organic compounds are the many carboxylic acids that are vital to life, but carbon is also present in numerous important inorganic compounds—most notably carbon dioxide and carbon monoxide.
HOW IT WORKS The Basics of Carbon Carbon’s name comes from the Latin word carbo, or charcoal—which, indeed, is almost pure carbon. Its chemical symbol is C, and it has an atomic number of 6, meaning that there are six protons in its nucleus. Its two stable isotopes are 12C, which constitutes 98.9% of all carbon found in nature, and 13C, which accounts for the other 1.1%.
for all other elements are measured: the amu is defined as exactly 1/12 the mass of a single 12C atom. The difference in mass between 12C and 13C, which is heavier because of its extra neutron, account for the fact that the atomic mass of carbon is 12.01 amu: were it not for the small quantities of 13C present in a sample of carbon, the mass would be exactly 12.00 amu. WHERE
CA R B O N
IS
FOUND.
Carbon makes up only a small portion of the known elemental mass in Earth’s crust, oceans, and atmosphere—just 0.08%, or 1/1250 of the whole—yet it is the fourteenth most abundant element on the planet. In the human body, carbon is second only to oxygen in abundance, and accounts for 18% of the body’s mass. Thus if a person weighs 100 lb (45.3 kg), she is carrying around 18 lb (8.2 kg) of carbon—the same material from which diamonds are made! Present in the inorganic rocks of the ground and in the living creatures above it, carbon is everywhere. Combined with other elements, it forms carbonates, most notably calcium carbonate (CaCO3), which appears in the form of limestone, marble, and chalk. In combination with hydrogen, it creates hydrocarbons, present in deposits of fossil fuels: natural gas, petroleum, and coal. In the environment, carbon—in the form of carbon dioxide (CO2)—is taken in by plants, which undergo the process of photosynthesis and release oxygen to animals. Animals breathe in oxygen and release carbon dioxide to the atmosphere.
Carbon and Bonding
The mass of the 12C atom is the basis for the atomic mass unit (amu), by which mass figures
Located in Group 4 of the periodic table of elements (Group 14 in the IUPAC system), carbon has a valence electron configuration of 2s22p2;
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likewise, all the members of Group 4—sometimes known as the “carbon family”—have configurations of ns2np2, where n is the number of the period or row that the element occupies on the table. There are two elements noted for their ability to form long strings of atoms and seemingly endless varieties of molecules: one is carbon, and the other is silicon, directly below it on the periodic table. Silicon, found in virtually all types of rocks except the calcium carbonates (mentioned above), is to the inorganic world what carbon is to the organic. Yet silicon atoms are about one and a half times as large as those of carbon; thus not even silicon can compete with carbon’s ability to form a seemingly limitless array of molecules in various shapes and sizes, and having various chemical properties. B AS I CS O F C H E M I CA L B O N D I N G . Carbon is further distinguished by its
high value of electronegativity, the relative ability of an atom to attract valence electrons. Electronegativity increases with an increase in group number, and decreases with an increase in period number. In other words, the elements with the highest electronegativity values lie in the upper right-hand corner of the periodic table. Actually, the previous statement requires one significant qualification: the extreme righthand side of the periodic table is occupied by elements with negligible electronegativity values. These are the noble gases, which have eight valence electrons each. Eight, as it turns out, is the “magic number” for chemical bonding: most elements follow what is known as the octet rule, meaning that when one element bonds to another, the two atoms have eight valence electrons. If the two atoms have an electric charge and thus are ions, they form strong ionic bonds. Ionic bonding occurs when a metal bonds with a nonmetal. The other principal type of bond is a covalent bond, in which two uncharged atoms share eight valence electrons. If the electronegativity values of the two elements involved are equal, they share the electrons equally; but if one element has a higher electronegativity value, the electrons will be more drawn to that element.
So why is fluorine—capable of forming multitudinous bonds—not as chemically significant as carbon? There are a number of answers, but a simple one is this: because fluorine is too strong, and tends to “overwhelm” other elements, precluding the possibility of forming long chains, it is less chemically significant than carbon. Carbon, on the other hand, has an electronegativity value of 2.5, which places it well behind fluorine. Yet it is still at sixth place (in a tie with iodine and sulfur) on the periodic table, behind only fluorine; oxygen (3.5); nitrogen and chlorine (3.0); and bromine (2.8). In addition, with four valence electrons, carbon is ideally suited to find other elements (or other carbon atoms) for forming covalent bonds according to the octet rule. M U LT I P L E B O N D S . Normally, an element does not necessarily have the ability to bond with as many other elements as it has valence electrons, but carbon—with its four valence electrons—happens to be tetravalent, or capable of bonding to four other atoms at once. Additionally, carbon is capable of forming not only a single bond, but also a double bond, or even a triple bond, with other elements.
Suppose a carbon atom bonds to two oxygen atoms to form carbon dioxide. Let us imagine these three atoms side by side, with the oxygen in the middle. (This, in fact, is how these bonds are depicted in the Couper and Lewis systems of chemical symbolism, discussed in the Chemical Bonding essay.) We know that the carbon has four valence electrons, that the oxygens have six, and that the goal is for each atom to have eight valence electrons—some of which it will share covalently.
periodic table, let us ignore the noble gases, which are the chemical equivalent of snobs.
Two of the valence electrons from the carbon bond with two valence electrons each from the oxygen atoms on either side. This means that the carbon is doubly bonded to each of the oxygen atoms. Therefore, the two oxygens each have four other unbonded valence electrons, which might bond to another atom. It is theoretically possible, also, for the carbon to form a triple
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(Hence the term “noble,” meaning that they are set apart.) To the left of the noble gases are the halogens, a wildly gregarious bunch—none more so than the element that occupies the top of the column, fluorine. With an electronegativity value of 4.0, fluorine is the most reactive of all elements, and the only one capable of bonding even to a few of the noble gases.
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bond with one of the oxygens by sharing three of its valence electrons. It would then have one electron free to share with the other oxygen.
cyanate, it does not. Thus, to reduce the specifics of organic chemistry even further, it can be said that this area of the field constitutes the study of carbon chains, and ways to rearrange them in order to create new substances.
REAL-LIFE A P P L I C AT I O N S
Rubber, vitamins, cloth, and paper are all organically based compounds we encounter in our daily lives. In each case, the material comes from something that once was living, but what truly makes these substance organic in nature is the common denominator of carbon, as well as the specific arrangements of the atoms. We have organic chemistry to thank for any number of things: aspirins and all manner of other drugs; preservatives that keep food from spoiling; perfumes and toiletries; dyes and flavorings, and so on.
Organic Chemistry We have stated that carbon forms tetravalent bonds, and makes multiple bonds with a single atom. In addition, we have mentioned the fact that carbon forms long chains of atoms and varieties of shapes. But how does it do these things, and why? These are good questions, but not ones we will attempt to answer here. In fact, an entire branch of chemistry is devoted to answering these theoretical questions, as well as to determining solutions to a host of other, more practical problems. Organic chemistry is the study of carbon, its compounds, and their properties. (There are carbon-containing compounds that are not considered organic, however. Among these are oxides such as carbon dioxide and monoxide; as well as carbonates, most notably calcium carbonate.) At one time, chemists thought that “organic” was synonymous with “living,” and even as recently as the early nineteenth century, they believed that organic substances contained a supernatural “life force.” Then, in 1828, German chemist Friedrich Wöhler (1800-1882) cracked the code that distinguished the living from the nonliving, and the organic from the inorganic. Wöhler took a sample of ammonium cyanate (NH4OCN), and by heating it, converted it into urea (H2N-CO-NH2), a waste product in the urine of mammals. In other words, he had turned an inorganic material into a organic one, and he did so, as he observed, “without benefit of a kidney, a bladder, or a dog.” It was almost as though he had created life. In fact, what Wöhler had glimpsed—and what other scientists who followed came to understand, was this: what separates the organic from the inorganic is the manner in which the carbon chains are arranged.
Carbon
Allotropes of Carbon G RA P H I T E . Carbon has several allotropes—different versions of the same element, distinguished by molecular structure. The first of these is graphite, a soft material with an unusual crystalline structure. Graphite is essentially a series of one-atom-thick sheets of carbon, bonded together in a hexagonal pattern, but with only very weak attractions between adjacent sheets. A piece of graphite is thus like a big, thick stack of carbon paper: on the one hand, the stack is heavy, but the sheets are likely to slide against one another.
Actually, people born after about 1980 may have little experience with carbon paper, which was gradually phased out as photocopiers became cheaper and more readily available. Today, carbon paper is most often encountered when signing a credit-card receipt: the signature goes through the graphite-based backing of the receipt, onto a customer copy.
Ammonium cyanate and urea have exactly the same numbers and proportions of atoms, yet they are different compounds. They are thus isomers: substances which have the same formula, but are different chemically. In urea, the carbon forms an organic chain, and in ammonium
In such a situation, one might notice that the copied image of the signature looks as though it were signed in pencil. This is not surprising, considering that pencil “lead” is, in fact, a mixture of graphite, clay, and wax. In ancient times, people did indeed use lead—the heaviest member of Group 4, the “carbon family”—for writing, because it left gray marks on a surface. Lead, of course, is poisonous, and is not used today in pencils or in most applications that would involve prolonged exposure of humans to the element. Nonetheless, people still use the word “lead” in reference to pencils, much as they still
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refer to a galvanized steel roof with a zinc coating as a “tin roof.” In graphite the atoms of each “sheet” are tightly bonded in a hexagonal, or six-sided, pattern, but the attractions between the sheets are not very strong. This makes it highly useful as a lubricant for locks, where oil would tend to be messy. A good conductor of electricity, graphite is also utilized for making high-temperature electrolysis cells. In addition, the fact that graphite resists temperatures of up to about 6,332°F (3,500°C) makes it useful in electric motors and generators. D I A M O N D . The second allotrope of carbon is also crystalline in structure. This is diamond, most familiar in the form of jewelry, but in fact widely applied for a number of other purposes. According to the Moh scale, which measures the hardness of minerals, diamond is a 10— in other words, the hardest type of material. It is used for making drills that bore through solid rock; likewise, small diamonds are used in dentists’ drills for boring through the ultra-hard enamel on teeth.
Neither diamonds nor graphite are, in the strictest sense of the term, formed of molecules. Their arrangement is definite, as with a molecule, but their size is not: they simply form repeating patterns that seem to stretch on forever. Whereas graphite is in the form of sheets, a diamond is basically a huge “molecule” composed of carbon atoms strung together by covalent bonds. The size of this “molecule” corresponds to the size of the diamond: a diamond of 1 carat, for instance, contains about 1022 (10,000,000,000,000,000,000,000 or 10 billion billion) carbon atoms. The diamonds used in industry look quite different from the ones that appear in jewelry. Industrial diamonds are small, dark, and cloudy in appearance, and though they have the same chemical properties as gem-quality diamonds, they are cut with functionality (rather than beauty) in mind. A diamond is hard, but brittle: in other words, it can be broken, but it is very difficult to scratch or cut a diamond—except with another diamond.
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monds—as well as the diamonds on an engagement ring—are cut to refract or bend light rays, and to disperse the colors of visible light. BUCKMINSTERFULLERENE.
Until 1985, carbon was believed to exist in only two crystalline forms, graphite and diamond. In that year, however, chemists at Rice University in Houston, Texas, and at the University of Sussex in England, discovered a third variety of carbon—and later jointly received a Nobel Prize for their work. This “new” carbon molecule composed of 60 bonded atoms in the shape of what is called a “hollow truncated icosahedron.” In plain language, this is rather like a soccer ball, with interlocking pentagons and hexagons. However, because the surface of each geometric shape is flat, the “ball” itself is not a perfect sphere. Rather, it describes the shape of a geodesic dome, a design created by American engineer and philosopher R. Buckminster Fuller (1895-1983). There are other varieties of buckminsterfullerene molecules, known as fullerenes. However, the 60-atom shape, designated as 60C, is the most common of all fullerenes, the result of condensing carbon slowly at high temperatures. Fullerenes potentially have a number of applications, particularly because they exhibit a whole range of electrical properties: some are insulators, while some are conductors, semiconductors, and even superconductors. Due to the high cost of producing fullerenes artificially, however, the ways in which they are applied remain rather limited. A M O R P H O U S CA R B O N . There is
a fourth way in which carbon appears, distinguished from the other three in that it is amorphous, as opposed to crystalline, in structure. An example of amorphous carbon is carbon black, obtained from smoky flames and used in ink, or for blacking rubber tires.
The cutting of fine diamonds for jewelry is an art, exemplified in the alluring qualities of such famous gems as the jewels in the British Crown or the infamous Hope Diamond in Washington, D.C.’s Smithsonian Institution. Such dia-
Though it retains some of the microscopic structures of the plant cells in the wood from which it is made, charcoal—wood or other plant material that has been heated without enough air present to make it burn—is mostly amorphous carbon. One form of charcoal is activated charcoal, in which steam is used to remove the sticky products of wood decomposition. What remains are porous grains of pure carbon with enormous microscopic surface areas. These are used in water purifiers and gas masks.
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Carbon
A
MONTREAL, QUEBEC, CANADA. SUCH DOMES ARE NAMED AFTER THEIR DESIGNER, R. BUCKFULLER, AND EVENTUALLY PROVIDED THE NAME FOR THE CARBON MOLECULES KNOWN AS BUCKMINSTERFULLERENES. (Lee Snider/Corbis. Reproduced by permission.) GEODESIC DOME IN
MINSTER
Coal and coke are particularly significant varieties of amorphous carbon. Formed by the decay of fossils, coal was one of the first “fossil fuels” (for example, petroleum) used to provide heat and power for industrial societies. Indeed, when the words “industrial revolution” are mentioned, many people picture tall black smokestacks belching smoke from coal fires. Fortunately— from an environmental standpoint—coal is not nearly so widely used today, and when it is (as for instance in electric power plants), the methods for burning it are much more efficient than those applied in the nineteenth century.
joins with two oxygens to produce a gas essential to plant life. In carbon monoxide (CO), a single oxygen joins the carbon, creating a toxic—but nonetheless important—compound.
Actually, much of what those smokestacks of yesteryear burned was coke, a refined version of coal that contains almost pure carbon. Produced by heating soft coal in the absence of air, coke has a much greater heat value than coal, and is still widely used as a reducing agent in the production of steel and other alloys.
Flemish chemist and physicist Johannes van Helmont (1579-1644) discovered in 1630 that air was not, as had been thought up to that time, a single element: it contained a second substance, produced in the burning of wood, which he called “gas sylvestre.” Thus he is recognized as the first scientist to note the existence of carbon dioxide.
Carbon Dioxide Carbon forms many millions of compounds, some families of which will be discussed below. Two others, formed by the bonding of carbon atoms with oxygen atoms, are of particular significance. In carbon dioxide, a single carbon
More than a century later, in 1756, Scottish chemist Joseph Black (1728-1799) showed that carbon dioxide—which he called “fixed air”— combines with other chemicals to form compounds. This and other determinations Black made concerning carbon dioxide led to enor-
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The first gas to be distinguished from ordinary air, carbon dioxide is an essential component in the natural balance between plant and animal life. Animals, including humans, produce carbon dioxide by breathing, and humans further produce it by burning wood and other fuels. Plants use carbon dioxide when they store energy in the form of food, and they release oxygen to be used by animals. D I S C O V E R Y.
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Carbon
SOFT
DRINKS ARE MADE POSSIBLE BY THE USE OF CARBONATED WATER. (Sergio Dorantes/Corbis. Reproduced by permission.)
mous progress in the discovery of gases by various chemists of the late eighteenth century. By that time, chemists had begun to arrive at a greater degree of understanding with regard to the relationship between plant life and carbon dioxide. Up until that time, it had been believed that plants purify the air by day, and poison it at night. Carbon dioxide and its role in the connection between animal and plant life provided a much more sophisticated explanation as to the ways plants “breathe.” U S E S . Around the same time that Black
made his observations on carbon dioxide, English chemist Joseph Priestley (1733-1804) became the first scientist to put the chemical to use. Dissolving it in water, he created carbonated water, which today is used in making soft drinks. Not only does the gas add bubbles to drinks, it also acts as a preservative.
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In the solid form of dry ice, carbon dioxide is used for chilling perishable food during transport. It is also one of the only compounds that experiences sublimation, or the instantaneous transformation of a solid to a gas without passing through an intermediate liquid state, at conditions of ordinary pressure and temperature. Dry ice has often been used in movies to generate “mists” or “smoke” in a particular scene.
Carbon Monoxide During the late eighteenth century, Priestley discovered a carbon-oxygen compound different from carbon dioxide: carbon monoxide. Scientists had actually known of this toxic gas, released in the incomplete combustion of wood, from the Middle Ages onward, but Priestley was the first to identify it scientifically.
Though the natural uses of carbon dioxide are by far the most important, the compound has numerous industrial and commercial applications. Used in fire extinguishers, carbon dioxide is ideal for controlling electrical and oil fires, which cannot be put out with water. Heavier than air, carbon dioxide blankets the flames and smothers them.
Industry uses carbon monoxide in a number of ways. By blowing air across very hot coke, the result is producer gas, which, along with water gas (made by passing hot steam over coal) is an important fuel. Producer gas constitutes a 6:1:18 mixture of carbon monoxide, carbon dioxide, and nitrogen, while water gas is 40% carbon monoxide, 50% hydrogen, and 10% carbon dioxide and other gases.
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Carbon
KEY TERMS Different versions of
ALLOTROPES:
the same element, distinguished by molecular structure.
ferent chemically due to differences in the arrangement of atoms. ISOTOPES:
Having no definite
AMORPHOUS:
structure.
Atoms that have an equal
number of protons, and hence are of the same element, but differ in their number of
Naturally occur-
neutrons. This results in a difference of
ring compounds of carbon, hydrogen, and
mass. Isotopes may be either stable or
oxygen. These are primarily produced by
unstable. The latter type, known as
green plants through the process of photo-
radioisotopes, are radioactive.
synthesis.
OCTET RULE:
CELLULAR
CARBOHYDRATES:
A term describing the
The
distribution of valence electrons that takes
process whereby nutrients from plants are
place in chemical bonding for most ele-
broken down in an animal’s body to create
ments, which usually end up with eight
carbon dioxide.
valence electrons.
RESPIRATION:
A type of
COVALENT BONDING:
ORGANIC CHEMISTRY:
The study of
chemical bonding in which two atoms
carbon, its compounds, and their proper-
share valence electrons.
ties. (Many carbon-containing oxides and
CRYSTALLINE:
A term describing a
carbonates are not considered organic,
type of solid in which the constituent
however.)
parts have a simple and definite geo-
PHOTOSYNTHESIS:
metric arrangement that is repeated in all
conversion of light energy (that is, electro-
directions.
magnetic energy) to chemical energy in
DOUBLE BOND:
A form of bonding
The biological
plants.
in which two atoms share two pairs of
RADIOACTIVITY:
valence electrons. Carbon is also capable of
phenomenon whereby certain isotopes
single bonds and triple bonds.
known as radioisotopes are subject to a
A term describing a
The relative
form of decay brought about by the emis-
ability of an atom to attract valence
sion of high-energy particles. “Decay” does
electrons.
not mean that the isotope “rots”; rather, it
ELECTRONEGATIVITY:
An atom or group of atoms that
decays to form another isotope until even-
has lost or gained one or more electrons,
tually (though this may take a long time) it
and thus has a net electric charge.
becomes stable.
ION:
IONIC BONDING:
A form of chemical
SINGLE BOND:
A form of bonding in
bonding that results from attractions
which two atoms share one pair of valence
between ions with opposite electric
electrons. Carbon is also capable of double
charges.
bonds and triple bonds.
ISOMERS:
Substances which have the
same chemical formula, but which are dif-
S C I E N C E O F E V E RY DAY T H I N G S
TETRAVALENT:
Capable of bonding
to four other elements.
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Carbon
KEY TERMS TRIPLE BOND:
A form of bonding in
VALENCE ELECTRONS:
Electrons
which two atoms share three pairs of
that occupy the highest principal energy
valence electrons. Carbon is also capable of
level in an atom. These are the electrons
single bonds and double bonds.
involved in chemical bonding.
Not only are producer and water gas used for fuel, they are also applied as reducing agents. Thus, when carbon monoxide is passed over hot iron oxides, the oxides are reduced to metallic iron, while the carbon monoxide is oxidized to form carbon dioxide. Carbon monoxide is also used in reactions with metals such as nickel, iron, and cobalt to form some types of carbonyls. Carbon monoxide—produced by burning petroleum in automobiles, as well as by the combustion of wood, coal, and other carbon-containing fuels—is extremely hazardous to human health. It bonds with iron in hemoglobin, the substance in red blood cells that transports oxygen throughout the body, and in effect fools the body into thinking that it is receiving oxygenated hemoglobin, or oxyhemoglobin. Upon reaching the cells, carbon monoxide has much less tendency than oxygen to break down, and therefore it continues to circulate throughout the body. Low concentrations can cause nausea, vomiting, and other effects, while prolonged exposure to high concentrations can result in death.
Carbon and the Environment Carbon is released into the atmosphere by one of three means: cellular respiration; the burning of fossil fuels; and the eruption of volcanoes. When plants take in carbon dioxide from the atmosphere, they combine this with water and manufacture organic compounds using energy they have trapped from sunlight by means of photosynthesis—the conversion of light to chemical energy through biological means. As a by-product of photosynthesis, plants release oxygen into the atmosphere.
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CONTINUED
carbon-based as well. Animals eat the plants, or eat other animals that eat the plants, and thus incorporate the fats, proteins, and sugars (a form of carbohydrate) from the plants into their bodies. Cellular respiration is the process whereby these nutrients are broken down to create carbon dioxide. Photosynthesis and cellular respiration are thus linked in what is known as the carbon cycle. Cellular respiration also releases carbon into the atmosphere through the action of decomposers—bacteria and fungi that feed on the remains of plants and animals. The decomposers extract the energy in the chemical bonds of the decomposing matter, thus releasing more carbon dioxide into the atmosphere. When creatures die and are buried in such a way that they cannot be reached by decomposers—for instance, at the bottom of the ocean, or beneath layers of rock—the carbon in their bodies is eventually converted to fossil fuels, including petroleum, natural gas, and coal. The burning of fossil fuels releases carbon (both monoxide and dioxide) into the atmosphere. Because the rate of such burning has increased dramatically since the late nineteenth century, this has raised fears that carbon dioxide in the atmosphere may create a greenhouse effect, leading to global warming. On the other hand, volcanoes release tons of carbon into the atmosphere regardless of whether humans burn fossil fuels or not.
Radiocarbon Dating
In the process of undergoing photosynthesis, plants produce carbohydrates, which are various compounds of carbon, hydrogen, and oxygen essential to life. The other two fundamental components of a diet are fats and proteins, both
Radiocarbon dating is used to date the age of charcoal, wood, and other biological materials. When an organism is alive, it incorporates a certain ratio of carbon-12 in proportion to the amount of the radioisotope (that is, radioactive isotope) carbon-14 that it receives from the
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atmosphere. As soon as the organism dies, however, it stops incorporating new carbon, and the ratio between carbon-12 and carbon-14 will begin to change as the carbon-14 decays to form nitrogen-14. Carbon-14 has a half-life of 5,730 years, meaning that it takes that long for half the isotopes in a sample to decay to nitrogen-14. Therefore a scientist can use the ratios of carbon-12, carbon-14, and nitrogen-14 to guess the age of an organic sample. The problem with radiocarbon dating, however, is that there is a good likelihood the sample can become contaminated by additional carbon from the soil. Furthermore, it cannot be said with certainty that the ratio of carbon-12 to carbon-14 in the atmosphere has been constant throughout time.
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WHERE TO LEARN MORE
Carbon
Blashfield, Jean F. Carbon. Austin, TX: Raintree SteckVaughn, 1999. “Carbon.” Xrefer (Web site). (May 30, 2001). “Diamonds.” American Museum of Natural History (Web site). (May 30, 2001). Knapp, Brian J. Carbon Chemistry. Illustrated by David Woodroffe. Danbury, CT: Grolier Educational, 1998. Loudon, G. Marc. Organic Chemistry. Menlo Park, CA: Benjamin/Cummings, 1988. “Organic Chemistry” (Web site). (May 30, 2001). “Organic Chemistry.” Frostburg State University Chemistry Helper (Web site). (May 30, 2001). Sparrow, Giles. Carbon. New York: Benchmark Books, 1999. Stille, Darlene. The Respiratory System. New York: Children’s Press, 1997.
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HYDROGEN Hydrogen
The atomic number of hydrogen is 1, meaning that it has a single proton in its nucleus. With its
single electron, hydrogen is the simplest element of all. Because it is such a basic elemental building block, figures for the mass of other elements were once based on hydrogen, but the standard today is set by 12C or carbon-12, the most common isotope of carbon. Hydrogen has two stable isotopes—forms of the element that differ in mass. The first of these, protium, is simply hydrogen in its most common form, with no neutrons in its nucleus. Protium (the name is only used to distinguish it from the other isotopes) accounts for 99.985% of all the hydrogen that appears in nature. The second stable isotope, deuterium, has one neutron, and makes up 0.015% of all hydrogen atoms. Tritium, hydrogen’s one radioactive isotope, will be discussed below. The fact that hydrogen’s isotopes have separate names, whereas all other isotopes are designated merely by element name and mass number (for example, “carbon-12”) says something about the prominence of hydrogen as an element. Not only is its atomic number 1, but in many ways, it is like the number 1 itself—the essential piece from which all others are ultimately constructed. Indeed, nuclear fusion of hydrogen in the stars is the ultimate source for the 90-odd elements that occur in nature. The mass of this number-one element is not, however, 1: it is 1.008 amu, reflecting the small quantities of deuterium, or “heavy hydrogen,” present in a typical sample. A gas at ordinary temperatures, hydrogen turns to a liquid at -423.2°F (-252.9°C), and to a solid at –434.°F (–259.3°C). These figures are its boiling point and melting point respectively; only the figures for helium are lower. As noted earlier, these two elements make up all but 0.01% of the known
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CONCEPT First element on the periodic table, hydrogen is truly in a class by itself. It does not belong to any family of elements, and though it is a nonmetal, it appears on the left side of the periodic table with the metals. The other elements with it in Group 1 form the alkali metal family, but obviously, hydrogen does not belong with them. Indeed, if there is any element similar to hydrogen in simplicity and abundance, it is the only other one on the first row, or period, of the periodic table: helium. Together, these two elements make up 99.9% of all known matter in the entire universe, because hydrogen atoms in stars fuse to create helium. Yet whereas helium is a noble gas, and therefore chemically unreactive, hydrogen bonds with all sorts of other elements. In one such variety of bond, with carbon, hydrogen forms the backbone for a vast collection of organic molecules, known as hydrocarbons and their derivatives. Bonded with oxygen, hydrogen forms the single most important compound on Earth, and the most important complex substance other than air: water. Yet when it bonds with sulfur, it creates toxic hydrogen sulfide; and on its own, hydrogen is extremely flammable. The only element whose isotopes have names, hydrogen has long been considered as a potential source of power and transportation: once upon a time for airships, later as a component in nuclear reactions—and, perhaps in the future, as a source of abundant clean energy.
HOW IT WORKS The Essentials
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Hydrogen
AMONG
THE USES OF TRITIUM IS IN FUEL FOR HYDROGEN BOMBS.
STATE OF
WASHINGTON,
SHOWN
HERE IS THE
HANFORD
PLANT IN THE
WHERE SUCH FUEL IS PRODUCED. (Roger Ressmeyer/Corbis. Reproduced by permission.)
elemental mass of the universe, and are the principal materials from which stars are formed. Normally hydrogen is diatomic, meaning that its molecules are formed by two atoms. At the interior of a star, however, where the temperature is many millions of degrees, H2 molecules are separated into atoms, and these atoms become ionized. In other words, the electron separates from the proton, resulting in an ion with a positive charge, along with a free electron. The positive ions experience fusion—that is, their nuclei bond, releasing enormous amounts of energy as they form new elements. Because the principal isotopic form of helium has two protons in the nucleus, it is natural that helium is the element usually formed; yet it is nonetheless true—amazing as it may seem— that all the elements found on Earth were once formed in stars. On Earth, however, hydrogen ranks ninth in its percentage of the planet’s known elemental mass: just 0.87%. In the human body, on the other hand, it is third, after oxygen and carbon, making up 10% of human elemental body mass.
is to combine its electron with one from the atom of a nonmetallic element to make a covalent bond, in which the two electrons are shared. Hydrogen is unusual in this regard, because most atoms conform to the octet rule, ending up with eight valence electrons. The bonding behavior of hydrogen follows the duet rule, resulting in just two electrons for bonding. Examples of this first type of bond include water (H2O), hydrogen sulfide (H2S), and ammonia (NH3), as well as the many organic compounds formed on a hydrogen-carbon backbone. But hydrogen can form a second type of bond, in which it gains an extra electron to become the negative ion H-, or hydride. It is then able to combine with a metallic positive ion to form an ionic bond. Ionic hydrides are convenient sources of hydrogen gas: for instance, calcium hydride, or CaH2, is sold commercially, and provides a very convenient means of hydrogen generation. The hydrogen gas produced by the reaction of calcium hydride with water can be used to inflate life rafts.
Having just one electron, hydrogen can bond to other atoms in one of two ways. The first option
The presence of hydrogen in certain types of molecules can also be a factor in intermolecular bonding. Intermolecular bonding is the attraction between molecules, as opposed to the bond-
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Hydrogen
THE
USE OF HYDROGEN IN AIRSHIPS EFFECTIVELY ENDED WITH THE CRASH OF THE
HINDENBURG in 1937. (UPI/Cor-
bis-Bettmann. Reproduced by permission.)
ing within molecules, which is usually what chemists mean when they talk about “bonding.”
Hydrogen’s Early History Because it bonds so readily with other elements, hydrogen almost never appears in pure elemental form on Earth. Yet by the late fifteenth century, chemists recognized that by adding a metal to an acid, hydrogen was produced. Only in 1766, however, did English chemist and physicist Henry Cavendish (1731-1810) recognize hydrogen as a substance distinct from all other “airs,” as gases then were called. Seventeen years later, in 1783, French chemist Antoine Lavoisier (1743-1794) named the substance after two Greek words: hydro (water) and genes (born or formed). It was another two decades before English chemist John Dalton (1766-1844) formed his atomic theory of matter, and despite the great strides he made for science, Dalton remained convinced that hydrogen and oxygen in water formed “water atoms.” Around the same time, however, Italian physicist Amedeo Avogadro (1776-1856) clarified the distinction between atoms and molecules, though this theory would not be generally accepted until the 1850s.
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Contemporary to Dalton and Avogadro was Swedish chemist Jons Berzelius (1779-1848), who developed a system of comparing the mass of various atoms in relation to hydrogen. This method remained in use for more than a century, until the discovery of neutrons, protons, and isotopes pointed the way toward a means of making more accurate determinations of atomic mass. In 1931, American chemist and physicist Harold Urey (1893-1981) made the first separation of an isotope: deuterium, from ordinary water.
REAL-LIFE A P P L I C AT I O N S Deuterium and Tritium Designated as 2H, deuterium is a stable isotope, whereas tritium—3H—is unstable, or radioactive. Not only do these two have names; they even have chemical symbols (D and T, respectively), as though they were elements on the periodic table. Just as hydrogen represents the most basic proton-electron combination against which other atoms are compared, these two are respectively the most basic isotope containing a single neu-
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tron, and the most basic radioisotope, or radioactive isotope. Deuterium is sometimes called “heavy hydrogen,” and its nucleus is called a deuteron. In separating deuterium—an achievement for which he won the 1934 Nobel Prize—Urey collected a relatively large sample of liquid hydrogen: 4.2 qt (4 l). He then allowed the liquid to evaporate very slowly, predicting that the more abundant protium would evaporate more quickly than the heavier isotope. When all but 0.034 oz (1 ml) of the sample had evaporated, he submitted the remainder to a form of analysis called spectroscopy, adding a burst of energy to the atoms and then analyzing the light spectrum they emitted for evidence of differing varieties of atoms. With an atomic mass of 2.014102 amu, deuterium is almost exactly twice as heavy as protium, which has an atomic mass of 1.007825. Its melting points and boiling points, respectively –426°F (–254°C) and –417°F (–249°C), are higher than for protium. Often, deuterium is applied as a tracer, an atom or group of atoms whose participation in a chemical, physical, or biological reaction can be easily observed. DEUTERIUM IN WAR AND P E AC E . In nuclear power plants, deuterium
is combined with oxygen to form “heavy water” (D2O), which likewise has higher boiling and melting points than ordinary water. Heavy water is often used in nuclear fission reactors to slow down the fission process, or the splitting of atoms. Deuterium is also present in nuclear fusion, both on the Sun and in laboratories. During the period shortly after World War II, physicists developed a means of duplicating the thermonuclear fusion process. The result was the hydrogen bomb—more properly called a fusion bomb—whose detonating device was a compound of lithium and deuterium called lithium deuteride. Vastly more powerful than the “atomic” (that is, fission) bombs dropped by the United States over Japan (Nagaski and Hiroshima) in 1945, the hydrogen bomb greatly increased the threat of worldwide nuclear annihilation in the postwar years.
process involving the fusion of two deuterons. This fusion would result in a triton, the nucleus of tritium, along with a single proton. Theoretically, the triton and deuteron would then be fused to create a helium nucleus, resulting in the production of vast amounts of energy.
Hydrogen
T R I T I U M . Whereas deuterium has a single neutron, tritium—as its mass number of 3 indicates—has two. And just as deuterium has approximately twice the mass of protium, tritium has about three times the mass, or 3.016 amu. Its melting and boiling points are higher still than those of deuterium: thus tritium heavy water (T2O) melts at 40°F (4.5°C), as compared with 32°F (0°C) for H2O.
Tritium has a half-life (the length of time it takes for half the radioisotopes in a sample to become stable) of 12.26 years. As it decays, its nucleus emits a low-energy beta particle, which is either an electron or a subatomic particle called a positron, resulting in the creation of the helium3 isotope. Due to the low energy levels involved, the radioactive decay of tritium poses little danger to humans. In fact, there is always a small quantity of tritium in the atmosphere, and this quantity is constantly being replenished by cosmic rays. Like deuterium, tritium is applied in nuclear fusion, but due to its scarcity, it is usually combined with deuterium. Sometimes it is released in small quantities into the groundwater as a means of monitoring subterranean water flow. It is also used as a tracer in biochemical processes, and as an ingredient in luminous paints.
Hydrogen and Oxygen WAT E R. Water, of course, is the most well-known compound involving hydrogen. Nonetheless, it is worthwhile to consider the interaction between hydrogen and oxygen, the two ingredients in water, which provides an interesting illustration of chemistry in action.
Yet the power that could destroy the world also has the potential to provide safe, abundant fusion energy from power plants—a dream as yet unrealized. Physicists studying nuclear fusion are attempting several approaches, including a
Chemically bonded as water, hydrogen and oxygen can put out any type of fire except an oil or electrical fire; as separate substances, however, hydrogen and oxygen are highly flammable. In an oxyhydrogen torch, the potentially explosive reaction between the two gases is controlled by a gradual feeding process, which produces combustion instead of the more violent explosion that sometimes occurs when hydrogen and oxygen come into contact.
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H Y D R O G E N P E R O X I D E . Aside from water, another commonly used hydrogenoxygen compound is hydrogen peroxide, or H2O2. A colorless liquid, hydrogen peroxide is chemically unstable (not “unstable” in the way that a radioisotope is), and decomposes slowly to form water and oxygen gas. In high concentrations, it can be used as rocket fuel.
By contrast, the hydrogen peroxide used in homes as a disinfectant and bleaching agent is only a 3% solution. The formation of oxygen gas molecules causes hydrogen peroxide to bubble, and this bubbling is quite rapid when the peroxide is placed on cuts, because the enzymes in blood act as a catalyst to speed up the reaction.
Hydrogen Chloride Another significant compound involving hydrogen is hydrogen chloride, or HCl—in other words, one hydrogen atom bonded to chlorine, a member of the halogens family. Dissolved in water, it produces hydrochloric acid, used in laboratories for analyses involving other acids. Normally, hydrogen chloride is produced by the reaction of salt with sulfuric acid, though it can also be created by direct bonding of hydrogen and chlorine at temperatures above 428°F (250°C). Hydrogen chloride and hydrochloric acid have numerous applications in metallurgy, as well as in the manufacture of pharmaceuticals, dyes, and synthetic rubber. They are used, for instance, in making pharmaceutical hydrochlorides, water-soluble drugs that dissolve when ingested. Other applications include the production of fertilizers, synthetic silk, paint pigments, soap, and numerous other products. Not all hydrochloric acid is produced by industry, or by chemists in laboratories. Active volcanoes, as well as waters from volcanic mountain sources, contain traces of the acid. So, too, does the human body, which generates it during digestion. However, too much hydrochloric acid in the digestive system can cause the formation of gastric ulcers.
Hydrogen Sulfide It may not be a pleasant subject, but hydrogen— in the form of hydrogen sulfide—is also present in intestinal gas. The fact that hydrogen sulfide is an extremely malodorous substance once again illustrates the strange things that happen when
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elements bond: neither hydrogen nor sulfur has any smell on its own, yet together they form an extremely noxious—and toxic—substance. Pockets of hydrogen sulfide occur in nature. If a person were to breathe the vapors for very long, it could be fatal, but usually, the foul odor keeps people away. The May 2001 National Geographic included two stories relating to such natural hydrogen-sulfide deposits, on opposite sides of the Earth, and in both cases the presence of these toxic fumes created interesting results. In southern Mexico is a system of caves known as Villa Luz, through which run some 20 underground springs, many of them carrying large quantities of hydrogen sulfide. The National Geographic Society’s team had to enter the caves wearing gas masks, yet the area teems with strange varieties of life. Among these are fish that are red from high concentrations of hemoglobin, or red blood cells. The creatures need this extra dose of hemoglobin, necessary to move oxygen through the body, in order to survive on the scant oxygen supplies. The waters of the cave are further populated by microorganisms that oxidize the hydrogen sulfide and turn it into sulfuric acid, which dissolves the rock walls and continually enlarges the cave. Thousands of miles away, in the Black Sea, explorers supported by a grant from the National Geographic Society examined evidence suggesting that there indeed had been a great ancient flood in the area, much like the one depicted in the Bible. In their efforts, they had an unlikely ally: hydrogen sulfide, which had formed at the bottom of the sea, and was covered by dense layers of salt water. Because the Black Sea lacks the temperature differences that cause water to circulate from the bottom upward, the hydrogen sulfide stayed at the bottom. Under normal circumstances, the wreck of a 1,500-year-old wooden ship would not have been preserved; but because oxygen could not reach the bottom of the Black Sea—and thus woodboring worms could not live in the toxic environment—the ship was left undisturbed. Thanks to the presence of hydrogen sulfide, explorers were able to study the ship, the first fully intact ancient shipwreck to be discovered.
Hydrocarbons Together with carbon, hydrogen forms a huge array of organic materials known as hydrocar-
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bons—chemical compounds whose molecules are made up of nothing but carbon and hydrogen atoms. Theoretically, there is no limit to the number of possible hydrocarbons. Not only does carbon form itself into seemingly limitless molecular shapes, but hydrogen is a particularly good partner. Because it has the smallest atom of any element on the periodic table, it can bond to one of carbon’s valence electrons without getting in the way of the others.
functional groups include aldehydes, ketones, carboxylic acids, and esters. Products of these functional groups range from aspirin to butyric acid, which is in part responsible for the smell both of rancid butter and human sweat. Hydrocarbons also form the basis for polymer plastics such as Nylon and Teflon.
Hydrocarbons may either be saturated or unsaturated. A saturated hydrocarbon is one in which the carbon atom is already bonded to four other atoms, and thus cannot bond to any others. In an unsaturated hydrocarbon, however, not all the valence electrons of the carbon atom are bonded to other atoms.
We have already seen that hydrogen is a component of petroleum, and that hydrogen is used in creating nuclear power—both deadly and peaceful varieties. But hydrogen has been applied in many other ways in the transportation and power industries.
Hydrogenation is a term describing any chemical reaction in which hydrogen atoms are added to carbon multiple bonds. There are many applications of hydrogenation, but one that is particularly relevant to daily life involves its use in turning unsaturated hydrocarbons into saturated ones. When treated with hydrogen gas, unsaturated fats (fats are complex substances that involve hydrocarbons bonded to other molecules) become saturated fats, which are softer and more stable, and stand up better to the heat of frying. Many foods contain hydrogenated vegetable oil; however, saturated fats have been linked with a rise in blood cholesterol levels— and with an increased risk of heart disease. P E T R O C H E M I CA L S A N D F U N C T I O N A L G R O U P S . One important variety
of hydrocarbons is described under the collective heading of petrochemicals—that is, derivatives of petroleum. These include natural gas; petroleum ether, a solvent; naphtha, a solvent (for example, paint thinner); gasoline; kerosene; fuel for heating and diesel fuel; lubricating oils; petroleum jelly; paraffin wax; and pitch, or tar. A host of other organic chemicals, including various drugs, plastics, paints, adhesives, fibers, detergents, synthetic rubber, and agricultural chemicals, owe their existence to petrochemicals.
Hydrogen
Hydrogen for Transportation and Power
There are only three gases practical for lifting a balloon: hydrogen, helium, and hot air. Each is much less dense than ordinary air, and this gives them their buoyancy. Because hydrogen is the lightest known gas and is relatively cheap to produce, it initially seemed the ideal choice, particularly for airships, which made their debut near the end of the nineteenth century. For a few decades in the early twentieth century, airships were widely used, first in warfare and later as the equivalent of luxury liners in the skies. One of the greatest such craft was Germany’s Hindenburg, which used hydrogen to provide buoyancy. Then, on May 6, 1937, the Hindenburg caught fire while mooring at Lakehurst, New Jersey, and 36 people were killed—a tragic and dramatic event that effectively ended the use of hydrogen in airships. Adding to the pathos of the Hindenburg crash was the voice of radio announcer Herb Morrison, whose audio report has become a classic of radio history. Morrison had come to Lakehurst to report on the landing of the famous airship, but ended up with the biggest—and most horrifying—story of his career. As the ship burst into flames, Morrison’s voice broke, and he uttered words that have become famous: “Oh, the humanity!”
Then there are the many hydrocarbon derivatives formed by the bonding of hydrocarbons to various functional groups—broad arrays of molecule types involving other elements. Among these are alcohols—both ethanol (the alcohol in beer and other drinks) and methanol, used in adhesives, fibers, and plastics, and as a fuel. Other
Half a century later, a hydrogen-related disaster destroyed a craft much more sophisticated than the Hindenburg, and this time, the medium of television provided an entire nation with a view of the ensuing horror. The event was the explosion of the space shuttle Challenger on January 28, 1986, and the cause was the failure of a rubber seal in the shuttle’s fuel tanks. As a result,
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Hydrogen
KEY TERMS COVALENT BONDING:
A type of
chemical bonding in which two atoms share valence electrons.
radioactive. The center of an atom, a
NUCLEUS:
A term describing an ele-
region where protons and neutrons are
ment that exists as molecules composed of
located, and around which electrons spin.
two atoms.
The plural of “nucleus” is nuclei.
DIATOMIC:
A term describing the
DUET RULE:
A term describing the
OCTET RULE:
distribution of valence electrons when
distribution of valence electrons that takes
hydrogen atoms—which end up with only
place in chemical bonding for most ele-
two valence electrons—experience chemi-
ments, which end up with eight valence
cal bonding with other atoms. Most other
electrons. Hydrogen is an exception, and
elements follow the octet rule.
follows the duet rule.
ELECTROLYSIS:
The use of an elec-
tric current to cause a chemical reaction. FISSION:
A nuclear reaction involving
FUSION:
A nuclear reaction that
involves the joining of atomic nuclei. HYDROCARBON:
ORGANIC:
At one time, chemists used
the term “organic” only in reference to living things. Now the word is applied to most compounds containing carbon, with
the splitting of atoms.
Any chemical com-
the exception of calcium carbonate (limestone) and oxides such as carbon dioxide. RADIOISOTOPE:
An isotope subject
pound whose molecules are made up of
to the decay associated with radioactivity.
nothing but carbon and hydrogen atoms.
A radioisotope is thus an unstable isotope.
HYDROGENATION:
A chemical reac-
SATURATED:
A term describing a
tion in which hydrogen atoms are added to
hydrocarbon in which each carbon is
carbon multiple bonds, as in a hydro-
already bound to four other atoms.
carbon.
TRACER:
An atom or group of atoms
An atom or group of atoms that
whose participation in a chemical, physi-
has lost or gained one or more electrons,
cal, or biological reaction can be easily
and thus has a net electrical charge.
observed. Radioisotopes are often used as
ION:
IONIC BONDING:
A form of chemical
tracers. A term describing a
bonding that results from attractions
UNSATURATED:
between ions with opposite electric
hydrocarbon, in which the carbons
charges. The bonding of a metal to a non-
involved in a multiple bond are free to
metal such as hydrogen is ionic.
bond with other atoms.
ISOTOPES:
258
mass. An isotope may either be stable or
Atoms that have an equal
VALENCE ELECTRONS:
Electrons
number of protons, and hence are of the
that occupy the highest principal energy
same element, but differ in their number of
level in an atom. These are the electrons
neutrons. This results in a difference of
involved in chemical bonding.
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hydrogen gas flooded out of the craft and straight into the jet of flame behind the rocket. All seven astronauts aboard were killed. THE FUTURE OF HYDROGEN P O W E R. Despite the misfortunes that have
occurred as a result of hydrogen’s high flammability, the element nonetheless holds out the promise of cheap, safe power. Just as it made possible the fusion, or hydrogen, bomb—which fortunately has never been dropped in wartime, but is estimated to be many hundreds of times more lethal than the fission bombs dropped on Japan—hydrogen may be the key to the harnessing of nuclear fusion, which could make possible almost unlimited power. A number of individuals and agencies advocate another form of hydrogen power, created by the controlled burning of hydrogen in air. Not only is hydrogen an incredibly clean fuel, producing no by-products other than water vapor, it is available in vast quantities from water. In order to separate it from the oxygen atoms, electrolysis would have to be applied—and this is one of the challenges that must be addressed before hydrogen fuel can become a reality. Electrolysis requires enormous amounts of electricity, which would have to be produced before the benefits of hydrogen fuel could be realized. Furthermore, though the burning of hydrogen could be controlled, there are the dan-
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gers associated with transporting it across country in pipelines. Nonetheless, a number of advocacy groups—some of whose Web sites are listed below—continue to promote efforts toward realizing the dream of nonpolluting, virtually limitless, fuel.
Hydrogen
WHERE TO LEARN MORE American Hydrogen Association (Web site). (June 1, 2001). Blashfield, Jean F. Hydrogen. Austin, TX: Raintree SteckVaughn, 1999. Farndon, John. Hydrogen. New York: Benchmark Books, 2001. “Hydrogen” (Web site). (June 1, 2001). Hydrogen Energy Center (Web site). (June 1, 2001). Hydrogen Information Network (Web site). (June 1, 2001). Knapp, Brian J. Carbon Chemistry. Illustrated by David Woodroffe. Danbury, CT: Grolier Educational, 1998. Knapp, Brian J. Elements. Illustrated by David Woodroffe and David Hardy. Danbury, CT: Grolier Educational, 1996. National Hydrogen Association (Web site). (June 1, 2001). Uehling, Mark. The Story of Hydrogen. New York: Franklin Watts, 1995.
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BONDING AND REACTIONS CHEMICAL BONDING COMPOUNDS CHEMICAL REACTIONS O X I D AT I O N - R E D U C T I O N REACTIONS CHEMICAL EQUILIBRIUM C A T A LY S T S ACIDS AND BASES ACID-BASE REACTIONS
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CHEMICAL BONDING
CONCEPT Almost everything a person sees or touches in daily life—the air we breathe, the food we eat, the clothes we wear, and so on—is the result of a chemical bond, or, more accurately, many chemical bonds. Though a knowledge of atoms and elements is essential to comprehend the subjects chemistry addresses, the world is generally not composed of isolated atoms; rather, atoms bond to one another to form molecules and hence chemical compounds. Not all chemical bonds are created equal: some are weak, and some very strong, a difference that depends primarily on the interactions of electrons between atoms.
HOW IT WORKS Early Ideas of Bonding The theory that all of matter is composed of atoms did not originate in modern times: the atomic model actually dates back to the fifth century B.C. in Greece. The leading exponent of atomic theory in ancient times was Democritus (c. 460-370 B.C.), who proposed that matter could not be infinitely subdivided. At its deepest substructure, Democritus maintained, the material world was made up of tiny fragments he called atomos, a Greek term meaning “no cut” or “indivisible” Forward-thinking though it was, Democritus’s idea was not what modern scientists today would describe as a proper scientific hypothesis. His “atoms” were not purely physical units, but rather idealized philosophical constructs, and thus, he was not really approaching the subject from the perspective of a scientist. In any case,
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there was no way for Democritus to test his hypothesis even if he had wanted to: by their very nature, the atoms he described were far too small to observe. Even today, what scientists know about atomic behavior comes not from direct observation, but indirect means. Hence, Democritus and the few other ancients who subscribed to atomic theory went more on instinct than by scientific methods. Yet, some of them were remarkably prescient in their description of the bonding of atoms, in view of the primitive scientific methods they had at their disposal. No other scientist came close to the accuracy of their theory for about 2,000 years. AS C L E P I A D E S A N D LU C R E T I U S D I S C U SS B O N D S . The physician
Asclepiades of Prusa (c.130-40 B.C.) drew on the ideas of the Greek philosopher Epicurus (341270 B.C., another proponent of atomism. Asclepiades speculated on the ways in which atoms interact, and discussed “clusters of atoms,” though, of course, he had no idea what force attracted the atoms to one another. A few years after Asclepiades, the Roman philosopher and poet Lucretius (c.95-c.55 B.C. espoused views that combined atomism with the idea of the “four elements”—earth, air, fire, and water. In his great work De rerum natura (“On the Nature of Things”), Lucretius described atoms as tiny spheres attached to each other by fishhook-like appendages that became entangled with one another. LAC K O F P R O G R E SS U N T I L 1 8 0 0 . Unfortunately, the competing idea of
the four elements, handed down by the great philosopher Aristotle (384-322 B.C.), prevailed over the atomic model. As the Roman Empire
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ELECTRON-DOT
DIAGRAMS OF SOME ELEMENTS IN THE PERIODIC TABLE. (Robert L. Wolke. Reproduced by permission.)
began to decline after A.D. 200, the pace of scientific inquiry slowed and—in Western Europe at least—eventually came to a virtual halt. Hence, the four elements theory, which had its own fanciful explanations as to why certain “elements” bonded with one another, held sway in Europe until the beginning of the modern era. During the seventeenth century, a mounting array of facts from the realms of astronomy and physics collectively disproved the Aristotelian model. In the area of chemistry, English physicist and chemist Robert Boyle (1627-1691) showed that the four elements were not elements at all, because they could be broken down into simpler substances. Yet, no one really understood what constituted an element until the very beginning of the nineteenth century, and until that question was addressed, it was difficult to move on to the mystery of why certain atoms bonded with one another.
Early Modern Advances in Bonding Theory
Though Dalton’s theory paved the way for enormous advances in the years that followed, there were a number of flaws in it. Mass alone, for instance, is not really what differentiates one atom from another: differences in mass reflect the presence of subatomic particles—protons and neutrons—of whose existence scientists were unaware at the time. Furthermore, the properties of atoms that cause them to bond relate to a third subatomic particle, the electron, which, though it contributes little to the mass of the atom, is allimportant to the energy it possesses. As for how atoms bond to one another, Dalton had little to say: in his conception of the atomic model, atoms simply sit adjacent to one another without forming true bonds, as such.
T H E O R Y.
AV O GA D R O A N D T H E M O L E C U L E . Though Dalton recognized that the
The birth of atomic theory in modern times occurred in 1803, when English chemist John Dalton (1766-1844) formulated the idea that all
structure of atoms in a particular element or compound is uniform, he maintained that compounds are made up of compound atoms: thus,
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elements are composed of tiny, indestructible particles. These he called by the name Democritus had given them nearly 23 centuries earlier: atoms. All known substances, he said, are composed of some combination of atoms, which differ from one another only in mass.
AT O M I C
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Chemical Bonding
HYDROGEN
BONDING IN
HF, H2O,
AND
NH3. (Robert L. Wolke. Reproduced by permission.)
water is a compound of “water atoms.” However, water is not an element, and therefore, there had to be some structure—still very small, but larger than the atom—in which atoms coalesced to form the basic materials of a compound.
the molecule resurrected by Italian chemist Stanislao Cannizzaro (1826-1910). Cannizzaro’s work was occasioned by disagreement among scientists regarding the determination of atomic mass; however, the establishment of the molecular model had far-reaching implications for theories of bonding.
That structure was the molecule, first described by Italian physicist Amedeo Avogadro (1776-1856). For several decades, Avogadro, who originated the idea of the mole as a means of comparing large groups of atoms or molecules, remained a more or less unsung hero. Only in 1860, four years after his death, was his idea of
In 1858, German chemist Friedrich August Kekulé (1829-1896) made the first attempt to define the concept of valency, or the property an atom of one element possesses that determines
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SYMBOLIZING ATOMIC BONDS.
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“PURE”
WATER FROM A MOUNTAIN STREAM IS ACTUALLY FILLED WITH TRACES OF THE ROCKS OVER WHICH IT
HAS FLOWED.
IN
FACT, WATER IS ALMOST IMPOSSIBLE TO FIND IN PURE FORM EXCEPT BY PURIFYING IT IN A LABO-
RATORY. (David Muench/Corbis. Reproduced by permission.)
266
its ability to bond with atoms of other elements. A pioneer in organic chemistry, which deals with chemical structures containing carbon, Kekulé described the carbon atom as tetravalent, mean-
ing that it can bond to four other atoms. (The Latin prefix tetra- means “four.”) He also speculated that carbon atoms are capable of bonding with one another in long chains.
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This was one of the first attempts to examine the subject of bonding using modern scientific terminology, complete with hypotheses that could be tested by experimentation. Kekulé also recognized that in order to discuss bonds understandably, there needed to be some means of representing those bonds with symbols. He even went so far as to develop a system for showing the arrangement of bonds in space; however, his system was so elaborate that it was replaced in favor of a simpler one developed by Scottish chemist Archibald Scott Couper (1831-1892). Couper, who also studied valency and the tetravalent carbon bond—he is usually given equal credit with Kekulé for these ideas—created an extremely straightforward schematic representation still in use by chemists today. In Couper’s system, short dashed lines serve to designate chemical bonds. Hence, the bond between two hydrogen atoms and an oxygen atom in a water molecule would be represented thus: H-OH. As the understanding of bonds progressed in modern times, this system was modified to take into account multiple bonds, discussed below.
REAL-LIFE A P P L I C AT I O N S Atoms, Electrons, and Ions Today, chemical bonding is understood as the joining of atoms through electromagnetic force. Before that understanding could be achieved, however, scientists had to unlock the secret of the electromagnetic interactions that take place within an atom.
and, like a bee, it buzzes to and fro, carrying a powerful “sting”—its negative electric charge, which attracts it to the positively charged proton.
Chemical Bonding
E L E C T R O N S A N D I O N S . Though the electron weighs much, much less than a proton, it possesses enough electric charge to counterbalance the positive charge of the proton. All atoms have the same number of protons as electrons, and hence the net electric charge is zero. However, as befits their highly active role, electrons are capable of moving from one atom to another under the proper circumstances. An atom that loses or acquires electrons has an electric charge, and is called an ion.
The atom that has lost an electron or electrons becomes a positively charged ion, or cation. On the other hand, an atom that gains an electron or electrons becomes a negatively charged ion, or anion. As we shall see, ionic bonds, such as those that join sodium and chlorine atoms to form NaCl, or salt, are extremely powerful. ELECTRON
C O N F I G U RAT I O N .
Even in covalent bonding, which does not involve ions, the configurations of electrons in two atoms are highly important. The basics of electron configuration are explained in the Electrons essay, though even there, this information is presented with the statement that the student should consult a chemistry textbook for a more exhaustive explanation.
The key to bonding is the electron, discovered in 1897 by English physicist J. J. Thomson (1856-1940). Atomic structure in general, and the properties of the electron in particular, are discussed at length elsewhere in this volume. However, because these specifics are critical to bonding, they will be presented here in the shortest possible form.
In the simplest possible terms, electron configuration refers to the distribution of electrons at various positions in an atom. However, because the behavior of electrons cannot be fully predicted, this distribution can only be expressed in terms of probability. An electron moving around the nucleus of an atom can be compared to a fly buzzing around some form of attractant (e.g., food or a female fly, if the moving fly is male) at the center of a sealed room. We can state positively that the fly is in the room, and we can predict that he will be most attracted to the center, but we can never predict his location at any given moment.
At the center of an atom is a nucleus, consisting of protons, with a positive electrical charge; and neutrons, which have no charge. These form the bulk of the atom’s mass, but they have little to do with bonding. In fact, the neutron has nothing to do with it, while the proton plays only a passive role, rather like a flower being pollinated by a bee. The “bee” is the electron,
As one moves along the periodic table of elements, electron configurations become ever more complex. The reason is that with an increase in atomic number, there is an increase in the energy levels of atoms. This indicates a greater range of energies that electrons can occupy, as well as a greater range of motion. Electrons occupying the highest energy level in an atom are
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called valence electrons, and these are the only ones involved in chemical bonding. By contrast, the core electrons, or the ones closest to the nucleus, play no role in the bonding of atoms.
Ionic and Covalent Bonds T H E G OA L O F E I G H T VA L E N C E E L E C T R O N S . The above dis-
cussion of the atom, and the electron’s place in it, refers to much that was unknown at the time Thomson discovered the electron. Protons were not discovered for several more years, and neutrons several decades after that. Nonetheless, the electron proved the key to solving the riddle of how substances bond, and not long after Thomson’s discovery, German chemist Richard Abegg (1869-1910) suggested as much. While studying noble gases, noted for their tendency not to bond, Abegg discovered that these gases always have eight valence electrons. His observation led to one of the most important principles of chemical bonding: atoms bond in such a way that they achieve the electron configuration of a noble gas. This has been shown to be the case in most stable chemical compounds. TWO DIFFERENT TYPES OF B O N D S . Perhaps, Abegg hypothesized, atoms
combine with one another because they exchange electrons in such a way that both end up with eight valence electrons. This was an early model of ionic bonding, which results from attractions between ions with opposite electric charges: when they bond, these ions “complete” one another. Ionic bonds, which occur when a metal bonds with a nonmetal are extremely strong. As noted earlier, salt is an example of an ionic bond: the metal sodium loses an electron, forming a cation; meanwhile, the nonmetal chlorine gains the electron to become an anion. Their ionic bond results from the attraction of opposite charges.
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In ionic bonding, two ions start out with different charges and end up forming a bond in which both have eight valence electrons. In the type of bond Lewis described, a covalent bond, two atoms start out as atoms do, with a net charge of zero. Each ends up possessing eight valence electrons, but neither atom “owns” them; rather, they share electrons. L E W I S S T R U C T U R E S . In addition to discovering the concept of covalent bonding, Lewis developed the Lewis structure, a means of showing schematically how valence electrons are arranged among the atoms in a molecule. Also known as the electron-dot system, Lewis structures represent the valence electrons as dots surrounding the chemical symbols of the atoms involved. These dots, which look rather like a colon, may be above or below, or on either side of, the chemical symbol. (The dots above or below the chemical symbol are side-by-side, like a colon turned at a 90°-angle.)
To obtain the Lewis structure representing a chemical bond, it is first necessary to know the number of valence electrons involved. One pair of electrons is always placed between elements, indicating the bond between them. Sometimes this pair of valence electrons is symbolized by a dashed line, as in the system developed by Couper. The remaining electrons are distributed according to the rules by which specific elements bond. M U LT I P L E BONDS. Hydrogen bonds according to what is known as the duet rule, meaning that a hydrogen atom has only two valence electrons. In most other elements—there are exceptions, but these will not be discussed here—atoms end up with eight valence electrons, and thus are said to follow the octet rule. If the bond is covalent, the total number of valence electrons will not be a multiple of eight, however, because the atoms share some electrons.
Ionic bonding, however, could not explain all types of chemical bonds for the simple reason that not all compounds are ionic. A few years after Abegg’s death, American chemist Gilbert Newton Lewis (1875-1946) discovered a very different type of bond, in which nonionic compounds share electrons. The result, once again, is eight valence electrons for each atom, but in this case, the nuclei of the two atoms share electrons.
When carbon bonds to two oxygen atoms to form carbon dioxide (CO2), it is represented in the Couper system as O-C-O. The Lewis structure also uses dashed lines, which stand for two valence electrons shared between atoms. In this case, then, the dashed line to the left of the carbon atom indicates a bond of two electrons with the oxygen atom to the left, and the dashed line to the right of it indicates a bond of two electrons with the oxygen atom on that side.
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The non-bonding valence electrons in the oxygen atoms can be represented by sets of two dots above, below, and on the outside of each atom, for a total of six each. Combined with the two dots for the electrons that bond them to carbon, this gives each oxygen atom a total of eight valence electrons. So much for the oxygen atoms, but something is wrong with the representation of the carbon atom, which, up to this point, is shown only with four electrons surrounding it, not eight.
values form a covalent bond, this is described as polar covalent bonding. Sometimes these are simply called “polar bonds,” but that is not as accurate: all ionic bonds, after all, are polar, due to the extreme differences in electronegativity. The term “polar covalent bond” is much more specific, describing a bond, for instance, between hydrogen (2.1) and sulfur (2.6). Because sulfur has a slightly greater electronegativity value, the valence electrons will be slightly more attracted to the sulfur atom than to the hydrogen atom.
In fact carbon in this particular configuration forms not a single bond, but a double bond, which is represented by two dashed lines—a symbol that looks like an equals sign. By showing the double bonds joining the carbon atom to the two oxygen atoms on either side, the carbon atom has the required number of eight valence electrons. The carbon atom may also form a triple bond (represented by three dashed lines, one above the other) with an oxygen atom, in which case the oxygen atom would have only two other valence electrons.
Another example of a polar covalent bond is the one that forms between hydrogen and oxygen (3.5) to form H2O or water, which has a number of interesting properties. For instance, the polar quality of a water molecule gives it a great attraction for ions, and thus ionic substances such as salt dissolve easily in water. “Pure” water from a mountain stream is actually filled with traces of the rocks over which it has flowed. In fact, water—sometimes called the “universal solvent”—is almost impossible to find in pure form, except when it is purified in a laboratory.
Electronegativity and Polar Covalent Bonds Today, chemists understand that most bonds are neither purely ionic nor purely covalent; rather, there is a wide range of hybrids between the two extremes. Credit for this discovery belongs to American chemist Linus Pauling (1901-1994), who, in the 1930s, developed the concept of electronegativity—the relative ability of an atom to attract valence electrons. Elements capable of bonding are assigned an electronegativity value ranging from a minimum of 0.7 for cesium to a maximum of 4.0 for fluorine. Fluorine is capable of bonding with some noble gases, which do not bond with any other elements or each other. The greater the electronegativity value, the greater the tendency of an element to draw valence electrons to itself. If fluorine and cesium bond, then, the bond would be purely ionic, because the fluorine exerts so much more attraction for the valence electrons. But if two elements have equal electronegativity values—for instance, cobalt and silicon, both of which are rated at 1.9—the bond is purely covalent. Most bonds, as stated earlier, fall somewhere in between these two extremes.
By contrast, molecules of petroleum (CH2) tend to be nonpolar, because carbon and hydrogen have almost identical electronegativity values—2.5 and 2.1 respectively. Thus, an oil molecule offers no electric charge to bond it with a water molecule, and for this reason, oil and water do not mix. It is a good thing that water molecules attract each other so strongly, because this means that a great amount of energy is required to change water from a liquid to a gas. If this were not so, the oceans and rivers would vaporize, and life on Earth could not exist as it does. B O N D E N E R GY. The last two paragraphs allude to attractions between molecules, which is not the same as (nor is it as strong as) the attraction between atoms within a molecule. In fact, the bond energy—the energy required to pull apart the atoms in a chemical bond—is low for water. This is due to the presence of hydrogen atoms, with their two (rather than eight) valence electrons. It is thus relatively easy to separate water into its constituent parts of hydrogen and oxygen, through a process known as electrolysis.
When substances of differing electronegativity
Covalent bonds that involve hydrogen are among the weakest bonds between atoms. (Again, this is different from bonds between molecules.) Stronger than hydrogen bonds are regular, octet-rule covalent bonds: as one might expect, double covalent bonds are stronger than
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Chemical Bonding
KEY TERMS ANION:
The negative ion that results
CHEMICAL SYMBOL:
A one-or two-
when an atom gains one or more electrons.
letter abbreviation for the name of an
An anion (pronounced “AN-ie-un”) of an
element.
element is never called, for instance, the
A substance made up of
COMPOUND:
chlorine anion. Rather, for an anion
atoms of more than one element. These
involving a single element, it is named by
atoms are usually joined in molecules.
adding the suffix -ide to the name of the original element—hence, “chloride.” Other rules apply for more complex anions. ATOM:
The smallest particle of an ele-
ment. An atom can exist either alone or in combination with other atoms in a molecule. The number of
protons in the nucleus of an atom. Since this number is different for each element, elements are listed on the periodic table of elements in order of atomic number. BOND ENERGY:
The energy required
to pull apart the atoms in a chemical bond. The positive ion that results
when an atom loses one or more electrons. A cation (pronounced “KAT-ie-un”) is named after the element of which it is an ion and thus is called, for instance, the aluminum ion or the aluminum cation. CHEMICAL BONDING:
The joining,
through electromagnetic force, of atoms
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chemical bonding in which two atoms share valence electrons. Atoms may bond by single, double, or triple covalent bonds, which, in representations of Lewis structures, are shown by single, double, or triple dashed lines. (The double dashed line
ATOMIC NUMBER:
CATION:
A type of
COVALENT BONDING:
looks like an equals sign.) When atoms have differing values of electronegativity, they form polar covalent bonds. A term describing the
DUET RULE:
distribution of valence electrons when hydrogen atoms—which end up with only two valence electrons—experience chemical bonding with other atoms. Most other elements follow the octet rule. ELECTRON:
Negatively charged parti-
cles in an atom. Electrons, which spin around the protons and neutrons that make up the atom’s nucleus, are essential to chemical bonding. The relative
representing different elements. The prin-
ELECTRONEGATIVITY:
cipal types of bonds are covalent bonding
ability of an atom to attract valence
and ionic bonding, though few bonds are
electrons.
purely one or the other. Rather, there is a
ELEMENT:
wide range of “hybrid” bonds, in accor-
only one kind of atom. Unlike compounds,
dance with the electronegativity values of
elements cannot be broken down chemi-
the elements involved.
cally into other substances.
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A substance made up of
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Chemical Bonding
KEY TERMS
CONTINUED
An atom that has lost or gained
place in chemical bonding for most ele-
one or more electrons, and thus has a net
ments, which end up with eight valence
electrical charge. Ions may either be anions
electrons. Hydrogen is an exception, and
or cations.
follows the duet rule. A few elements fol-
ION:
A form of chemical
low other rules, and some (most notably
bonding that results from attractions
the noble gases) do not typically bond with
between ions with opposite electrical
other elements.
IONIC BONDING:
charges.
PERIODIC TABLE OF ELEMENTS:
A means of
A chart showing the elements arranged in
showing schematically how valence elec-
order of atomic number. Vertical columns
trons are distributed among the atoms in a
within the periodic table indicate groups
molecule. Also known as the electron-dot
or “families” of elements with similar
system, Lewis structure represents pairs of
chemical characteristics.
LEWIS
STRUCTURE:
electrons with a symbol rather like a colon, which—depending on the situation—can be placed above, below, or on either side of the chemical symbol. In the Lewis structure, the pairs of electrons involved in chemical bonds are usually represented by a dashed line.
POLAR COVALENT BONDING:
The
type of chemical bonding between atoms that have differing values of electronegativity. If the difference is extreme, of course, the bond is not a covalent bond at all, but an ionic bond. Thus, although these are sometimes called polar bonds, they are
A group of atoms, usual-
MOLECULE:
ly, but not always, representing more
more properly identified as polar covalent bonds.
than one element, joined in a structure. Compounds are typically made of up
PROTON:
molecules.
in an atom.
NEUTRON:
A subatomic particle that
A positively charged particle
VALENCE ELECTRONS:
Electrons
has no electrical charge. Neutrons are
that occupy the highest energy levels in an
found at the nucleus of an atom, alongside
atom. These are the only electrons involved
protons.
in chemical bonding. By contrast, the core
NUCLEUS:
The center of an atom, a
electrons, or the ones at lower energy lev-
region where protons and neutrons are
els, play no role in the bonding of atoms.
located, and around which electrons spin.
VALENCY:
OCTET RULE:
A term describing the
distribution of valence electrons that takes
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The property of the atom of
one element that determines its ability to bond with atoms of other elements.
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single ones, and triple covalent bonds are stronger still. Strongest of all are ionic bonds, involved in the bonding of a metal to a metal, or a metal to a nonmetal, as in salt. The strength of the bond energy in salt is reflected by its boiling point of 1,472°F (800°C), much higher than that of water, at 212°F (100°C). WHERE TO LEARN MORE “Chemical Bond” (Web site). (May 18, 2001). “Chemical Bonding” Oklahoma State University (Web site). (May 19, 2001).
272
“Chemical Bonding” (Web site). (May 19, 2001). “The Colored Periodic Table and Chemical Bonding” (Web site). (May 19, 2001). Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: Houghton Mifflin, 1995. Linus Pauling and the Twentieth Century: An Exhibition (Web site). (May 19, 2001). “Valence Shell Electron Pair Repulsion (VSEPR).” (May 18, 2001). White, Florence Meiman. Linus Pauling, Scientist and Crusader. New York: Walker, 1980.
“Chemical Bonding” (Web site). (May 19, 2001).
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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Compounds
CONCEPT A compound is a chemical substance in which atoms combine in such a way that the compound always has the same composition, unless it is chemically altered in some way. Elements make up compounds, and although there are only about 90 elements that occur in nature, there are literally many millions of compounds. A compound is not the same as a mixture, which has a variable composition, but until chemists understood the atomic and molecular substructure of compounds, the distinction was not always clear. When atoms of one element bond to atoms of another, they form substances quite different from either element. Sugar, for instance, is made up of carbon, the material in coal and graphite, along with two gases, hydrogen and oxygen. None of these is sweet, yet when they are brought together in just the right way, they make the compound that sweetens everything from breakfast cereals to colas. A compound cannot be understood purely in terms of its constituent elements; an awareness of the structure is also needed. Likewise, it is important to know just how to name a compound, using a uniform terminology, since there are far too many substances in the world to give each an individual name.
HOW IT WORKS
COMPOUNDS
composed of two hydrogen atoms bonded to a single oxygen atom. It can be frozen or boiled, but the molecules themselves are unchanged, because freezing and boiling are merely physical processes. To transform one compound into another, on the other hand, requires a chemical change or reaction. Likewise, a chemical change is required to break down a compound into its constituent elements. Water can be broken down by passing a powerful electric current through it. This process, known as electrolysis, separates water into hydrogen and oxygen, both of which are highly flammable gases. The fact that they can be joined to form water, a substance used for putting out most kinds of fires, illustrates the types of changes elements undergo when they join to form compounds. The atoms in a compound do not change into other atoms; or to put it another way, the elements do not change into other elements. Though two hydrogen atoms bond with an oxygen atom to form water, they are still hydrogens, and the oxygen is still an oxygen. The atoms’ elemental identity thus remains intact, and if these elements are separated, they can join with other elements to form entirely different compounds.
Letters and Elements; Words and Compounds
Elements and Compounds A compound is a substance made up of atoms representing more than one element, and these atoms are typically joined in molecules. The composition of a compound is always the same: for instance, water always contains molecules
The nature of a compound is almost paradoxical: the constituent elements remain the same, yet the compound typically bears little resemblance to the elements that form it. How can this be? Perhaps an analogy to language, and the symbols used to express it, will serve to show that this
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There are between 88 and 92 elements that appear in nature; figures vary, because a handful of the elements with atomic numbers less than 92 have not actually been found in nature, but were produced in laboratories. (All elements with an atomic number higher than that of uranium, which is 92, are artificial.) In any case, there are far more elements than there are letters in the English alphabet; yet even with 26 characters, it is possible to form an almost limitless vocabulary.
Compounds
Let us focus on a single letter, g. Phonetically, it can make a hard sound, as in great, or a soft one, as in geranium. It may be silent, as in light, or it may combine with another letter to make either a typical “g” sound (edge) or a totally unexpected one (rough). It can slide into a vowel sound smoothly, as in singer, or with an almost imperceptible pause, as in finger. The complexities multiply when we consider the range of possibilities for the letter g, and all the resultant meanings involved: from God to dog, or from glory to degeneration. W H AT T H I S A N A LO GY S H O W S A B O U T C H E M I S T RY. One could go on
endlessly in this vein, and all with just one letter; however, a few points need to be made regarding the analogy between letters of the alphabet and elements. First of all, in all of the examples given above, or any number of others, the g still remained a g. In the same way, an atom of hydrogen (another g-word!) is always a hydrogen, whether it combines with oxygen to form water, nitrogen to make ammonia, or carbon to produce petroleum.
A
MIXTURE VERSUS A COMPOUND. (Robert L. Wolke. Repro-
duced by permission.)
larger combination.
A third point to consider is the fact that there is nothing about g itself that provides any information as to the meaning of the word it helps to form. Here the analogy to elements is imperfect, because the nature of the element’s subatomic structure—particularly the configuration of electrons on the outer shell of the atom—
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Secondly, note that this illustration would have been more difficult if the letter chosen had been q or z, since these are used more rarely. Likewise, there are elements such as technetium or praseodymium that seldom come up in discussions of compounds. On the other hand, one cannot go far in the study of chemistry without running across compounds involving hydrogen, carbon, oxygen, nitrogen, various metals, or halogens such as fluorine.
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provides a great deal of information as to how it will combine with other atoms. Still, it is evident, as we have seen, that the properties of a compound cannot easily be predicted by studying the properties of its constituent elements—just as one cannot begin to define a word simply because it contains a g. On the other hand, knowledge of the sounds that g makes may help us to pronounce a word containing that letter. In the same way, the fact that a compound includes carbon provides a clue that the compound might be organic. Even when we have all the letters to form a word, we still need to know how they are ordered. Loge and ogle contain the same letters, but one is a noun referring to a theater box, whereas the other is a verb meaning the act of looking at someone in an improper fashion. In chemistry, these are called isomers: two substances having identical chemical formulas, but differing chemical structures. It so happens that g is also part of the suffix -ing, used in forming a gerund. Aside from being yet another g-word, a gerund is a substantive, or noun form of a verb: for instance, going. Once again, there is a similarity between words and compounds. Just as certain classes of words are formed by the addition of regular suffixes, so the naming of whole classes of compounds can be achieved by means of a uniform system of nomenclature.
Tea, whether iced or hot, is a mixture. So is coffee, or even wine. In each case, substances are added together and subjected to a process, but the result is not a compound. We know this because the composition varies. Depending on the coffee beans used, for instance, coffee can have a wide variety of flavors. If, in the brewing process, too much coffee is used in proportion to the water, the resulting mixture will be strong or bitter; on the hand, an insufficient coffee-towater ratio will produce coffee that is too weak.
Compounds
Note that a number of terms have been used here that, from a scientific standpoint at least, are vague. How weak is “too weak”? That all depends on the tastes of the person making the coffee. But as long as coffee beans and hot water are used, no matter what the proportion, the mixture is still coffee. On the other hand, when two oxygen atoms, rather than one, are chemically combined with two hydrogen atoms, the result is not “strong water.” Nor is it “oxygenated water”: it is hydrogen peroxide, a substance no one should drink.
REAL-LIFE A P P L I C AT I O N S
Three principal characteristics serve to differentiate a compound from a mixture. First, as we have seen, a compound has a definite and constant composition, whereas a mixture can exist with virtually any proportion between its constituent parts. Second, elements lose their characteristic elemental properties once they form a compound, but the parts of a mixture do not. (For example, when mixed with water, sugar is still sweet.) Third, the formation of a compound involves a chemical reaction, whereas a mixture can be created simply by the physical act of stirring items together.
Distinguishing Between Compounds and Mixtures
The Atomic and Molecular Keys
To continue the analogy used above just one step further, a word is not just a collection of letters; it has to have a meaning. Likewise, the fact that various substances are mixed together does not necessarily make them a compound. Actually, the difference between a word and a mere collection of letters is somewhat greater than the difference between a compound and a mixture—a substance in which elements are not chemically bonded, and in which the composition is variable. A nonsensical string of characters serves no linguistic purpose; on the other hand, mixtures are an integral part of life.
The means by which compounds are formed are discussed numerous times, and in various ways, throughout this book. A few of those particulars will be mentioned briefly below, in relation to the naming of compounds, but for the most part, there will be no attempt to explain the details of the processes involved in chemical bonding. The reader is therefore encouraged to consult the essays on Chemical Bonding and Electrons.
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It is important, nonetheless, to recognize that chemists’ knowledge is based on their understanding of the atom and the ways that electrons, negatively charged particles in the atom, bring
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about bonds between elements. Awareness of these specifics emerged only at the beginning of the twentieth century, with the discovery of subatomic particles. Another important threshold had been crossed a century before, with the development of atomic theory by English chemist John Dalton (1766-1844), and of molecular theory by Italian physicist Amedeo Avogadro (1776-1856). Around the same time, French chemists Antoine Lavoisier (1743-1794) and Joseph-Louis Proust (1754-1826), respectively, clarified the definitions of “element” and “compound.” Until then, the idea of a compound had little precise meaning for chemists, who often used the term to describe a mixture. Thus, French chemist Claude Louis Berthollet (1748-1822) asserted that compounds have variable composition, and for evidence he pointed to the fact that when some metals are heated, they form oxides, in which the percentage of oxygen increases with temperature. Proust, on the other hand, maintained that compounds must have a constant composition, an argument supported by Dalton’s atomic theory. Proust worked to counter Berthollet’s positions on a number of particulars, but was still unable to explain why metals form variable alloys, or combinations of metals; no chemist at the time understood that an alloy is a mixture, not a compound. Nonetheless, Proust was right in his theory of constant composition, and Berthollet was incorrect on this score. With the discovery of subatomic structures, it became possible to develop highly sophisticated theories of chemical bonding, which in turn facilitated understanding of compounds.
Types of Compounds O R GA N I C C O M P O U N D S . Though
there are millions of compounds, these can be grouped into just a few categories. Organic compounds, of which there are many millions, are compounds containing carbon. The only major groupings of carbon-containing compounds that are not considered organic are carbonates, such as limestone, and oxides, such as carbon dioxide. Organic compounds can be further subdivided into a number of functional groups, such as alcohols. Within the realm of organic compounds, whether natural or artificial, are petroleum and
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its many products, as well as plastics and other synthetic materials. The term “organic,” as applied in chemistry, does not necessarily refer to living things, since the definition is based on the presence of carbon. Nonetheless, all living organisms are organic, and the biochemical compounds in living things form an important subset of organic compounds. Biochemical compounds are, in turn, divided into four families: carbohydrates, proteins, nucleic acids, and lipids. I N O R GA N I C C O M P O U N D S . Inorganic compounds can be classified according to five major groupings: acids, bases, salts, oxides, and others. An acid is a compound which, when dissolved in water, produces positive ions (atoms with an electric charge) of hydrogen. Bases are substances that produce negatively charged hydroxide (OH–) ions when dissolved in water. An oxide is a compound in which the only negatively charged ion is an oxygen, and a salt is formed by the reaction of an acid with a base. Generally speaking, a salt is any combination of a metal and a nonmetal, and it can contain ions of any element but hydrogen.
The remaining inorganic compounds, classified as “others,” are those that do not fit into any of the groupings described above. An important subset of this broad category are the coordination compounds, formed when one or more ions or molecules contributes both electrons necessary for a bonding pair, in order to bond with a metallic ion or atom.
Naming Compounds In the early days of chemistry as a science, common names were applied to compounds. Water is an example of a common name; so is sugar, as well as salt. These names work well enough in everyday life, and in fact, chemists still refer to water simply as “water.” (The only other common name still used in chemistry is ammonia.) But as the number of compounds discovered and developed by chemists began to proliferate, the need for a systematic means of naming them became apparent. With millions of compounds, it would be nearly impossible to come up with names for every one. Furthermore, common names tell chemists nothing about the chemical properties of a particular substance.
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Today, chemists use a system of nomenclature that is rather detailed but fairly easy to understand, once the rules are understood. We will examine this system briefly, primarily as it relates to binary compounds—compounds containing just two elements. Binary compounds are divided into three groups. The first two are ionic compounds, involving metals that form positively charged ions, or cations (pronounced KAT-ieunz). The third consists of compounds that contain only nonmetals. These groups are:
of substances, its chemical name is sodium chloride.
• Type I: Ionic compounds involving a metal that always forms a cation of a certain electric charge. • Type II: Ionic compounds involving a metal (typically a transition metal) that forms cations with differing charges. • Type III: Compounds containing only nonmetals. CAT I O N S A N D A N I O N S . Cations are represented symbolically thus: H+, or Mg2+. The first, a hydrogen cation, has a positive charge of 1, but note that the 1 is not shown—just as the first power of a number is never designated in mathematics. In the second example, a magnesium cation, the superscript number, combined with the plus sign (which can either follow the number, as is shown here, or proceed it) indicates that the atom has a positive charge of two. Thus, even if one were not told that this is a cation, it would be easy enough to discern from the notation.
The chemical nomenclature for type II binary compounds is somewhat more complicated, because they involve metals that can have multiple positive charges. This is particularly true of the transition metals, a family of 40 elements in the middle of the periodic table distinguished from other elements by a number of characteristics. The name “transition” thus implies a break in the even pattern of the periodic table.
Anions (AN-ie-unz), or negatively charged ions, are represented in a similar way: H- for hydride, an anion of hydrogen; or O2– for oxide. Note, however, that the naming of anions and cations is different. Cations are always called, for example, a hydrogen cation, or a magnesium cation. On the other hand, names of simple anions (involving a single atom) are formed by taking the root of the element name and adding an -ide: for example, fluoride (F–). T Y P E I B I N A RY C O M P O U N D S .
In a binary ionic compound, a metal combines with a nonmetal. The metal loses one or more electrons to become a cation, while the nonmetal gains one or more electrons to become an anion. Thus, table salt is formed by the joining of a cation of the metal sodium (Na+) and an anion of the nonmetal chlorine (Cl–). Instead of the common name “salt,” which can apply to a range
S C I E N C E O F E V E RY DAY T H I N G S
Compounds
In naming Type I binary compounds, of which sodium chloride is an example, the cation is always represented first by the name of the element. The anion follows, with the root name of the element attached to the -ide suffix, as described above. Another example is calcium sulfide, formed by a cation of the metal calcium (Ca2+) and an anion of the nonmetal sulfur (S2–). T Y P E I I B I N A RY C O M P O U N D S .
Iron (Fe), for instance, is a transition metal, and it can form cations with charges of 2+ or 3+, while copper (Cu) can form cations with charges of 1+ or 2+. When encountering positively charged cations, it is not enough to say, for instance, “iron oxide,” or “copper sulfide,” because it is not clear which iron cation is involved. To solve the problem, chemists use a system of Roman numerals. According to this system, the cations referred to above are expressed in the name of a Type II binary compound thus: iron (II), iron (III), copper (I), and copper (II). This is followed with the name of the anion, as before, using the -ide suffix. Note that the Roman numeral is usually the same as the number of positive charges in the cation. It should be noted, also, that there is an older system for naming Type II binary compounds with terms that incorporate the element name— often the Latin original, reflected in the chemical symbol—with a suffix. For instance, this system uses the word “ferrous” for iron (II) and “ferric” for iron (III). However, this method of nomenclature is increasingly being replaced by the one we have described here. T Y P E I I I B I N A RY C O M P O U N D S .
In a Type III binary compound involving only nonmetals, the first element in the formula is referred to simply by its element name, as though it were a cation, while the second element is given an -ide suffix, as though it were an anion. If there
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is more than one atom present, prefixes are used to indicate the number of atoms. These prefixes are listed below. It should be noted that mono- is never used for naming the first element in a type III binary compound. • • • • • • • •
mono-: 1 di-: 2 tri-: 3 tetra-: 4 penta-: 5 hexa-: 6 hepta-: 7 octa-: 8 Thus CO2 is called carbon dioxide, indicating one carbon atom and two oxygens. Again, mono- is not used for the first element, but it is used for the second: hence, the name of the compound with the formula CO is carbon monoxide. It is also possible to know the formula for a compound simply from the name: if confronted with a name such as “dinitrogen pentoxide,” for instance, it is fairly easy to apply the rules governing these prefixes to discern that the substance is N2O5. Note that vowels at the end of a prefix are dropped when the name of the element that follows it also begins with a vowel: we say monoxide, not “monooxide”; and pentoxide, not “pentaoxide.” This makes pronunciation much easier. POLYATOMIC IONS AND ACIDS.
More complicated rules apply for polyatomic ions, which are charged groupings of atoms such as NH4NO3, or ammonium nitrate. The only way to learn how to name polyatomic ions is by memorizing the names of the constituent parts. In the above example, for instance, the first part of the formula, which has a positive charge, is always called ammonium, while the second part, which has a negative charge, is always called nitrate. A good chemistry textbook should provide a table listing the names of common polyatomic ions. A number of polyatomic ions are called oxyanions, meaning that they include varying numbers of oxygen atoms combined with atoms of other elements. There are rules for designating the names of these polyatomic ions, some of which are listed in the essay on Ions and Ionization. Still other rules govern the naming of acids; here again, the operative factor is the presence of oxygen. Thus, if the anion does not contain oxy-
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gen, the name of the acid is created by adding the prefix hydro- and the suffix -ic, as in hydrochloric acid. If the anion does contain oxygen, the root name of the principal element is joined to a suffix: depending on the relative numbers of oxygen atoms, this may be -ic or -ous.
Isomers As observed much earlier, isomers are like two words with the same letters, but arranged in different ways. Specifically, isomers are chemical compounds having the same formula, but in which the atoms are arranged differently, thereby forming different compounds. There are two principal types of isomer: structural isomers, which differ according to the attachment of atoms on the molecule, and stereoisomers, which differ according to the locations of the atoms in space. An example of structural isomerism is the difference between propyl alcohol and isopropyl (rubbing) alcohol: these two have differing properties, because their alcohol functional groups are not attached to the same carbon atom in the carbon chain to which the functional group is attached. In a stereoisomer, on the other hand, atoms are attached in the same order, but have different spatial relationships. If functional groups are aligned on the same side of a double bond between two carbon atoms, this is called a cis isomer, from a Latin word meaning “on this side.” If they are on opposite sides, it is called a trans (“across”) isomer. Hence the term “trans fats,” which are saturated fats that improve certain properties of foods—including taste—but which may contribute to heart disease. WHERE TO LEARN MORE “Chemical Compounds” (Web site). (June 2, 2001). “Chemtutor Compounds.” Chemtutor (Web site). (June 2, 2001). Fullick, Ann. Matter. Des Plaines, IL: Heinemann Library, 1999. “Glossary of Products with Hazards A to Z” Environmental Protection Agency (Web site). (June 2, 2001). Knapp, Brian J. Elements, Compounds, and Mixtures, Volume 2. Edited by Mary Sanders. Danbury, CT: Grolier
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Compounds
KEY TERMS An inorganic compound that,
electrons necessary for a bonding pair in
when dissolved in water, produces positive
order to bond with a metallic ion or atom.
ACID:
ions—that is, cations—of hydrogen, designated symbolically as H+ ions. (This is just
A negatively charged par-
ELECTRON:
ticle in an atom.
one definition; see Acids and Bases; AcidFor the
INORGANIC COMPOUND:
Base Reactions for more.)
most part, inorganic compounds are any The negatively charged ion
compounds that do not contain carbon.
that results when an atom gains one or
However, carbonates and carbon oxides are
more electrons. The word is pronounced
also inorganic compounds. Compare with
“AN-ie-un.”
organic compounds.
ANION:
BASE:
An inorganic compound that
ION:
An atom or group of atoms that
produces negative hydroxide ions when it
has lost or gained one or more electrons,
is dissolved in water. These anions are des-
and thus has a net electric charge.
ignated by the symbol OH-. (This is just one definition; see Acids and Bases; AcidBase Reactions for more.) BINARY COMPOUND:
A form of chemical
bonding that results from attractions between ions with opposite electric
A compound
that contains just two elements. For the purposes of establishing compound names, binary compounds are divided into Type I, Type II, and Type III. CATION:
IONIC BONDING:
charges. IONIC COMPOUND:
A compound in
which ions are present. Ionic compounds contain at least one metal joined to another element by an ionic bond.
The positively charged ion
ISOMERS:
Substances which have the
that results when an atom loses one or
same chemical formula, but which have
more electrons. The word “cation” is pro-
different chemical properties due to differ-
nounced “KAT-ie-un.”
ences in the arrangement of atoms.
CHEMICAL BONDING:
The joining,
MIXTURE:
A substance in which ele-
through electromagnetic force, of atoms
ments are not chemically bonded, and in
representing different elements.
which the composition is variable. A mix-
COMPOUND:
A substance made up of
ture is distinguished from a compound.
atoms of more than one element, which are
ORGANIC COMPOUND:
chemically bonded and usually joined in
speaking, a compound containing carbon.
molecules. The composition of a com-
The only exceptions are the carbonates (for
pound is always the same, unless it is
example, calcium carbonate or limestone)
changed chemically.
and oxides, such as carbon dioxide.
COORDINATION
COMPOUNDS:
OXIDE:
Generally
An inorganic compound in
Inorganic compounds formed when one
which the only negatively charged ion is an
or more ions or molecules contribute both
oxygen.
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Compounds
KEY TERMS SALT:
An inorganic compound formed
by the reaction of an acid with a base. Generally speaking, a salt is a combination of a metal and a nonmetal, and it can contain
TYPE
II
BINARY
COMPOUNDS:
Ionic compounds involving a metal (typically a transition metal) that forms cations with differing charges.
ions of any element but hydrogen.
TYPE
TYPE
VALENCE ELECTRONS:
I
BINARY
COMPOUNDS:
Ionic compounds involving a metal that always forms a cation of a certain electric charge.
Educational, 1998. “List of Compounds” (Web site). (June 2, 2001). Maton, Anthea. Exploring Physical Science. Upper Saddle River, N.J.: Prentice Hall, 1997.
280
CONTINUED
III
BINARY
COMPOUNDS:
Compounds containing only nonmetals. Electrons that occupy the highest energy levels in an atom. These are the only electrons involved in chemical bonding.
(Web site). (June 2, 2001). Oxlade, Chris. Elements and Compounds. Chicago, IL: Heinemann Library, 2001.
“Molecules and Compounds.” General Chemistry Online
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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CHEMICAL REACTIONS
CONCEPT If chemistry were compared to a sport, then the study of atomic and molecular properties, along with learning about the elements and how they relate on the periodic table, would be like going to practice. Learning about chemical reactions, which includes observing them and sometimes producing them in a laboratory situation, is like stepping out onto the field for the game itself. Just as every sport has its “vocabulary”—the concepts of offense and defense, as well as various rules and strategies—the study of chemical reactions involves a large set of terms. Some aspects of reactions may seem rather abstract, but the effects are not. Every day, we witness evidence of chemical reactions—for instance, when a fire burns, or metal rusts. To an even greater extent, we are surrounded by the products of chemical reactions: the colors in the clothes we wear, or artificial materials such as polymers, used in everything from nylon running jackets to plastic milk containers.
HOW IT WORKS
tric current is run through a sample, separating it into oxygen and hydrogen gas. Chemical change requires a chemical reaction, a process whereby the chemical properties of a substance are altered by a rearrangement of the atoms in the substance. Of course we cannot see atoms with the naked eye, but fortunately, there are a number of clues that tell us when a chemical reaction has occurred. In many chemical reactions, for instance, the substance may experience a change of state or phase—as for instance when liquid water turns into gaseous oxygen and hydrogen as a result of electrolysis. HOW DO WE KNOW WHEN A C H E M I CA L R E AC T I O N H AS O C C U R R E D ? Changes of state may of course be
merely physical—as for example when liquid water is boiled to form a vapor. (These and other examples of physical changes resulting from temperature changes are discussed in the essays on Properties of Matter; Temperature and Heat.) The vapor produced by boiling water, as noted above, is still water; on the other hand, when liquid water is turned into the elemental gases hydrogen and oxygen, a more profound change has occurred.
What Is a Chemical Reaction? If liquid water is boiled, it is still water; likewise frozen water, or ice, is still water. Melting, boiling, or freezing simply by the application of a change in temperature are examples of physical changes, because they do not affect the internal composition of the item or items involved. A chemical change, on the other hand, occurs when the actual composition changes—that is, when one substance is transformed into another. Water can be chemically changed, for instance, when an elec-
Likewise the addition of liquid potassium chromate (K2CrO4) to a solution of barium nitrate (Ba[NO3]2 forms solid barium chromate (BaCrO4). In the reaction described, a solution is also formed, but the fact remains that the mixture of two solids has resulted in the formation of a solid in a different solution. Again, this is a far more complex phenomenon than the mere freezing of water to form ice: here the fundamental properties of the materials involved have changed.
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A
MICROSCOPIC CLOSE-UP OF NYLON FIBERS.
NYLON
IS FORMED THROUGH A SYNTHESIS REACTION. (Science Pictures
Limited/Corbis. Reproduced by permission.)
The physical change of water to ice or steam, of course, involves changes in temperature; likewise, chemical changes are often accompanied by changes in temperature, the crucial difference being that these changes are the result of alterations in the chemical properties of the substances involved. Such is the case, for instance, when wood burns in the presence of oxygen: once wood is turned to ash, it has become an entirely different mixture than it was before. Obviously, the ashes cannot be simply frozen to turn them back into wood again. This is an example of an irreversible chemical reaction.
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right conditions, carbon—which is black—can be combined with colorless hydrogen and oxygen to produce white sugar. This suggests another kind of change: a change in taste. (Of course, not every product of a chemical reaction should be tasted—some of the compounds produced may be toxic, or at the very least, extremely unpleasant to the taste buds.) Smell, too, can change. Sulfur is odorless in its elemental form, but when combined with hydrogen to form hydrogen sulfide (H2S), it becomes an evil-smelling, highly toxic gas.
Chemical reactions may also involve changes in color. In specific proportions and under the
The bubbling of a substance is yet another clue that a chemical reaction has occurred. Though water bubbles when it boils, this is mere-
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ly because heat has been added to the water, increasing the kinetic energy of its molecules. But when hydrogen peroxide bubbles when exposed to oxygen, no heat has been added. As with many of the characteristics of a chemical reaction described above, bubbling does not always occur when two chemicals react; however, when one of these clues is present, it tells us that a chemical reaction may have taken place.
Chemical Reactions
REAL-LIFE A P P L I C AT I O N S Chemical Equations In every chemical reaction, there are participants known as reactants, which, by chemically reacting to one another, result in the creation of a product or products. As stated earlier, a chemical reaction involves changes in the arrangement of atoms. The atoms in the reactants (or, if the reactant is a compound, the atoms in its molecules) are rearranged. The atomic or molecular structure of the product is different from that of either reactant. Note, however, that the number of atoms does not change. Atoms themselves are neither created nor destroyed, and in a chemical reaction, they merely change partners, or lose partners altogether as they return to their elemental form. This is a critical principle in chemistry, one that proves that medieval alchemists’ dream of turning lead into gold was based on a fallacy. Lead and gold are both elements, meaning that each has different atoms. To imagine a chemical reaction in which one becomes the other is like saying “one plus one equals one.” SYMBOLS IN A CHEMICAL E Q UAT I O N . In a mathematical equation,
the sums of the numbers on one side of the equals sign must be the same as the sum of the numbers on the other side. The same is true of a chemical equation, a representation of a chemical reaction in which the chemical symbols on the left stand for the reactants, and those on the right are the product or products. Instead of an equals sign separating them, an arrow, pointing to the right to indicate the direction of the reaction, is used.
A
CLOSE-UP OF RUST ON A PIECE OF METAL.
RUST
IS
AN EXAMPLE OF A COMBINATION REACTION, NOT A DECOMPOSITION REACTION. (Marko Modic/Corbis. Reproduced
by permission.)
reactants and products. These symbols are as follows: • • • •
(s): solid (l): liquid (g): gas (aq): dissolved in water (an aqueous solution) The fourth symbol, of course, does not indicate a phase of matter per se (though obviously it appears to be a liquid); but as we shall see, aqueous solutions play a role in so many chemical reactions that these have their own symbol. At any rate, using this notation, we begin to symbolize the reaction of hydrogen and oxygen to form water thus: H(g) + O(g) 4H2O(l).
Chemical equations usually include notation indicating the state or phase of matter for the
This equation as written, however, needs to be modified in several ways. First of all, neither hydrogen nor oxygen is monatomic. In other words, in their elemental form, neither appears as a single atom; rather, these form diatomic (two-atom) molecules. Therefore, the equation must be rewritten as H2(g) + O2(g) 4H2O(l). But this is still not correct, as a little rudimentary analysis will show.
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Balancing Chemical Equations When checking a chemical equation, one should always break it down into its constituent elements, to determine whether all the atoms on the left side reappear on the right side; otherwise, the result may be an incorrect equation, along the lines of “1 + 1 = 1.” That is exactly what has happened here. On the left side, we have two hydrogen atoms and two oxygen atoms; on the right side, however, there is only one oxygen atom to go with the two hydrogens. Obviously, this equation needs to be corrected to account for the second oxygen atom, and the best way to do that is to show a second water molecule on the right side. This will be represented by a 2 before the H2O, indicating that two water molecules now have been created. The 2, or any other number used for showing more than one of a particular chemical species in a chemical equation, is called a coefficient. Now we have H2(g) + O2(g) 42H2O(l). Is this right? Once again, it is time to analyze the equation, to see if the number of atoms on the left equals the number on the right. Such analysis can be done in a number of ways: for instance, by symbolizing each chemical species as a circle with chemical symbols for each element in it. Thus a single water molecule would be shown as a circle containing two H’s and one O. Whatever the method used, analysis will reveal that the problem of the oxygen imbalance has been solved: now there are two oxygens on the left, and two on the right. But solving that problem has created another, because now there are four hydrogen atoms on the right, as compared with two on the left. Obviously, another coefficient of 2 is needed, this time in front of the hydrogen molecule on the left. The changed equation is thus written as: 2H2(g) + O2(g) 4 2H2O(l). Now, finally, the equation is correct. T H E P R O C E SS O F B A LA N C I N G C H E M I CA L E Q UAT I O N S . What
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In writing and balancing a chemical equation, the first step is to ascertain the identities, by formula, of the chemical species involved, as well as their states of matter. After identifying the reactants and product, the next step is to write an unbalanced equation. After that, the unbalanced equation should be subjected to analysis, as demonstrated above. The example used, of course, involves a fairly simple substance, but often, much more complex molecules will be part of the equation. In performing analysis to balance the equation, it is best to start with the most complex molecule, and determine whether the same numbers and proportions of elements appear in the product or products. After the most complicated molecule has been dealt with, the second-most complex can then be addressed, and so on. Assuming the numbers of atoms in the reactant and product do not match, it will be necessary to place coefficients before one or more chemical species. After this has been done, the equation should again be checked, because as we have seen, the use of a coefficient to straighten out one discrepancy may create another. Note that only coefficients can be changed; the formulas of the species themselves (assuming they were correct to begin with) should not be changed. After the equation has been fully balanced, one final step is necessary. The coefficients must be checked to ensure that the smallest integers possible have been used. Suppose, in the above exercise, we had ended up with an equation that looked like this: 12H2(g) + 6O2(g) 412H2O(l). This is correct, but not very “clean.” Just as a fraction such as 12/24 needs to be reduced to its simplest form, 1/2, the same is true of a chemical equation. The coefficients should thus always be the smallest number that can be used to yield a correct result.
Types of Chemical Reactions
we have done is to balance an unbalanced equation. An unbalanced equation is one in which the numbers of atoms on the left are not the same as the number of atoms on the right. Though an unbalanced equation is incorrect, it is sometimes a necessary step in the process of finding the balanced equation—one in which the number of atoms in the reactants and those in the product are equal.
Note that in chemical equations, one of the symbols used is (aq), which indicates a chemical species that has been dissolved in water—that is, an aqueous solution. The fact that this has its own special symbol indicates that aqueous solutions are an important part of chemistry. Examples of reactions in aqueous solutions are discussed, for instance, in the essays on Acid-Base Reactions; Chemical Equilibrium; Solutions.
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Another extremely important type of reaction is an oxidation-reduction reaction. Sometimes called a redox reaction, an oxidationreduction reaction occurs during the transfer of electrons. The rusting of iron is an example of an oxidation-reduction reaction; so too is combustion. Indeed, combustion reactions—in which oxygen produces energy so rapidly that a flame or even an explosion results—are an important subset of oxidation-reduction reactions. R E AC T I O N S T H AT F O R M WA T E R, S O L I D S , O R GAS E S . Another
type of reaction is an acid-base reaction, in which an acid is mixed with a base, resulting in the formation of water along with a salt. Other reactions form gases, as for instance when water is separated into hydrogen and oxygen. Similarly, heating calcium carbonate (limestone) to make calcium oxide or lime for cement also yields gaseous carbon dioxide: CaCO3(s) + heat 4CaO(s) + CO2(g). There are also reactions that form a solid, such as the one mentioned much earlier, in which solid BaCrO4(s) is formed. Such reactions are called precipitation reactions. But this is also a reaction in an aqueous solution, and there is another product: 2KNO3(aq), or potassium nitrate dissolved in water. SINGLE AND DOUBLE DISP LAC E M E N T. The reaction referred to in
the preceding paragraph also happens to be an example of another type of reaction, because two anions (negatively charged ions) have been exchanged. Initially K+ and CrO42- were together, and these reacted with a compound in which Ba2+ and NO3-were combined. The anions changed places, an instance of a double-displacement reaction, which is symbolized thus: AB + CD 4AD + CB.
als be elements or simple compounds. A basic example of this is the reaction described earlier in relation to chemical equations, when hydrogen and oxygen combine to form water. On the other hand, some extremely complex substances, such as the polymers in plastics and synthetic fabrics such as nylon, also involve synthesis reactions. When iron rusts (in other words, it oxidizes in the presence of air), this is both an oxidationreduction and a synthesis reaction. This also represents one of many instances in which the language of science is quite different from everyday language. If a piece of iron—say, a railing on a balcony—rusts due to the fact that the paint has peeled off, it would seem from an unscientific standpoint that the iron has “decomposed.” However, rust (or rather, metal oxide) is a more complex substance than the iron, so this is actually a synthesis or combination reaction. A true decomposition reaction occurs when a compound is broken down into simpler compounds, or even into elements. When water is subjected to electrolysis such that the hydrogen and oxygen are separated, this is a decomposition reaction. The fermentation of grapes to make wine is also a form of decomposition. And then, of course, there are the processes that normally come to mind when we think of “decomposition”: the decay or rotting of a formerly living thing. This could also include the decay of something, such as an item of food, made from a formerly living thing. In such instances, an organic substance is eventually broken down through a number of processes, most notably the activity of bacteria, until it ultimately becomes carbon, nitrogen, oxygen, and other elements that are returned to the environment. SOME
OTHER
PA RA M E T E R S .
C O M B I N AT I O N A N D D E C O M P O S I T I O N . A synthesis, or combination,
Obviously, there are numerous ways to classify chemical reactions. Just to complicate things a little more, they can also be identified as to whether they produce heat (exothermic) or absorb heat (endothermic). Combustion is clearly an example of an exothermic reaction, while an endothermic reaction can be exemplified by the process that takes place in a cold pack. Used for instance to prevent swelling on an injured ankle, a cold pack contains an ampule that absorbs heat when broken.
reaction is one in which a compound is formed from simpler materials—whether those materi-
Still another way to identify chemical reactions is in terms of the phases of matter involved.
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It is also possible to have a single-displacement reaction, in which an element reacts with a compound, and one of the elements in the compound is released as a free element. This can be represented symbolically as A + BC 4B + AC. Single-displacement reactions often occur with metals and with halogens. For instance, a metal (A) reacts with an acid (BC) to produce hydrogen (B) and a salt (AC).
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We have already seen that some reactions form gases, some solids, and some yield water as one of the products. If reactants in one phase of matter produce a substance or substances in the same phase (liquid, solid, or gas), this is called a homogeneous reaction. On the other hand, if the reactants are in different phases of matter, or if they produce a substance or substances that are in a different phase, this is called a heterogeneous reaction. An example of a homogeneous reaction occurs when gaseous nitrogen combines with oxygen, also a gas, to produce nitrous oxide, or “laughing gas.” Similarly, nitrogen and hydrogen combine to form ammonia, also a gas. But when hydrogen and oxygen form water, this is a heterogeneous reaction. Likewise, when a metal undergoes an oxidation-reduction reaction, a gas and a solid react, resulting in a changed form of the metal, along with the production of new gases. Finally, a chemical reaction can be either reversible or irreversible. Much earlier, we described how wood experiences combustion, resulting in the production of ash. This is clearly an example of an irreversible reaction. The atoms in the wood and the air that oxidized it have not been destroyed, but it would be impossible to put the ash back together to make a piece of wood. By contrast, the formation of water by hydrogen and oxygen is reversible by means of electrolysis. KEEPING
IT
ALL
S T RA I G H T.
The different classifications of reactions discussed above are clearly not mutually exclusive; they simply identify specific aspects of the same thing. This is rather like the many physical characteristics that describe a person: gender, height, weight, eye color, hair color, race, and so on. Just because someone is blonde, for instance, does not mean that the person cannot also be browneyed; these are two different parameters that are more or less independent. On the other hand, there is some relation between these parameters in specific instances: for example, females over six feet tall are rare, simply because women tend to be shorter than men. But there are women who are six feet tall, or even considerably taller. In the same way, it is unlikely that a reaction in an aqueous solution will be a combustion reaction—yet it does happen, as for instance when potassium reacts with water.
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Studying Chemical Reactions Several aspects or subdisciplines of chemistry are brought to bear in the study of chemical reactions. One is stoichiometry (stoy-kee-AH-muhtree), which is concerned with the relationships among the amounts of reactants and products in a chemical reaction. The balancing of the chemical equation for water earlier in this essay is an example of basic stoichiometry. Chemical thermodynamics is the area of chemistry that addresses the amounts of heat and other forms of energy associated with chemical reactions. Thermodynamics is also a branch of physics, but in that realm, it is concerned purely with physical processes involving heat and energy. Likewise physicists study kinetics, associated with the movement of objects. Chemical kinetics, on the other hand, involves the study of the collisions between molecules that produce a chemical reaction, and is specifically concerned with the rates and mechanisms of reaction. S P E E D I N G U P A C H E M I CA L R E AC T I O N . Essentially, a chemical reaction
is the result of collisions between molecules. According to this collision model, if the collision is strong enough, it can break the chemical bonds in the reactants, resulting in a rearrangement of the atoms to form products. The more the molecules collide, the faster the reaction. Increase in the numbers of collisions can be produced in two ways: either the concentrations of the reactants are increased, or the temperature is increased. In either case, more molecules are colliding. Increases of concentration and temperature can be applied together to produce an even faster reaction, but rates of reaction can also be increased by use of a catalyst, a substance that speeds up the reaction without participating in it either as a reactant or product. Catalysts are thus not consumed in the reaction. One very important example of a catalyst is an enzyme, which speeds up complex reactions in the human body. At ordinary body temperatures, these reactions are too slow, but the enzyme hastens them along. Thus human life can be said to depend on chemical reactions aided by a wondrous form of catalyst. WHERE TO LEARN MORE Bender, Hal. “Chemical Reactions.” Clackamas Community College (Web site). (June 3, 2001).
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Chemical Reactions
KEY TERMS A chemical
istry—whether it be an element, com-
reaction in which an acid is mixed with a
pound, mixture, atom, molecule, ion, and
base, resulting in the formation of water
so forth.
ACID-BASE REACTION:
along with a salt. CHEMICAL
THERMODYNAMICS:
A mixture
The study of the amounts of heat and
of water and any substance that is solvent
other forms of energy associated with
in it.
chemical reactions.
AQUEOUS SOLUTIONS:
A chemical
BALANCED EQUATION:
COEFFICIENT:
A number used to
equation in which the numbers of atoms in
indicate the presence of more than one
the reactants and those in the product are
unit—typically, more than one molecule—
equal. In the course of balancing an equa-
of a chemical species in a chemical equa-
tion, coefficients may need to be applied to
tion. For instance, 2H2O indicates two
one or more of the chemical species
water molecules. (Note that 1 is never used
involved; however, the actual formulas of
as a coefficient.)
the species cannot be changed. COLLISION MODEL:
The theory that
A substance that speeds up
chemical reactions are the result of colli-
a chemical reaction without participating
sions between molecules that are strong
in it either as a reactant or product.
enough to break bonds in the reactants,
Catalysts are thus not consumed in the
resulting in a rearrangement of atoms to
reaction.
form a product or products.
CATALYST:
A represen-
CHEMICAL EQUATION:
DECOMPOSITION
REACTION:
A
tation of a chemical reaction in which
chemical reaction in which a compound is
the chemical symbols on the left stand for
broken down into simpler compounds, or
the reactants, and those on the right for the
even into elements. This is the opposite of
product or products. On paper, a chemical
a synthesis or combination reaction.
equation looks much like a mathematical one; however, instead of an equals sign, a chemical equation uses an arrow to show the direction of the reaction.
the rate at which chemical reactions occur. CHEMICAL REACTION:
TION:
REAC-
A chemical reaction in which
the partners in two compounds change places. This can be symbolized as
the study of
CHEMICAL KINETICS:
DOUBLE-DISPLACEMENT
A process
AB + CD 4AD + CB. Compare singledisplacement reaction. ENDOTHERMIC:
A term describing a
whereby the chemical properties of a sub-
chemical reaction in which heat is
stance are changed by a rearrangement of
absorbed or consumed.
the atoms in the substance. EXOTHERMIC: CHEMICAL SPECIES:
A generic term
used for any substance studied in chem-
S C I E N C E O F E V E RY DAY T H I N G S
A term describing a
chemical reaction in which heat is produced.
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Chemical Reactions
KEY TERMS A term describ-
product is in a different phase from that of
element reacts with a compound, and one of the elements in the compound is released as a free element. This can be represented symbolically as A + BC 4B + AC. Compare double-displacement reaction.
the reactants.
STOICHIOMETRY:
HETEROGENEOUS:
ing a chemical reaction in which the reactants are in different phases of matter (liquid, solid, or gas), or one in which the
HOMOGENEOUS:
A term describing
a chemical reaction in which the reactants and the product are all in the same phase of matter (liquid, solid, or gas). OXIDATION-REDUCTION REACTION:
The study of the relationships among the amounts of reactants and products in a chemical reaction. Producing a balanced equation requires application of stoichiometry (pronounced “stoy-kee-AH-muh-tree”).
A chemical reaction involving the transfer
SYNTHESIS
of electrons.
REACTION:
PRECIPITATION
REACTION:
A
chemical reaction in which a solid is formed. PRODUCT:
The substance or sub-
stances that result from a chemical reaction. REACTANT:
A substance that inter-
acts with another substance in a chemical reaction, resulting in the formation of a product. SINGLE-DISPLACEMENT TION:
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CONTINUED
REAC-
A chemical reaction in which an
OR
COMBINATION
A chemical reaction in which a compound is formed from simpler materials—either elements or simple compounds. It is the opposite of a decomposition reaction.
A chemical equation in which the sum of atoms in the product or products does not equal the sum of atoms in the reactants. Initial observations of a chemical reaction usually produce an unbalanced equation, which needs to be analyzed and corrected (by the use of coefficients) to yield a balanced equation.
UNBALANCED EQUATION:
“Catalysis, Separations, and Reactions.” Accelrys (Web site). (June 3, 2001). Goo, Edward. “Chemical Reactions” (Web site). (June 3, 2001). Knapp, Brian J. Oxidation and Reduction. Illustrated by David Woodroffe. Danbury, CT: Grolier Educational, 1998. Knapp, Brian J. Energy and Chemical Change. Illustrated by David Woodroffe. Danbury, CT: Grolier Educational, 1998. Newmark, Ann. Chemistry. New York: Dorling Kindersley, 1993.
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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“Periodic Table: Chemical Reaction Data.” WebElements (Web site). (June 3, 2001). Richards, Jon. Chemicals and Reactions. Brookfield, CT: Copper Beech Books, 2000. “Types of Chemical Reactions” (Web site). (June 3, 2001).
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O X I D AT I O N - R E D U C T I O N REACTIONS
Oxidation-Reduction Reactions
CONCEPT Most people have heard the term “oxidation” at some point or another, and, from the sound of the word, may have developed the impression that it has something to do with oxygen. Indeed it does, because oxygen has a tendency to draw electrons to itself. This tendency, rather than the presence of oxygen itself, is actually what identifies oxidation, defined as a process in which a substance loses electrons. The oxidation of one substance is always accompanied by reduction, or the gaining of electrons, on the part of another substance—hence the term “oxidation-reduction reaction,” sometimes called a redox reaction. The world is full of examples of this highly significant form of chemical reaction. One such example is combustion, or an even more rapid form of combustion, explosion. Likewise the metabolism of food, as well as other biological processes, involves oxidation and reduction reactions. So, too, do a number of processes that take place on the surfaces of metals: when iron rusts; when copper turns green; or when aluminum forms a coating of aluminum oxide that prevents it from rusting. Oxidation-reduction reactions also play a major role in electrochemistry, which has a highly useful application to daily life in the form of batteries.
affect the fundamental properties of the substance itself. A piece of copper can be heated, melted, beaten into different shapes, and so forth, yet throughout all those changes, it remains pure copper, an element of the transition metals family. But suppose a copper roof is exposed to the elements for many years. Copper is famous for its highly noncorrosive quality, and this, combined with its beauty, has made it a favored material for use in the roofs of imposing buildings. (Because it is relatively expensive, few middle-class people today can afford a roof entirely made of copper, but sometimes it is used as a decorative touch— for instance, over the entryway of a house.) Eventually, however, copper does begin to corrode when exposed to air for long periods of time. Over the years, exposed copper develops a thin layer of black copper oxide, and as time passes, traces of carbon dioxide in the air contribute to the formation of greenish copper carbonate. This explains why the Statue of Liberty, covered in sheets of copper, is green, rather than having the reddish-golden hue of new, uncorroded copper. EXTERNAL The CHANGE.
VS.
INTERNAL
A chemical reaction is a process whereby the chemical properties of a substance are changed by a rearrangement its atoms. The change produced by a chemical reaction is quite different from a purely physical change, which does not
preceding paragraphs describe two very different phenomena. The first was a physical change in which the chemical properties of a substance—copper—remained unaltered. The second, on the other hand, involved a chemical change on the surface of the copper, as copper atoms bonded with carbon and oxygen atoms in the air to form something different from copper. The difference between these two types of changes can be likened to varieties of changes in a person’s life—an external change
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on the one hand, and a deeply rooted change on the other. A person may move to another house, job, school, or town, yet the person remains the same. Many sayings in the English language express this fact: for instance, “Wherever you go, there you are,” or “You can take the boy out of the country, but you can’t take the country out of the boy.” Moving is simply a physical change. On the other hand, if a person changes belief systems, overcomes old feelings (or succumbs to new ones), changes lifestyles in a profound manner, or in any other way changes his or her mind about something important—this is analogous to a chemical change. In these instances, the person, like the surface of the copper described above, has changed not merely in external properties, but in inner composition.
“LEO the Lion Says ‘GER’” Chemical reactions are addressed in depth within the essay devoted to that subject, which discusses—among other subjects—many ways of classifying chemical reactions. These varieties of chemical reaction are not all mutually exclusive, as they relate to different aspects of the reaction. As noted in the review of various reaction types, one of the most significant is an oxidationreduction reaction (sometimes called a redox reaction) involving the transfer of electrons. As its name implies, an oxidation-reduction reaction is really two processes: oxidation, in which electrons are lost, and reduction, in which electrons are gained. Though these are defined separately here, they do not occur independently; hence the larger reaction of which each is a part is called an oxidation-reduction reaction. In order to keep the two straight, chemistry teachers long ago developed a useful, if nonsensical, mnemonic device: “LEO the lion says ‘GER’.” LEO stands for “Loss of Electrons, Oxidation,” and “GER” means “Gain of Electrons, Reduction.” Many, though not all, oxidation-reduction reactions involve oxygen. Oxygen combines readily with other elements, and in so doing, it tends to grab electrons from those other elements’ atoms. As a result, the oxygen atom becomes an ion (an atom with an electric charge)—specifically, an anion, or negatively charged ion.
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In interacting with another element, oxygen becomes reduced, while the other element is oxidized to become a cation, or a positively charged ion. This, too, is easy to remember: oxygen itself, obviously, cannot be oxidized, so it must be the one being reduced. But since not all oxidationreduction reactions involve oxygen, perhaps the following is a better way to remember it. Electrons are negatively charged, and the element that takes them on in an oxidation-reduction reaction is reduced—just as a person who thinks negative thoughts are “reduced” if those negative thoughts overcome positive ones.
Oxidation Numbers An oxidation number (sometimes called an oxidation state) is a whole-number integer assigned to each atom in an oxidation-reduction reaction. This makes it easier to keep track of the electrons involved, and to observe the ways in which they change positions. Here are some rules for determining oxidation number. • 1. The oxidation number for an atom of an element not combined with other elements in a compound is always zero. • 2. For an ion of any element, the oxidation number is the same as its charge. Thus a sodium ion, which has a charge of +1 and is designated symbolically as Na+, has an oxidation number of +1. • 3. Certain elements or families form ions in predictable ways: • a. Alkali metals, such as sodium, always form a +1 ion; oxidation number = +1. • b. Alkaline earth metals, such as magnesium, always form a +2 ion; oxidation number = +2. • c. Halogens, such as fluorine, form –1 ions; oxidation number = –1. • d. Other elements have predictable ways to form ions; but some, such as nitrogen, can have numerous oxidation numbers. • 4. The oxidation number for oxygen is –2 for most compounds involving covalent bonds. • 5. When hydrogen is involved in covalent bonds with nonmetals, its oxidation number is +1. • 6. In binary compounds (compounds with two elements), the element having greater electronegativity is assigned a negative oxidation number that is the same as its charge
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Batteries use oxidation-reduction reactions to produce electrical current. (Lester V. Bergman/ Corbis. Reproduced by permission.)
when it appears as an anion in ionic compounds. • 7. When a compound is electrically neutral, the sum of its elements’ oxidation states is zero. • 8. In an ionic chemical species, the sum of the oxidation states for its constituent elements must equal the overall charge. These rules will not be discussed here; rather, they are presented to show some of the complexities involved in analyzing an oxidationreduction reaction from a structural standpoint—that is, in terms of the atomic or molecular reactions. For the most part, we will be observing oxidation-reductions phenomenologically, or in terms of their outward effects. A good chemistry textbook should provide a more detailed review of these rules, along with a table showing oxidation numbers of elements and binary compounds. Oxidation-reduction reactions are easier to understand if they are studied as though they were two half-reactions. Half the reaction involves what happens to the substances and electrons in the oxidizing portion, while the other half-reaction indicates the activities of substances and electrons in the reduction portion. S C I E N C E O F E V E RY DAY T H I N G S
REAL-LIFE A P P L I C AT I O N S Combustion and Explosions As with any type of chemical reaction, combustion takes place when chemical bonds are broken and new bonds are formed. It so happens that combustion is a particularly dramatic type of oxidation-reduction reaction: whereas we cannot watch iron rust, combustion is a noticeable event. Even more dramatic is combustion that takes place at a rate so rapid that it results in an explosion. Coal is almost pure carbon, and its combustion in air is a textbook example of oxidationreduction. Although there is far more nitrogen than oxygen in air (which is a mixture rather than a compound), nitrogen is very unreactive at low temperatures. For this reason, it can be used to clean empty fuel tanks, a situation in which the presence of pure oxygen is extremely dangerous. In any case, when a substance burns, it is reacting with the oxygen in air. As one might expect from what has already been said about oxidation-reduction, the oxygen is reduced while the carbon is oxidized. In terms of oxidation numbers, the oxidation number of VOLUME 1: REAL-LIFE CHEMISTRY
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tary application, incidentally, was “Greek fire,” created by the Byzantines in the seventh century A.D. A mixture of petroleum, potassium nitrate, and possibly quicklime, Greek fire could burn on water, and was used in naval battles to destroy enemy ships.
OxidationReduction Reactions
For the most part, however, the range of activities to which combustion could be applied was fairly narrow until the development of the steam engine in the period from the late seventeenth century to the early nineteenth century. The steam engine applied the combustion of coal to the production of heat for boiling water, which in turn provided the power to run machinery. By the beginning of the twentieth century, combustion had found a new application in the internal combustion engine, used to power automobiles. EXPLOSIONS AND EXPLOS I V E S . An internal combustion engine does
Oxidation-reduction reactions fuel the space-shuttle at take-off. (Corbis. Reproduced by permission.)
carbon jumps from 0 to 4, while that of oxygen is reduced to –2. As they burn, these two form carbon dioxide or CO2, in which the two –2 charges of the oxygen atoms cancel out the +4 charge of the carbon atom to yield a compound that is electrically neutral. COMBUSTION IN HUMAN EXP E R I E N C E . Combustion has been a signifi-
cant part of human life ever since our prehistoric ancestors learned how to harness the power of fire to cook food and light their caves. We tend to think of premodern times—to use the memorable title of a book by American historian William Manchester, about the Middle Ages—as A World Lit Only By Fire. In fact, our modern age is even more combustion-driven than that of our forebears. For centuries, burning animal fat—in torches, lamps, and eventually in candles—provided light for humans. Wood fires supplied warmth, as well as a means to cook meals. These were the main uses of combustion, aside from the occasional use of fire in warfare or for other purposes (including that ghastly medieval form of execution, burning at the stake). One notable mili-
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not simply burn fuel; rather, by the combined action of the fuel injectors (in a modern vehicle), in concert with the pistons, cylinders, and spark plugs, it actually produces small explosions in the molecules of gasoline. These produce the output of power necessary to turn the crankshaft, and ultimately the wheels. An explosion, in simple terms, is a sped-up form of combustion. The first explosives were invented by the Chinese during the Middle Ages, and these included not only fireworks and explosive rockets, but gunpowder. Ironically, however, China rejected the use of gunpowder in warfare for many centuries, while Europeans took to it with enthusiasm. Needless to say, Europeans’ possession of firearms aided their conquest of the Americas, as well as much of Africa, Asia, and the Pacific, during the period from about 1500 to 1900. The late nineteenth and early twentieth centuries saw the development of new explosives, such as TNT or trinitrotoluene, a hydrocarbon. Then in the mid-twentieth century came the most fearsome explosive of all: the nuclear bomb. A nuclear explosion is not itself the result of an oxidation-reduction reaction, but of something much more complex—either the splitting of atoms (fission) or the forcing together of atomic nuclei (fusion). Nuclear bombs release far more energy than any ordinary explosive, but the resulting blast also causes plenty of ordinary combustion. When the United States dropped atomic bombs on the
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OxidationReduction Reactions
If not polished regularly, silver responds to oxidation by tarnishing—forming a surface of silver sulfide, or Ag2S. (Mimmo Jodice/Corbis. Reproduced by permission.)
Japanese cities of Hiroshima and Nagasaki in August 1945, those cities suffered not only the effects of the immediate blast, but also massive fires resulting from the explosion itself. FUELING
THE
S PAC E
SHUT-
T L E . Oxidation-reduction reactions also fuel
the most advanced form of transportation known today, the space shuttle. The actual orbiter vehicle is relatively small compared to its
solid rocket boosters on either side, along with an external fuel tank. Inside the solid rocket boosters are ammonium perchlorate (NH4ClO4) and powdered aluminum, which undergo an oxidation-reduction reaction that gives the shuttle enormous amounts of extra thrust. As for the larger single external fuel tank, this contains the gases that power the rocket: hydrogen and oxygen.
external power apparatus, which consists of two
Because these two are extremely explosive, they must be kept in separate compartments.
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When they react, they form water, of course, but in doing so, they also release vast quantities of energy. The chemical equation for this is: 2H2 + O2 42H2O + energy. On January 28, 1986, something went terribly wrong with this arrangement on the space shuttle Challenger. Cold weather had fatigued the O-rings that sealed the hydrogen and oxygen compartments, and the gases fed straight into the flames behind the shuttle itself. This produced a powerful and uncontrolled oxidation-reduction reaction, an explosion that took the lives of all seven astronauts aboard the shuttle.
The Environment and Human Health Combustion, though it can do much good, can also do much harm. This goes beyond the obvious: by burning fossil fuels or hydrocarbons, excess carbon (in the form of carbon dioxide and carbon monoxide) is released to the atmosphere, with a damaging effect on the environment. In fact, oxidation-reduction reactions are intimately connected with the functioning of the natural environment. For example, photosynthesis, the conversion of light to chemical energy by plants, is a form of oxidation-reduction reaction that produces two essentials of human life: oxygen and carbohydrates. Likewise cellular respiration, which along with photosynthesis is discussed in the Carbon essay, is an oxidationreduction reaction in which living things break down molecules of food to produce energy, carbon dioxide, and water. Enzymes in the human body regulate oxidation-reduction reactions. These complex proteins, of which several hundred are known, act as catalysts, speeding up chemical processes in the body. Oxidation-reduction reactions also take place in the metabolism of food for energy, with substances in the food broken down into components the body can use.
To forestall the effects of oxidation, some doctors and scientists recommend antioxidants—natural reducing agents such as vitamin C and vitamin E. The vitamin C in lemon juice can be used to prevent oxidizing on the cut surface of an apple, to keep it from turning brown. Perhaps, some experts maintain, natural reducing agents can also slow the pace of oxidation in the human body.
Forming a New Surface on Metal Clearly, oxidization can have a corrosive effect, and nowhere is this more obvious than in the corrosion of metals by exposure to oxidizing agents—primarily oxygen itself. Most metals react with O2, and might corrode so quickly that they become useless, were it not for the formation of a protective coating—an oxide. Iron forms an oxide, commonly known as rust, but this in fact does little to protect it from corrosion, because the oxide tends to flake off, exposing fresh surfaces to further oxidation. Every year, businesses and governments devote millions of dollars to protecting iron and steel from oxidation by means of painting and other measures, such as galvanizing with zinc. In fact, oxidation-reduction reactions virtually define the world of iron. Found naturally only in ores, the element is purified by heating the ore with coke (impure carbon) in the presence of oxygen, such that the coke reduces the iron.
Oxidation may also be linked with the effects of aging in humans, as well as with other condi-
C O I N AG E M E TA L S . Copper, as we have seen, responds to oxidation by corroding in a different way: not by rusting, but by changing color. A similar effect occurs in silver, which tarnishes, forming a surface of silver sulfide, or Ag2S. Copper and silver are two of the “coinage metals,” so named because they have often been used to mint coins. They have been used for this purpose not only because of their beauty, but also due to their relative resistance to corrosion. This resistance has, in fact, earned them the nickname “noble metals.”
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O X I D AT I O N : S P O I L I N G A N D AG I N G . At the same time, oxidation-reduc-
tion reactions are responsible for the spoiling of food, the culprit here being the oxidation portion of the reaction. To prevent spoilage, manufacturers of food items often add preservatives, which act as reducing agents.
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tions such as cancer, hardening of the arteries, and rheumatoid arthritis. It appears that oxygen molecules and other oxidizing agents, always hungry for electrons, extract these from the membranes in human cells. Over time, this can cause a gradual breakdown in the body’s immune system.
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OxidationReduction Reactions
KEY TERMS ANION:
An ion with a negative charge;
pronounced “AN-ie-un.”
ION:
An atom or group of atoms that
has acquired an electric charge due to the A compound
BINARY COMPOUND:
involving two elements.
loss or gain of electrons. OXIDATION:
A chemical reaction in
A process
which a substance loses electrons. It is
whereby the chemical properties of a sub-
always accompanied by reduction; hence
stance are changed by a rearrangement of
the term oxidation-reduction reaction.
the atoms in the substance.
OXIDATION
CHEMICAL REACTION:
NUMBER:
A number
A generic term
assigned to each atom in an oxidation-
used for any substance studied in chem-
reduction reaction as a means of keeping
istry—whether it be an element, com-
track of the electrons involved. Another
pound, mixture, atom, molecule, ion, and
term for oxidation number is “oxidation
so forth.
state.”
CHEMICAL SPECIES:
A type of
OXIDATION-REDUCTION REACTION:
chemical bonding in which two atoms
A chemical reaction involving the transfer
share valence electrons.
of electrons.
COVALENT BONDING:
ELECTROCHEMISTRY:
The study of
the relationship between chemical and electrical energy.
REDOX REACTION:
Another name
for an oxidation-reduction reaction. REDUCTION:
A chemical reaction in
The use of an elec-
which a substance gains electrons. It is
tric current to produce a chemical change.
always accompanied by oxidation; hence
ELECTROLYSIS:
ELECTRONEGATIVITY:
The relative
the term oxidation-reduction reaction.
ability of an atom to attract valence
VALENCE ELECTRONS:
electrons.
that occupy the highest energy levels in an
CATION:
An ion with a positive charge;
pronounced “KAT-ie-un.”
The third member of this mini-family is gold, which is virtually noncorrosive. Wonderful as gold is in this respect, however, no one is likely to use it as a roofing material, or for any such large-scale application involving its resistance to oxidation. Aside from the obvious expense, gold is soft, and not very good for structural uses, even if it were much cheaper. Yet there is such a “wonder metal”: one that experiences virtually no corrosion, is cheap, and strong enough in alloys to be used for structural purposes. Its name is aluminum.
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Electrons
atom. These are the only electrons involved in chemical bonding.
A LU M I N U M . There was a time, in fact,
when aluminum was even more expensive than gold. When the French emperor Napoleon III wanted to impress a dinner guest, he arranged for the person to be served with aluminum utensils, while less distinguished personages had to settle for “ordinary” gold and silver. In 1855, aluminum sold for $100,000 a pound, whereas in 1990, the going rate was about $0.74. Demand did not go down—in fact, it increased exponentially—but rather, supply increased, thanks to the development of an inex-
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pensive aluminum-reduction process. Two men, one American and one French, discovered this process at the same time: interestingly, their years of birth and death were the same. Aluminum was once a precious metal because it proved extremely difficult to separate from oxygen. The Hall-Heroult process overcame the problem by applying electrolysis—the use of an electric current to produce a chemical change—as a way of reducing Al3+ ions (which have a high affinity for oxygen) to neutral aluminum atoms. In the United States today, 4.5% of the total electricity output is used for the production of aluminum through electrolysis. The foregoing statistic is staggering, considering just how much electricity Americans use, and it indicates the importance of this once-precious metal. Actually, aluminum oxidizes just like any other metal—and does so quite quickly, as a matter of fact, by forming a coating of aluminum oxide (Al2O3). But unlike rust, the aluminum oxide is invisible, and acts as a protective coating. Chromium, nickel, and tin react to oxygen in a similar way, but these are not as inexpensive as aluminum.
Electrochemistry and Batteries Electrochemistry is the study of the relationship between chemical and electrical energy. Among its applications is the creation of batteries, which use oxidation-reduction reactions to produce an electric current. A basic battery can be pictured schematically as two beakers of solution connected by a wire. In one solution is the oxidizing agent; in the other, a reducing agent. The wire allows electrons to pass back and forth between the two solutions, but to ensure that the flow goes both ways, the two solutions are also connected by a “salt bridge.” The salt bridge contains a gel or solution that permits ions to pass back and forth, but a porous membrane prevents the solutions from actually mixing.
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oxide (PbO2) acts as the oxidizing agent. A highly efficient type of battery, able to withstand wide extremes in temperature, the lead storage battery has been in use since 1915. Along the way, features have been altered, but the basic principles have remained—a testament to the soundness of its original design. The batteries people use for powering all kinds of portable appliances, from flashlights to boom boxes, are called dry cell batteries. In contrast to the model described above, using solutions, a dry cell (as its name implies) involves no liquid components. Instead, it utilizes various elements in a range of combinations, including zinc, magnesium, mercury, silver, nickel, and cadmium. The last two are applied in the nickelcadmium battery, which is particularly useful because it can be recharged over and over again by an external current. The current turns the products of the chemical reactions in the battery back into reactants. WHERE TO LEARN MORE “Batteries.” Oregon State University Department of Chemistry (Web site). (June 4, 2001). “Batteries and Fuel Cells” (Web site). (June 4, 2001). Borton, Paula and Vicky Cave. The Usborne Book of Batteries and Magnets. Tulsa, OK: EDC Publishing, 1995. Craats, Rennay. The Science of Fire. Milwaukee, WI: Gareth Stevens Publishing, 2000. Knapp, Brian J. Oxidation and Reduction. Danbury, CT: Grolier Educational, 1998. “Oxidation Reduction Links” (Web site). (June 4, 2001). “Oxidation-Reduction Reactions.” General Chemistry (Web site). (June 4, 2001). “Oxidation-Reduction Reactions: Redox.” UNC-Chapel Hill Chemistry Fundamentals (Web site). (June 4, 2001). Yount, Lisa. Antoine Lavoisier: Founder of Modern Chemistry. Springfield, NJ: Enslow Publishers, 1997.
In the lead storage battery of an automobile, lead itself is the reducing agent, while lead (IV)
Zumdahl, Steven S. Introductory Chemistry: A Foundation, fourth edition. Boston: Houghton Mifflin, 2000.
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CHEMICAL EQUILIBRIUM Chemical Equilibrium
CONCEPT Reactions are the “verbs” of chemistry—the activity that chemists study. Many reactions move to their conclusion and then stop, meaning that the reactants have been completely transformed into products, with no means of returning to their original state. In some cases, the reaction truly is irreversible, as for instance when combustion changes both the physical and chemical properties of a substance. There are plenty of other circumstances, however, in which a reverse reaction is not only possible but an ongoing process, as the products of the first reaction become the reactants in a second one. This dynamic state, in which the concentrations of reactants and products remains constant, is referred to as equilibrium. It is possible to predict the behavior of substances in equilibrium through the use of certain laws, which are applied in industries seeking to lower the costs of producing specific chemicals. Equilibrium is also useful in understanding processes that preserve—or potentially threaten—human health.
HOW IT WORKS Chemical Reactions in Brief What follows is a highly condensed discussion of chemical reactions, and particularly the methods for writing equations to describe them. For a more detailed explanation of these principles, the reader is encouraged to consult the Chemical Reactions essay.
The changes produced by a chemical reaction are fundamentally different from physical changes, such as boiling or melting liquid water, changes that alter the physical properties of water without affecting its molecular structure. I N D I CAT I O N S T H AT A C H E M I CA L R E AC T I O N H AS O C C U R R E D .
Though chemical reactions are most effectively analyzed in terms of molecular properties and behaviors, there are numerous indicators that suggest to us when a chemical reaction has occurred. It is unlikely that all of these will result from any one reaction, and in fact chances are that a particular reaction will manifest only one or two of these effects. Nonetheless, these offer us hints that a reaction has taken place: Signs that a substance has undergone a chemical reaction: • • • • • • •
Water is produced A solid forms Gases are produced Bubbles are formed There is a change in color The temperature changes The taste of a consumable substance changes • The smell changes C H E M I CA L CHANGES CONTRASTED WITH PHYSICAL CHANGES OF TEMPERATURE. Many of these
A chemical reaction is a process whereby the chemical properties of a substance are altered by a rearrangement of the atoms in the substance.
effects can be produced simply by changing the temperature of a substance, but again, the mere act of applying heat from outside (or removing heat from the substance itself) does not constitute a chemical change. Water can be “produced” by melting ice, but the water was already there— it only changed form. By contrast, when an acid
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the early nineteenth and the early twentieth centuries, however, the entire character of chemistry changed, as did the terms in which chemists discussed reactions. Today, those reactions are analyzed primarily in terms of subatomic, atomic, and molecular properties and activities.
Chemical Equilibrium
Despite all this progress, however, chemists still do not know exactly what happens in a chemical reaction—but they do have a good approximation. This is the collision model, which explains chemical reactions in terms of collisions between molecules. If the collision is strong enough, it can break the chemical bonds in the reactants, resulting in a re-formation of atoms within different molecules. The more the molecules collide, the more bonds are being broken, and the faster the reaction.
MANY
MOUNTAIN CLIMBERS USE PRESSURIZED OXYGEN
AT VERY HIGH ALTITUDES TO MAINTAIN PROPER HEMOGLOBIN-OXYGEN EQUILIBRIUM. (Galen Rowell/Corbis. Repro-
duced by permission.)
and a base react to form water and a salt, that is a true chemical reaction. Similarly, the freezing of water forms a solid, but no new substance has been formed; in a chemical reaction, by contrast, two liquids can react to form a solid. When water boils through the application of heat, bubbles form, and a gas or vapor is produced; yet in chemical changes, these effects are not the direct result of applying heat. In this context, a change in temperature, noted as another sign that a reaction has taken place, is a change of temperature from within the substance itself. Chemical reactions can be classified as heat-producing (exothermic) or heatabsorbing (endothermic). In either case, the transfer of heat is not accomplished simply by creating a temperature differential, as would occur if heat were transferred merely through physical means.
Raising the temperature and the concentrations of reactants can increase the energy and hasten the reactions, but in some cases it is not possible to do either. Fortunately, the rate of reaction can be increased in a third way, through the introduction of a catalyst, a substance that speeds up the reaction without participating in it either as a reactant or product. Catalysts are thus not consumed in the reaction. Many chemistry textbooks discuss catalysts within the context of equilibrium; however, because catalysts play such an important role in human life, in this book they are the subject of a separate essay.
Chemical Equations Involving Equilibrium
At one time, chemists could only study reactions from “outside,” as it were—purely in terms of effects noticeable through the senses. Between
A chemical equation, like a mathematical equation, symbolizes an interaction between entities that produces a particular result. In the case of a chemical equation, the entities are not numbers but reactants, and they interact with each other not through addition or multiplication, but by
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Increase in the numbers of collisions can be produced in two ways: either the concentrations of the reactants are increased, or the temperature is increased. By raising the temperature, the speeds of the molecules themselves increase, and the collisions possess more energy. A certain energy threshold, the activation energy (symbolized Ea) must be crossed in order for a reaction to occur. A temperature increase raises the likelihood that a given collision will cross the activation-energy threshold, producing the energy to break the molecular bonds and promote the chemical reaction.
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chemical reaction. Yet just as a product is the result of multiplication in mathematics, a product in a chemical equation is the substance or substances that result from the reaction. Instead of an equals sign between the reactants and the product, an arrow is used. When the arrow points to the right, this indicates a forward reaction; conversely, an arrow pointing to the left symbolizes a reverse reaction. In a reverse reaction, the products of a forward reaction have become the reactants, and the reactants of the forward reaction are now the products. This is indicated by an arrow that points toward the left. Chemical equilibrium, which occurs when the ratio between the reactants and products is constant, and in which the forward and reverse reactions take place at the same rate, is symbolized thus: 1. Note that the arrows, the upper one pointing right and the lower one pointing left, are of the same length. There may be certain cases, discussed below, in which it is necessary to show these arrows as unequal in length as a means of indicating the dominance of either the forward or reverse reaction. Chemical equations usually include notation indicating the state or phase of matter for the reactants and products: (s) for a solid; (l) for a liquid; (g) for a gas. A fourth symbol, (aq), indicates a substance dissolved in water—that is, an aqueous solution. In the following paragraphs, we will apply a chemical equation to the demonstration of equilibrium, but will not discuss the balancing of equations. The reader is encouraged to consult the passage in the Chemical Reactions essay that addresses that process, vital to the recording of accurate data. A SIMPLE EQUILIBRIUM EQUATION. Let us now consider a simple equation,
involving the reaction between water and carbon monoxide (CO) at high temperatures in a closed container. The initial equation is written thus: H2O(g) + CO(g) 4H2(g) + CO2g). In plain English, water in the gas phase (steam) has reacted with carbon monoxide to produce hydrogen gas and carbon dioxide.
CO(g) ! H2(g) + CO2g). Assuming that the system is not disturbed (that is, that the container is kept closed and no outside substances are introduced), equilibrium will continue to be maintained, because the reverse reaction is occurring at the same rate as the forward one.
Chemical Equilibrium
Note what has been said here: reactions are still occurring, but the forward and rearward reactions balance one another. Thus equilibrium is not a static condition, but a dynamic one, and indeed, chemical equilibrium is sometimes referred to as “dynamic equilibrium.” On the other hand, some chemists refer to chemical equilibrium simply as equilibrium, but here the qualifier chemical has been used to distinguish this from the type of equilibrium studied in physics. Physical equilibrium, which involves factors such as center of gravity, does help us to understand chemical equilibrium, but it is a different phenomenon.
REAL-LIFE A P P L I C AT I O N S Homogeneous and Heterogeneous Equilibria It should be noted that the equation used above identifies a situation of homogeneous equilibrium, in which all the substances are in the same phase or state of matter—gas, in this case. It is also possible to achieve chemical equilibrium in a reaction involving substances in more than one phase of matter. An example of such heterogeneous equilibrium is the decomposition of calcium carbonate for the production of lime, a process that involves the application of heat. Here the equation would be written thus: CaCO3(s) ! CaO(s) + CO2(g). Both the calcium carbonate (CaCO3) and the lime (CaO) are solids, whereas the carbon dioxide produced in this reaction is a gas.
The Equilibrium Constant
As the reaction proceeds, the amount of reactants decreases, and the concentration of products increases. At some point, however, there will be a balance between the numbers of products and reactants—a state of chemical equilibrium represented by changing the right-pointing arrow to an equilibrium symbol: H2O(g) +
In 1863, Norwegian chemists Cato Maximilian Guldberg (1836-1902) and Peter Waage (18331900)—who happened to be brothers-in-law— formulated what they called the law of mass action. Today, this is called the law of chemical equilibrium, which states that the direction taken by a reaction is dependant not merely on the mass of the various components of the reaction,
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but also upon the concentration—that is, the mass present in a given volume. This can be expressed by the formula aA + bB 1 cC +dD, where the capital letters represent chemical species, and the italicized lowercase letters indicate their coefficients. The equation [C]c[D]d/[A]a[B]b yields what is called an equilibrium constant, symbolized K. The above formula expresses the equilibrium constant in terms of molarity, the amount of solute in a given volume of solution, but in the case of gaseous reactants and products, the equilibrium constant can also be expressed in terms of partial pressures. In the reaction of water and carbon monoxide to produce hydrogen molecules and carbon dioxide (H2O + CO ! H2 + CO2). In chemical reactions involving solids, however, the concentration of the solid—because it is considered to be invariant—does not appear in the equilibrium constant. In the reaction described earlier, in which calcium carbonate was in equilibrium with solid lime and gaseous carbon dioxide, K = pressure of CO2. We will not attempt here to explore the equilibrium constant in any depth, but it is important to recognize its usefulness. For a particular reaction at a specific temperature, the ratio of concentrations between reactants and products will always have the same value—the equilibrium constant, or K. Because it is not dependant on the amounts of reactants and products mixed together initially, K remains the same: the concentrations themselves may vary, but the ratios between the concentrations in a given situation do not.
Le Châtelier’s Principle Not all situations of equilibrium are alike: depending on certain factors, the position of equilibrium may favor one side of the equation or the other. If a company is producing chemicals for sale, for example, its production managers will attempt to influence reactions in such a way as to favor the forward reaction. In such a situation, it is said that the equilibrium position has been shifted to the right. In terms of physical equilibrium, mentioned above, this would be analogous to what would happen if you were holding your arms out on either side of your body, with a heavy lead weight in your left hand and a much smaller weight in the right hand.
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Your center of gravity, or equilibrium position, would shift to the left to account for the greater force exerted by the heavier weight. A value of K significantly above 1 causes a shift to the right, meaning that at equilibrium, there will be more products than reactants. This is a situation favorable to a chemical company’s managers, who desire to create more of the product from less of the reactants. However, nature abhors an imbalance, as expressed in Le Châtelier’s principle. Named after French chemist Henri Le Châtelier (1850-1936), this principle maintains that whenever a stress or change is imposed on a chemical system in equilibrium, the system will adjust the amounts of the various substances to reduce the impact of that stress. Suppose we add more of a particular substance to increase the rate of the forward reaction. In an equation for this reaction, the equilibrium symbol is altered, with a longer arrow pointing to the right to indicate that the forward reaction is favored. Again, the equilibrium position has shifted to the right—just as one makes physical adjustments to account for an imbalanced weight. The system responds by working to consume more of the reactant, thus adjusting to the stress that was placed on it by the addition of more of that substance. By the same token, if we were to remove a particular reactant or product, the system would shift in the direction of the detached component. Note that Le Châtelier’s principle is mathematically related to the equilibrium constant. Suppose we have a basic equilibrium equation of A + B 1 C, with A and B each having molarities of 1, and C a molarity of 4. This tells us that K is equal to the molarity of C divided by that of A multiplied by B = 4/(1 • 1). Suppose, now, that enough of C were added to bring its concentration up to 6. This would mean that the system was no longer at equilibrium, because C/(A • B) no longer equals 4. In order to return the ratio to 4, the numerator (C) must be decreased, while the denominator (A • B) is increased. The reaction thus shifts from right to left. CHANGES IN VOLUME AND T E M P E RAT U R E . If the volume of gases in
a closed container is decreased, the pressure increases. An equilibrium system will therefore shift in the direction that reduces the pressure; but if the volume is increased, thus reducing the pressure, the system will respond by shifting to
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increase pressure. Note, however, that not all increases in pressure lead to a shift in the equilibrium. If the pressure were increased by the addition of a noble gas, the gas itself—since these elements are noted for their lack of reactivity— would not be part of the reaction. Thus the species added would not be part of the equilibrium constant expression, and there would be no change in the equilibrium.
material in red blood cells responsible for transporting oxygen to the cells. Each hemoglobin molecule attaches to four oxygen atoms, and the equilibrium conditions of the hemoglobin-oxygen interaction can be expressed thus: Hb(aq) + 4O2(g) ! Hb(O2)4(aq), where “Hb” stands for hemoglobin. As long as there is sufficient oxygen in the air, a healthy equilibrium is maintained; but at high altitudes, considerable changes occur.
In any case, no change in volume alters the equilibrium constant K; but where changes in temperature are involved, K is indeed altered. In an exothermic, or heat-producing reaction, the heat is treated as a product. Thus, when nitrogen and hydrogen react, they produce not only ammonia, but a certain quantity of heat. If this system is at equilibrium, Le Châtelier’s principle shows that the addition of heat will induce a shift in equilibrium to the left—in the direction that consumes heat or energy.
At significant elevations above sea level, the air pressure is lowered, and thus it is more difficult to obtain the oxygen one needs. The result, in accordance with Le Châtelier’s principle, is a shift in equilibrium to the left, away from the oxygenated hemoglobin. Without adequate oxygen fed to the body’s cells and tissues, a person tends to feel light-headed.
The reverse is true in an endothermic, or heat-absorbing reaction. As in the process described earlier, the thermal decomposition of calcium carbonate produces lime and carbon dioxide. Because heat is used to cause this reaction, the amount of heat applied is treated as a reactant, and an increase in temperature will cause the equilibrium position to shift to the right.
Equilibrium and Health Discussions of chemical equilibrium tend to be rather abstract, as the foregoing sections on the equilibrium constant and Le Châtelier’s principle illustrate. (The reader is encouraged to consult additional sources on these topics, which involve a number of particulars that have been touched upon only briefly here.) Despite the challenges involved in addressing the subject of equilibrium, the results of chemical equilibrium can be seen in processes involving human health.
When someone not physically prepared for the change is exposed to high altitudes, it may be necessary to introduce pressurized oxygen from an oxygen tank. This shifts the equilibrium to the right. For people born and raised at high altitudes, however, the body’s chemistry performs the equilibrium shift—by producing more hemoglobin, which also shifts equilibrium to the right. HEMOGLOBIN AND CARBON M O N OX I D E . When someone is exposed to
carbon monoxide gas, a frightening variation on the normal hemoglobin-oxygen interaction occurs. Carbon monoxide “fools” hemoglobin into mistaking it for oxygen because it also bonds to hemoglobin in groups of four, and the equilibrium expression thus becomes: Hb(aq) + 4CO(g) ! Hb(CO)4(aq). Instead of hemoglobin, what has been produced is called carboxyhemoglobin, which is even redder than hemoglobin. Therefore, one sign of carbon monoxide poisoning is a flushed face.
Hemoglobin, a protein containing iron, is the
The bonds between carbon monoxide and hemoglobin are about 300 times as strong as those between hemoglobin and oxygen, and this means a shift in equilibrium toward the right side of the equation—the carboxyhemoglobin side. It also means that K for the hemoglobin-carbon monoxide reaction is much higher than for the hemoglobin-oxygen reaction. Due to the affinity of hemoglobin for carbon monoxide, the hemoglobin puts a priority on carbon monoxide bonds, and hemoglobin that has bonded with carbon monoxide is no longer available to carry oxygen.
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The cooling of food with refrigerators, along with means of food preservation that do not involve changes in temperature, maintains chemical equilibrium in the foods and thereby prevents or at least retards spoilage. Even more important is the maintenance of equilibrium in reactions between hemoglobin and oxygen in human blood. H E M O G LO B I N
AND
OX Y G E N .
Chemical Equilibrium
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Chemical Equilibrium
KEY TERMS ACTIVATION ENERGY:
The minimal
A process
energy required to convert reactants into
whereby the chemical properties of a sub-
products, symbolized Ea.
stance are changed by a rearrangement of
AQUEOUS SOLUTION:
A mixture of
water and a substance that is dissolved in it. CATALYST:
A substance that speeds up
a chemical reaction without participating in it, either as a reactant or product. Catalysts are thus not consumed in the reaction. CHEMICAL EQUATION:
the atoms in the substance. CHEMICAL SPECIES:
A represen-
chemical symbols on the left stand for the
A generic term
used for any substance studied in chemistry—whether it be an element, compound, mixture, atom, molecule, ion, and so forth. COEFFICIENT:
tation of a chemical reaction in which the
a number used to indi-
cate the presence of more than one unit— typically, more than one molecule—of a chemical species in a chemical equation. The theory that
reactants, and those on the right are the
COLLISION MODEL:
product or products.
chemical reactions are the result of colli-
CHEMICAL EQUILIBRIUM:
A situa-
tion in which the ratio between the reactants and products in a chemical reaction is
sions between molecules that are strong enough to break bonds in the reactants, resulting in a reformation of atoms. A term describing a
constant, and in which the forward reac-
ENDOTHERMIC:
tions and reverse reactions take place at the
chemical reaction in which heat is
same rate.
absorbed or consumed.
Carbon monoxide in small quantities can cause headaches and dizziness, but larger concentrations can be fatal. To reverse the effects of the carbon monoxide, pure oxygen must be introduced to the body. It will react with the carboxyhemoglobin to produce properly oxygenated hemoglobin, along with carbon monoxide: Hb(CO)4(aq) + 4O2(g) ! Hb(O2)4(aq) + 4CO(g). The gaseous carbon monoxide thus produced is dissipated when the person exhales.
Challoner, Jack. The Visual Dictionary of Chemistry. New York: DK Publishing, 1996.
“Chemical Equilibrium.” Davidson College Department of Chemistry (Web site). (June 9, 2001). “Chemical Equilibrium in the Gas Phase.” Virginia Tech Chemistry Department (Web site). (June 9, 2001). “Chemical Sciences: Mechanism of Catalysis.” University of Alberta Department of Chemistry (Web site). (June 9, 2001). Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: Houghton Mifflin, 1995. Hauser, Jill Frankel. Super Science Concoctions: 50 Mysterious Mixtures for Fabulous Fun. Charlotte, VT: Williamson Publishing, 1996. “Mark Rosen’s Chemical Equilibrium Links” (Web site). (June 9, 2001).
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WHERE TO LEARN MORE “Catalysts” (Web site). (June 9, 2001).
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CHEMICAL REACTION:
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Chemical Equilibrium
KEY TERMS EXOTHERMIC:
A term describing a
chemical reaction in which heat is
CONTINUED
the various substances in such a way as to reduce the impact of that stress.
produced. PRODUCT: FORWARD REACTION:
A chemical
reaction symbolized by a chemical equa-
stances that result from a chemical reaction.
tion in which the reactants and product are separated by an arrow that points to the right, toward the products.
The substance or sub-
REACTANT:
A substance that interacts
with another substance in a chemical reaction, resulting in a product.
HETEROGENEOUS EQUILIBRIUM:
A chemical
Chemical equilibrium in which the sub-
REVERSE REACTION:
stances involved are in different phases of
reaction symbolized by a chemical equa-
matter (solid, liquid, gas.)
tion in which the products of a forward reaction have become the reactants, and
HOMOGENEOUS
EQUILIBRIUM:
the reactants of the forward reaction are
Chemical equilibrium in which the sub-
now the products. This is indicated by an
stances involved are in the same phase of
arrow that points toward the left.
matter. SYSTEM:
In chemistry and other sci-
A
ences, the term “system” usually refers to
statement, formulated by French chemist
any set of interactions isolated from the
Henri Le Châtelier (1850-1936), which
rest of the universe. Anything outside of
holds that whenever a stress or change is
the system, including all factors and forces
imposed on a system in chemical equilibri-
irrelevant to a discussion of that system, is
um, the system will adjust the amounts of
known as the environment.
LE CHÂTELIER’S PRINCIPLE:
Oxlade, Chris. Chemistry. Illustrated by Chris Fairclough. Austin, TX: Raintree Steck-Vaughn, 1999.
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Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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C A T A LY S T S Catalysts
CONCEPT In most of the processes studied within the physical sciences, the lesson again and again is that nature provides no “free lunch”; in other words, it is not possible to get something for nothing. A chemical reaction, for instance, involves the creation of substances different from those that reacted in the first place, but the number of atoms involved does not change. In view of nature’s inherently conservative tendencies, then, the idea of a catalyst—a substance that speeds up a reaction without being consumed—seems almost like a magic trick. But catalysts are very real, and their presence in the human body helps to sustain life. Similarly, catalysts enable the synthesis of foods, and catalytic converters in automobiles protect the environment from dangerous exhaust fumes. Yet the presence of one particular catalyst in the upper atmosphere poses such a threat to Earth’s ozone layer that production of certain chemicals containing that substance has been banned.
HOW IT WORKS Reactions and Collisions In a chemical reaction, substances known as reactants interact with one another to create new substances, called products. In the present context, our concern is not with the reactants and products themselves, but with an additional entity, an agent that enables the reaction to move forward at faster rates and lower temperatures.
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that are sufficiently energetic break the chemical bonds that hold molecules together; as a result, the atoms in those molecules are free to recombine with other atoms to form new molecules. Hastening of a chemical reaction can be produced in one of three ways. If the concentrations of the reactants are increased, this means that more molecules are colliding, and potentially more bonds are being broken. Likewise if the temperature is increased, the speeds of the molecules themselves increase, and their collisions possess more energy. Energy is an important component in the chemical reaction because a certain threshold, called the activation energy (Ea), must be crossed before a reaction can occur. A temperature increase raises the energy of the collisions, increasing the likelihood that the activationenergy threshold will be crossed, resulting in the breaking of molecular bonds.
Catalysts and Catalysis It is not always feasible or desirable, however, to increase the concentration of reactants, or the temperature of the system in which the reaction is to occur. Many of the processes that take place in the human body, for instance, “should” require high temperatures—temperatures too high to sustain human life. But fortunately, our bodies contain proteins called enzymes, discussed later in this essay, that facilitate the necessary reactions without raising temperatures or increasing the concentrations of substances.
According to the collision model generally accepted by chemists, chemical reactions are the result of collisions between molecules. Collisions
An enzyme is an example of a catalyst, a substance that speeds up a reaction without participating in it either as a reactant or product. Catalysts are thus not consumed in the reaction. The
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Catalysts
CATALYTIC
CONVERTERS EMPLOY A CATALYST TO FACILITATE THE TRANSFORMATION OF POLLUTION-CAUSING EXHAUSTS
TO LESS HARMFUL SUBSTANCES. (Ian Harwood; Ecoscene/Corbis. Reproduced by permission.)
catalyst does its work—catalysis—by creating a different path for the reaction, and though the means whereby it does this are too complex to discuss in detail here, the process of catalyst can at least be presented in general terms. Imagine a graph whose x-axis is labeled “reaction progress,” while the y-axis bears the legend “energy.” There is some value of y equal to the normal activation energy, and in the course of experiencing the molecular collisions that lead to a reaction, the reactants reach this level. In a catalyzed reaction, however, the level of activation energy necessary for the reaction is represented by a lower y-value on the graph. The catalyzed substances do not need to have as much energy as they do without a catalyst, and there-
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fore the reaction can proceed more quickly— without changing the temperature or concentrations of reactants.
REAL-LIFE A P P L I C AT I O N S A Brief History of Catalysis Long before chemists recognized the existence of catalysts, ordinary people had been using the process of catalysis for a number of purposes: making soap, for instance, or fermenting wine to create vinegar, or leavening bread. Early in the nineteenth century, chemists began to take note of this phenomenon.
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kata (“down”) and lyein (“loosen.”) As Berzelius defined it, catalysis involved an activity quite different from that of an ordinary chemical reaction. Catalysis induced decomposition in substances, resulting in the formation of new compounds—but without the catalyst itself actually entering the compound.
Catalysts
Berzelius’s definition assumed that a catalyst manages to do what it does without changing at all. This was perfectly adequate for describing heterogeneous catalysis, in which the catalyst and the reactants are in different phases of matter. In the platinum-catalyzed reactions that Davy and Faraday observed, for instance, the platinum is a solid, while the reaction itself takes place in a gaseous or liquid state. However, homogeneous catalysis, in which catalyst and reactants are in the same state, required a different explanation, which English chemist Alexander William Williamson (1824-1904) provided in an 1852 study. FRITZ HABER. (Austrian Archives/Corbis. Reproduced by permission.)
In 1812, Russian chemist Gottlieb Kirchhof was studying the conversion of starches to sugar in the presence of strong acids when he noticed something interesting. When a suspension of starch in water was boiled, Kirchhof observed, no change occurred in the starch. However, when he added a few drops of concentrated acid before boiling the suspension (that is, particles of starch suspended in water), he obtained a very different result. This time, the starch broke down to form glucose, a simple sugar, while the acid—which clearly had facilitated the reaction—underwent no change. Around the same time, English chemist Sir Humphry Davy (1778-1829) noticed that in certain organic reactions, platinum acted to speed along the reaction without undergoing any change. Later on, Davy’s star pupil, the great British physicist and chemist Michael Faraday (1791-1867), demonstrated the ability of platinum to recombine hydrogen and oxygen that had been separated by the electrolysis of water. The catalytic properties of platinum later found application in catalytic converters, as we shall see.
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In discussing the reaction observed by Kirchhof, of liquid sulfuric acid with starch in an aqueous solution, Williamson was able to show that the catalyst does break down in the course of the reaction. As the reaction takes place, it forms an intermediate compound, but this too is broken down before the reaction ends. The catalyst thus emerges in the same form it had at the beginning of the reaction.
Enzymes: Helpful Catalysts in the Body In 1833, French physiologist Anselme Payen (1795-1871) isolated a material from malt that accelerated the conversion of starch to sugar, as for instance in the brewing of beer. Payen gave the name “diastase” to this substance, and in 1857, the renowned French chemist Louis Pasteur (1822-1895) suggested that lactic acid fermentation is caused by a living organism.
A N I M P R O V E D D E F I N I T I O N . In 1835, Swedish chemist Jons Berzelius (17791848) provided a name to the process Kirchhof and Davy had observed from very different perspectives: catalysis, derived from the Greek words
In fact, the catalysts studied by Pasteur are not themselves separate organisms, as German biochemist Eduard Buchner (1860-1917) showed in 1897. Buchner isolated the catalysts that bring about the fermentation of alcohol from living yeast cells—what Payen had called “diastase,” and Pasteur “ferments.” Buchner demonstrated that these are actually chemical substances, not organisms. By that time, German physiologist Willy Kahne had suggested the name “enzyme” for these catalysts in living systems.
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Enzymes are made up of amino acids, which in turn are constructed from organic compounds called proteins. About 20 amino acids make up the building blocks of the many thousands of known enzymes. The beauty of an enzyme is that it speeds up complex, life-sustaining reactions in the human body—reactions that would be too slow at ordinary body temperatures. Rather than force the body to undergo harmful increases in temperature, the enzyme facilitates the reaction by opening up a different reaction pathway that allows a lower activation energy. One example of an enzyme is cytochrome, which aids the respiratory system by catalyzing the combination of oxygen with hydrogen within the cells. Other enzymes facilitate the conversion of food to energy, and make possible a variety of other necessary biological functions. Because numerous interactions are required in their work of catalysis, enzymes are very large, and may have atomic mass figures as high as 1 million amu. However, it should be noted that reactions are catalyzed at very specific locations—called active sites—on an enzyme. The reactant molecule fits neatly into the active site on the enzyme, much like a key fitting in a lock; hence the name of this theory, the “lock-andmodel.”
Catalysis and the Environment The exhaust from an automobile contains many substances that are harmful to the environment. As a result of increased concerns regarding the potential damage to the atmosphere, the federal government in the 1970s mandated the adoption of catalytic converters, devices that employ a catalyst to transform pollutants in the exhaust to less harmful substances. Platinum and palladium are favored materials for catalytic converters, though some nonmetallic materials, such as ceramics, have been used as well. In any case, the function of a catalytic converter is to convert exhausts through oxidation-reduction reactions. Nitric oxide is reduced to molecular oxygen and nitrogen; at the same time, the hydrocarbons in petroleum, along with carbon monoxide, are oxidized to form carbon dioxide and water. Sometimes a reducing agent, such as ammonia, is used to make the reduction process more effective.
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A DA N G E R O U S CATA LY S T I N T H E AT M O S P H E R E . Around the same
Catalysts
time that automakers began rolling out models equipped with catalytic converters, scientists and the general public alike became increasingly concerned about another threat to the environment. In the upper atmosphere of Earth are traces of ozone, a triatomic (three-atom) molecular form of oxygen which protects the planet from the Sun’s ultraviolet rays. During the latter part of the twentieth century, it became apparent that a hole had developed in the ozone layer over Antarctica, and many chemists suspected a culprit in chlorofluorocarbons, or CFCs. CFCs had long been used in refrigerants and air conditioners, and as propellants in aerosol sprays. Because they were nontoxic and noncorrosive, they worked quite well for such purposes, but the fact that they are chemically unreactive had an extremely negative side-effect. Instead of reacting with other substances to form new compounds, they linger in Earth’s atmosphere, eventually drifting to high altitudes, where ultraviolet light decomposes them. The real trouble begins when atoms of chlorine, isolated from the CFC, encounter ozone. Chlorine acts as a catalyst to transform the ozone to elemental oxygen, which is not nearly as effective as ozone for shielding Earth from ultraviolet light. It does so by interacting also with monatomic, or single-atom oxygen, with which it produces ClO, or the hypochlorite ion. The end result of reactions between chlorine, monatomic oxygen, hypochlorite, and ozone is the production of chlorine, hypochlorite, and diatomic oxygen—in other words, no more ozone. It is estimated that a single chlorine atom can destroy up to 1 million ozone molecules per second. Due to concerns about the danger to the ozone layer, an international agreement called the Montreal Protocol, signed in 1996, banned the production of CFCs and the coolant Freon that contains them. But people still need coolants for their homes and cars, and this has led to the creation of substitutes—most notably hydrochlorofluorocarbons (HCFCs), organic compounds that do not catalyze ozone.
Other Examples of Catalysts Catalysts appear in a number of reactions, both natural and artificial. For instance, catalysts are used in the industrial production of ammonia,
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Catalysts
KEY TERMS The minimal energy required to convert reactants into products, symbolized Ea ACTIVATION ENERGY:
AQUEOUS SOLUTIONS: A mixture of water and a substance that is dissolved in it.
A substance that speeds up a chemical reaction without participating in it, either as a reactant or product. Catalysts are thus not consumed in the reaction. CATALYST:
CHEMICAL REACTION: A process whereby the chemical properties of a substance are changed by a rearrangement of the atoms in the substance. COLLISION MODEL: The theory that chemical reactions are the result of collisions between molecules strong enough to break bonds in the reactants, resulting in a reformation of atoms.
A reaction in which the catalyst and the reactants are in different phases of matter. HETEROGENEOUS CATALYSIS:
CATALYSIS: A reaction in which catalyst and reactants are in the same phase of matter.
HOMOGENEOUS
The substance or substances that result from a chemical reaction. PRODUCT:
A substance that interacts with another substance in a chemical reaction, resulting in a product. REACTANT:
SYSTEM: In chemistry and other sciences, the term “system” usually refers to any set of interactions isolated from the rest of the universe. Anything outside of the system, including all factors and forces irrelevant to a discussion of that system, is known as the environment.
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nitric acid (produced from ammonia), sulfuric acid, and other substances. The ammonia process, developed in 1908 by German chemist Fritz Haber (1868-1934), is particularly noteworthy. Using iron as a catalyst, Haber was able to combine nitrogen and hydrogen under pressure to form ammonia—one of the world’s most widely used chemicals. Eighteen ninety-seven was a good year for catalysts. In that year, it was accidentally discovered that mercury catalyzes the reaction by which indigo dye is produced; also in 1897, French chemist Paul Sabatier (1854-1941) found that nickel catalyzes the production of edible fats. Thanks to Sabatier’s discovery, nickel is used to transform inedible plant oils to margarine and shortening. Another good year for catalysts—particularly those involved in the production of polymers—was 1953. That was the year when German chemist Karl Ziegler (1898-1973) discovered a resin catalyst for the production of polyethylene, which produced a newer, tougher product with a much higher melting point than polyethylene as it was produced up to that time. Also in 1953, Italian chemist Giulio Natta (19031979) adapted Ziegler’s idea, and developed a new type of plastic he called “isotactic” polymers. These could be produced easily, and in abundance, through the use of catalysts. One of the lessons of chemistry, or indeed of any science, is that there are few things chemists can do that nature cannot achieve on a far more wondrous scale. No artificial catalyst can compete with enzymes, and no use of a catalyst in a laboratory can compare with the grandeur of that which takes place on the Sun. As GermanAmerican physicist Hans Bethe (1906-) showed in 1938, the reactions of hydrogen that form helium on the surface of the Sun are catalyzed by carbon—the same element, incidentally, found in all living things on Earth.
WHERE TO LEARN MORE “Bugs in the News: What the Heck Is an Enzyme?” University of Kansas (Web site). (June 9, 2001). “Catalysis.” University of Idaho Department of Chemistry (Web site). (June 9, 2001).
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“Catalysts” (Web site). (June 9, 2001).
Oxlade, Chris. Chemistry. Illustrated by Chris Fairclough. Austin, TX: Raintree Steck-Vaughn, 1999.
Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: Houghton Mifflin, 1995.
“Ozone Depletion” (Web site). (June 9, 2001).
“Enzymes.” Strategis (Web site). (June 9, 2001). “Enzymes: Classification, Structure, Mechanism.” The Hebrew University (Web site). (June 9, 2001).
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Catalysts
“University Chemistry: Chemical Kinetics: Catalysis.” University of Alberta Department of Chemistry (Web site). (June 9, 2001). Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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ACIDS AND BASES Acids and Bases
CONCEPT The name “acid” calls to mind vivid sensory images—of tartness, for instance, if the acid in question is meant for human consumption, as with the citric acid in lemons. On the other hand, the thought of laboratory- and industrialstrength substances with scary-sounding names, such as sulfuric acid or hydrofluoric acid, carries with it other ideas—of acids that are capable of destroying materials, including human flesh. The name “base,” by contrast, is not widely known in its chemical sense, and even when the older term of “alkali” is used, the sense-impressions produced by the word tend not to be as vivid as those generated by the thought of “acid.” In their industrial applications, bases too can be highly powerful. As with acids, they have many household uses, in substances such as baking soda or oven cleaners. From a taste standpoint, (as anyone who has ever brushed his or her teeth with baking soda knows), bases are bitter rather than sour. How do we know when something is an acid or a base? Acid-base indicators, such as litmus paper and other materials for testing pH, offer a means of judging these qualities in various substances. However, there are larger structural definitions of the two concepts, which evolved in three stages during the late nineteenth and early twentieth centuries, that provide a more solid theoretical underpinning to the understanding of acids and bases.
The phenomenological distinctions between acids and bases, gathered by scientists from ancient times onward, worked well enough for many centuries. The word “acid” comes from the Latin term acidus, or “sour,” and from an early period, scientists understood that substances such as vinegar and lemon juice shared a common acidic quality. Eventually, the phenomenological definition of acids became relatively sophisticated, encompassing such details as the fact that acids produce characteristic colors in certain vegetable dyes, such as those used in making litmus paper. In addition, chemists realized that acids dissolve some metals, releasing hydrogen in the process. W H Y “ B AS E ” A N D N O T “A L KA L I ” ? The word “alkali” comes from the Arabic
Prior to the development of atomic and molecular theory in the nineteenth century, followed by
al-qili, which refers to the ashes of the seawort plant. The latter, which typically grows in marshy areas, was often burned to produce soda ash, used in making soap. In contrast to acids, bases— caffeine, for example—have a bitter taste, and many of them feel slippery to the touch. They also produce characteristic colors in the vegetable dyes of litmus paper, and can be used to promote certain chemical reactions. Note that today chemists use the word “base” instead of “alkali,”
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the discovery of subatomic structures in the late nineteenth and early twentieth centuries, chemists could not do much more than make measurements and observations. Their definitions of substances were purely phenomenological—that is, the result of experimentation and the collection of data. From these observations, they could form general rules, but they lacked any means of “seeing” into the atomic and molecular structures of the chemical world.
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the reason being that the latter term has a narrower meaning: all alkalies are bases, but not all bases are alkalies.
Acids and Bases
Originally, “alkali” referred only to the ashes of burned plants, such as seawort, that contained either sodium or potassium, and from which the oxides of sodium and potassium could be obtained. Eventually, alkali came to mean the soluble hydroxides of the alkali and alkaline earth metals. This includes sodium hydroxide, the active ingredient in drain and oven cleaners; magnesium hydroxide, used for instance in milk of magnesia; potassium hydroxide, found in soaps and other substances; and other compounds. Broad as this range of substances is, it fails to encompass the wide array of materials known today as bases—compounds which react with acids to form salts and water.
Toward a Structural Definition SVANTE ARRHENIUS. (Hulton-Deutsch Collection/Corbis. Repro-
The reaction to form salts and water is, in fact, one of the ways that acids and bases can be defined. In an aqueous solution, hydrochloric acid and sodium hydroxide react to form sodium chloride—which, though it is suspended in an aqueous solution, is still common table salt— along with water. The equation for this reaction is HCl(aq) + NaOH(aq) 4H2O + NaCl(aq). In other words, the sodium (Na) ion in sodium hydroxide switches places with the hydrogen ion in hydrochloric acid, resulting in the creation of NaCl (salt) along with water. But why does this happen? Useful as this definition regarding the formation of salts and water is, it is still not structural—in other words, it does not delve into the molecular structure and behavior of acids and bases. Credit for the first truly structural definition of the difference goes to the Swedish chemist Svante Arrhenius (18591927). It was Arrhenius who, in his doctoral dissertation in 1884, introduced the concept of an ion, an atom possessing an electric charge. His understanding was particularly impressive in light of the fact that it was 13 more years before the discovery of the electron, the subatomic particle responsible for the creation of ions. Atoms have a neutral charge, but when an electron or electrons depart, the atom becomes a positive ion or cation. Similarly, when an electron or electrons join a previously uncharged
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duced by permission.)
atom, the result is a negative ion or anion. Not only did the concept of ions greatly influence the future of chemistry, but it also provided Arrhenius with the key necessary to formulate his distinction between acids and bases.
The Arrhenius Definition Arrhenius observed that molecules of certain compounds break into charged particles when placed in liquid. This led him to the Arrhenius acid-base theory, which defines an acid as any compound that produces hydrogen ions (H+) when dissolved in water, and a base as any compound that produces hydroxide ions (OH-) when dissolved in water. This was a good start, but two aspects of Arrhenius’s theory suggested the need for a definition that encompassed more substances. First of all, his theory was limited to reactions in aqueous solutions. Though many acid-base reactions do occur when water is the solvent, this is not always the case. Second, the Arrhenius definition effectively limited acids and bases only to those ionic compounds, such as hydrochloric acid or sodium hydroxide, which produced either hydrogen or
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Acids and Bases
THE
TARTNESS OF LEMONS AND LIMES IS A FUNCTION OF THEIR ACIDITY—SPECIFICALLY THE WAY IN WHICH CITRIC
ACID MOLECULES FIT INTO THE TONGUE’S
“SWEET”
RECEPTORS. (Orion Press/Corbis. Reproduced by permission.)
hydroxide ions. However, ammonia, or NH3, acts like a base in aqueous solutions, even though it does not produce the hydroxide ion. The same is true of other substances, which behave like acids or bases without conforming to the Arrhenius definition. These shortcomings pointed to the need for a more comprehensive theory, which arrived with the formulation of the Brønsted-Lowry definition by English chemist Thomas Lowry (1874-1936) and Danish chemist J. N. Brønsted (1879-1947). Nonetheless, Arrhenius’s theory represented an important first step, and in 1903, he was awarded the Nobel Prize in Chemistry for his work on the dissociation of molecules into ions.
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The Brønsted-Lowry Definition The Brønsted-Lowry acid-base theory defines an acid as a proton (H+) donor, and a base as a proton acceptor, in a chemical reaction. Protons are represented by the symbol H+, and in representing acids and bases, the symbols HA and A-, respectively, are used. These symbols indicate that an acid has a proton it is ready to give away, while a base, with its negative charge, is ready to receive the positively charged proton. Though it is used here to represent a proton, it should be pointed out that H+ is also the hydrogen ion—a hydrogen atom that has lost its sole electron and thus acquired a positive charge.
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It is thus really nothing more than a lone proton, but this is the one and only case in which an atom and a proton are exactly the same thing. In an acid-base reaction, a molecule of acid is “donating” a proton, in the form of a hydrogen ion. This should not be confused with a far more complex process, nuclear fusion, in which an atom gives up a proton to another atom. A N AC I D - B AS E R E AC T I O N I N B R Ø N S T E D - LO W RY T H E O RY. The
most fundamental type of acid-base reaction in Brønsted-Lowry theory can be symbolized thus HA(aq) + H2O(l) 4H3O+(aq) + A-(aq). The first acid shown—which, like three of the four “players” in this equation, is dissolved in an aqueous solution—combines with water, which can serve as either an acid or a base. In the present context, it functions as a base. Water molecules are polar, meaning that the negative charges tend to congregate on one end of the molecule with the oxygen atom, while the positive charges remain on the other end with the hydrogen atoms. The Brønsted-Lowry model emphasizes the role played by water, which pulls the proton from the acid, resulting in the creation of H3O+, known as the hydronium ion. The hydronium ion produced here is an example of a conjugate acid, an acid formed when a base accepts a proton. At the same time, the acid has lost its proton, becoming A–, a conjugate base—that is, the base formed when an acid releases a proton. These two products of the reaction are called a conjugate acid-base pair, a term that refers to two substances related to one another by the donating of a proton. Brønsted and Lowry’s definition represents an improvement over that of Arrhenius, because it includes all Arrhenius acids and bases, as well as other chemical species not encompassed in Arrhenius theory. An example, mentioned earlier, is ammonia. Though it does not produce OH– ions, ammonia does accept a proton from a water molecule, and the reaction between these two (with water this time serving the function of acid) produces the conjugate acid-base pair of NH4+ (an ammonium ion) and OH-. Note that the latter, the hydroxide ion, was not produced by ammonia, but is the conjugate base that resulted when the water molecule lost its H+ atom or proton.
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The Lewis Definition Despite the progress offered to chemists by the Brønsted-Lowry model, it was still limited to describing compounds that contain hydrogen. As American chemist Gilbert N. Lewis (1875-1946) recognized, this did not encompass the full range of acids and bases; what was needed, instead, was a definition that did not involve the presence of a hydrogen atom.
Acids and Bases
Lewis is particularly noted for his work in the realm of chemical bonding. The bonding of atoms is the result of activity on the part of the valence electrons, or the electrons at the “outside” of the atom. Electrons are arranged in different ways, depending on the type of bonding, but they always bond in pairs. According to the Lewis acid-base theory, an acid is the reactant that accepts an electron pair from another reactant in a chemical reaction, while a base is the reactant that donates an electron pair to another reactant. As with the Brønsted-Lowry definition, the Lewis definition is reaction-dependant, and does not define a compound as an acid or base in its own right. Instead, the manner in which the compound reacts with another serves to identify it as an acid or base. AN IMPROVEMENT OVER ITS P R E D E C E S S O R S . The beauty of the
Lewis definition lies in the fact that it encompasses all the situations covered by the others— and more. Just as Brønsted-Lowry did not disprove Arrhenius, but rather offered a definition that covered more substances, Lewis expanded the range of substances beyond those covered by Brønsted-Lowry. In particular, Lewis theory can be used to differentiate the acid and base in bond-producing chemical reactions where ions are not produced, and in which there is no proton donor or acceptor. Thus it represents an improvement over Arrhenius and BrønstedLowry respectively. An example is the reaction of boron trifluoride (BF3) with ammonia (NH3), both in the gas phases, to produce boron trifluoride ammonia complex (F3BNH3). In this reaction, boron trifluoride accepts an electron pair and is therefore a Lewis acid, while ammonia donates the electron pair and is thus a Lewis base. Though hydrogen is involved in this particular reaction, Lewis theory also addresses reactions involving no hydrogen.
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REAL-LIFE A P P L I C AT I O N S pH and Acid-Base Indicators Though chemists apply the sophisticated structural definitions for acids and bases that we have discussed, there are also more “hands-on” methods for identifying a particular substance (including complex mixtures) as an acid or base. Many of these make use of the pH scale, developed by Danish chemist Søren Sørensen (18681939) in 1909.
At the alkaline end of the scale is borax, with a pH of 9, while household ammonia has a pH value of 11, or 10-11 mol/l. Sodium hydroxide, or lye, an extremely alkaline chemical with a pH of 14, has a value equal to 10-14 moles of hydronium per liter of solution.
The term pH stands for “potential of hydrogen,” and the pH scale is a means of determining the acidity or alkalinity of a substance. (Though, as noted, the term “alkali” has been replaced by “base,” alkalinity is still used as an adjectival term to indicate the degree to which a substance displays the properties of a base.) There are theoretically no limits to the range of the pH scale, but figures for acidity and alkalinity are usually given with numerical values between 0 and 14.
urements are made with electronic pH meters, which can provide figures accurate to 0.001 pH. However, simpler materials are also used. Best known among these is litmus paper (made from an extract of two lichen species), which turns blue in the presence of bases and red in the presence of acids. The term “litmus test” has become part of everyday language, referring to a makeor-break issue—for example, “views on abortion rights became a litmus test for Supreme Court nominees.”
T H E M E A N I N G O F p H VA LU E S .
L I T M U S PA P E R A N D O T H E R I N D I CAT O R S . The most precise pH meas-
A rating of 0 on the pH scale indicates a substance that is virtually pure acid, while a 14 rating represents a nearly pure base. A rating of 7 indicates a neutral substance. The pH scale is logarithmic, or exponential, meaning that the numbers represent exponents, and thus an increased value of 1 represents not a simple arithmetic addition of 1, but an increase of 1 power. This, however, needs a little further explanation.
Litmus is just one of many materials used for making pH paper, but in each case, the change of color is the result of the neutralization of the substance on the paper. For instance, paper coated with phenolphthalein changes from colorless to pink in a pH range from 8.2 to 10, so it is useful for testing materials believed to be moderately alkaline. Extracts from various fruits and vegetables, including red cabbages, red onions, and others, are also applied as indicators.
The pH scale is actually based on negative logarithms for the values of H3O+ (the hydronium ion) or H+ (protons) in a given substance. The formula is thus pH = -log[H3O+] or -log[H+], and the presence of hydronium ions or protons is measured according to their concentration of moles per liter of solution.
Some Common Acids and Bases
p H VA LU E S O F VA R I O U S S U B S TA N C E S . The pH of a virtually pure acid,
such as the sulfuric acid in car batteries, is 0, and this represents 1 mole (mol) of hydronium per liter (l) of solution. Lemon juice has a pH of 2, equal to 10-2 mol/l. Note that the pH value of 2 translates to an exponent of -2, which, in this case, results in a figure of 0.01 mol/l. Distilled water, a neutral substance with a pH of 7, has a hydronium equivalent of 10-7 mol/l. It is interesting to observe that most of the
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fluids in the human body have pH values in the neutral range blood (venous, 7.35; arterial, 7.45); urine (6.0—note the higher presence of acid); and saliva (6.0 to 7.4).
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The tables below list a few well-known acids and bases, along with their formulas and a few applications Common Acids • Acetic acid (CH3COOH): vinegar, acetate • Acetylsalicylic acid (HOOCC6H4OOCCH3): aspirin • Ascorbic acid (H2C6H6O6): vitamin C • Carbonic acid (H2CO3): soft drinks, seltzer water • Citric acid (C6H8O7): citrus fruits, artificial flavorings • Hydrochloric acid (HCl): stomach acid • Nitric acid (HNO3): fertilizer, explosives • Sulfuric acid (H2SO4): car batteries
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Common Bases • Aluminum hydroxide (Al[OH]3): antacids, deodorants • Ammonium hydroxide (NH4OH): glass cleaner • Calcium hydroxide (Ca[OH]2): caustic lime, mortar, plaster • Magnesium hydroxide (Mg[OH]2): laxatives, antacids • Sodium bicarbonate/sodium hydrogen carbonate (NaHCO3): baking soda • Sodium carbonate (Na2CO3): dish detergent • Sodium hydroxide (NaOH): lye, oven and drain cleaner • Sodium hypochlorite (NaClO): bleach Of course these represent only a few of the many acids and bases that exist. Selected substances listed above are discussed briefly below.
Acids AC I D S I N T H E H U M A N B O DY A N D F O O D S . As its name suggests, citric
acid is found in citrus fruits—particularly lemons, limes, and grapefruits. It is also used as a flavoring agent, preservative, and cleaning agent. Produced commercially from the fermentation of sugar by several species of mold, citric acid creates a taste that is both tart and sweet. The tartness, of course, is a function of its acidity, or a manifestation of the fact that it produces hydrogen ions. The sweetness is a more complex biochemical issue relating to the ways that citric acid molecules fit into the tongue’s “sweet” receptors. Citric acid plays a role in one famous stomach remedy, or antacid. This in itself is interesting, since antacids are more generally associated with alkaline substances, used for their ability to neutralize stomach acid. The fizz in Alka-Seltzer, however, comes from the reaction of citric acids (which also provide a more pleasant taste) with sodium bicarbonate or baking soda, a base. This reaction produces carbon dioxide gas. As a preservative, citric acid prevents metal ions from reacting with, and thus hastening the degradation of, fats in foods. It is also used in the production of hair rinses and low-pH shampoos and toothpastes.
acids combine to make up proteins, one of the principal components in human muscles, skin, and hair. Carboxylic acids are also applied industrially, particularly in the use of fatty acids for making soaps, detergents, and shampoos.
Acids and Bases
S U L F U R I C AC I D . There are plenty of acids found in the human body, including hydrochloric acid or stomach acid—which, in large quantities, causes indigestion, and the need for neutralization with a base. Nature also produces acids that are toxic to humans, such as sulfuric acid.
Though direct exposure to sulfuric acid is extremely dangerous, the substance has numerous applications. Not only is it used in car batteries, but sulfuric acid is also a significant component in the production of fertilizers. On the other hand, sulfuric acid is damaging to the environment when it appears in the form of acid rain. Among the impurities in coal is sulfur, and this results in the production of sulfur dioxide and sulfur trioxide when the coal is burned. Sulfur trioxide reacts with water in the air, creating sulfuric acid and thus acid rain, which can endanger plant and animal life, as well as corrode metals and building materials.
Bases The alkali metal and alkaline earth metal families of elements are, as their name suggests, bases. A number of substances created by the reaction of these metals with nonmetallic elements are taken internally for the purpose of settling gastric trouble or clearing intestinal blockage. For instance, there is magnesium sulfate, better known as Epsom salts, which provide a powerful laxative also used for ridding the body of poisons. Aluminum hydroxide is an interesting base, because it has a wide number of applications, including its use in antacids. As such, it reacts with and neutralizes stomach acid, and for that reason is found in commercial antacids such as Di-Gel™, Gelusil™, and Maalox™. Aluminum hydroxide is also used in water purification, in dyeing garments, and in the production of certain kinds of glass. A close relative, aluminum hydroxychloride or Al2(OH)5Cl, appears in many commercial antiperspirants, and helps to close pores, thus stopping the flow of perspiration.
The carboxylic acid family of hydrocarbon derivatives includes a wide array of substances— not only citric acids, but amino acids. Amino
Baking soda, known by chemists both as sodium bicar-
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Acids and Bases
KEY TERMS A substance that, in its edible
aqueous solution: an acid produces hydro-
form, is sour to the taste, and in non-edible
gen ions (H+), and a base hydroxide ions
forms, is often capable of dissolving met-
(OH–).
ACID:
als. Acids and bases react to form salts and water. These are all phenomenological definitions, however, in contrast to the three structural definitions of acids and bases— the Arrhenius, Br Ønsted-Lowry, and Lewis acid-base theories.
A substance that, in its edible
BASE:
form, is bitter to the taste. Bases tend to be slippery to the touch, and in reaction with acids they produce salts and water. Bases and acids are most properly defined, however, not in these phenomenological terms,
A term referring to the soluble
but by the three structural definitions of
hydroxides of the alkali and alkaline earth
acids and bases—the Arrhenius, Br Ønsted-
metals. Once “alkali” was used for the class
Lowry, and Lewis acid-base theories.
ALKALI:
of substances that react with acids to form salts; today, however, the more general
BRØNSTED-LOWRY ACID-BASE THE-
term base is preferred.
ORY:
ALKALINITY:
definitions of acids and bases. Formulated
An adjectival term used
to identify the degree to which a substance displays the properties of a base. ANION:
The second of three structural
The negatively charged ion
that results when an atom gains one or
by English chemist Thomas Lowry (18741936) and Danish chemist J. N. Br Ønsted (1879-1947),
defines an acid as a proton
AQUEOUS SOLUTION:
(H+)
theory
donor, and
a base as a proton acceptor.
more electrons. “Anion” is pronounced CATION:
“AN-ie-un”.
Br Ønsted-Lowry
The positively charged ion
that results when an atom loses one or A substance
in which water constitutes the solvent. A
more electrons. “Cation” is pronounced “KAT-ie-un”.
large number of chemical reactions take place in an aqueous solution.
CHEMICAL SPECIES:
A generic term
used for any substance studied in chemARRHENIUS ACID-BASE THEORY:
The first of three structural definitions of acids and bases. Formulated by Swedish chemist Svante Arrhenius (1859-1927), the
316
istry—whether it be an element, compound, mixture, atom, molecule, ion, and so forth. An acid formed
Arrhenius theory defines acids and bases
CONJUGATE ACID:
according to the ions they produce in an
when a base accepts a proton (H+).
bonate and sodium hydrogen carbonate, is another example of a base with multiple purposes. As noted earlier, it is used in Alka-Seltzer™, with the addition of citric acid to improve the flavor; in fact, baking soda alone can perform the
function of an antacid, but the taste is rather unpleasant. Baking soda is also used in fighting fires, because at high temperatures it turns into carbon dioxide, which smothers flames by obstructing
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Acids and Bases
KEY TERMS CONJUGATE
ACID-BASE
PAIR:
CONTINUED
A logarithmic scale for
PH SCALE:
The acid and base produced when an acid
determining the acidity or alkalinity of a
donates a single proton to a base. In the
substance, from 0 (virtually pure acid) to 7
reaction that produces this pair, the acid
(neutral) to 14 (virtually pure base).
and base switch identities. By donating a
PHENOMENOLOGICAL:
A
term
proton, the acid becomes a conjugate base,
describing scientific definitions based
and by receiving the proton, the base
purely on experimental phenomena. These
becomes a conjugate acid.
convey only part of the picture, however—
CONJUGATE BASE:
A base formed
primarily, the part a chemist can perceive either through measurement or through
when an acid releases a proton.
the senses, such as sight. A structural defiION:
An atom or atoms that has lost or
gained one or more electrons, and thus has a net electric charge. There are two types of ions: anions and cations. IONIC BONDING:
nition is therefore usually preferable to a phenomenological one. A substance that interacts
REACTANT:
with another substance in a chemical reac-
A form of chemical
tion, resulting in the creation of a product. Ionic compounds formed by
bonding that results from attractions
SALTS:
between ions with opposite electric
the reaction between an acid and a base. In
charges.
this reaction, one or more of the hydrogen ions of an acid is replaced with another
IONIC COMPOUND:
A compound in
which ions are present. Ionic compounds
positive ion. In addition to producing salts, acid-base reactions produce water.
contain at least one metal and nonmetal
A homogeneous mixture
SOLUTION:
joined by an ionic bond.
in which one or more substances (the The
solute) is dissolved in one or more other
third of three structural definitions of
substances (the solvent)—for example,
acids and bases. Formulated by American
sugar dissolved in water.
chemist Gilbert N. Lewis (1875-1946),
SOLVENT:
Lewis theory defines an acid as the reactant
another, called a solute, in a solution.
that accepts an electron pair from another
STRUCTURAL:
reactant in a chemical reaction, and a base
entific definitions based on aspects of
as the reactant that donates an electron
molecular structure and behavior rather
pair to another reactant.
than purely phenomenological data.
LEWIS ACID-BASE THEORY:
A substance that dissolves A term describing sci-
the flow of oxygen to the fire. Of course, baking soda is also used in baking, when it is combined with a weak acid to make baking powder. The reaction of the acid and the baking soda produces carbon dioxide, which causes dough and
batters to rise. In a refrigerator or cabinet, baking soda can absorb unpleasant odors, and additionally, it can be applied as a cleaning product.
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HYDROXIDE
( LY E ) .
Another base used for cleaning is sodium
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hydroxide, known commonly as lye or caustic soda. Unlike baking soda, however, it is not to be taken internally, because it is highly damaging to human tissue—particularly the eyes. Lye appears in drain cleaners, such as Drano™, and oven cleaners, such as Easy-Off™, which make use of its ability to convert fats to water-soluble soap. In the process of doing so, however, relatively large amounts of lye may generate enough heat to boil the water in a drain, causing the water to shoot upward. For this reason, it is not advisable to stand near a drain being treated with lye. In a closed oven, this is not a danger, of course; and after the cleaning process is complete, the converted fats (now in the form of soap) can be dissolved and wiped off with a sponge. WHERE TO LEARN MORE
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“Acids, Bases, and Salts.” Chemistry Coach (Web site). (June 7, 2001). “Acids, Bases, and Salts.” University of Akron, Department of Chemistry (Web site). (June 7, 2001). ChemLab. Danbury, CT: Grolier Educational, 1998. Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: Houghton Mifflin, 1995. Haines, Gail Kay. What Makes a Lemon Sour? Illustrated by Janet McCaffery. New York: Morrow, 1977. Oxlade, Chris. Acids and Bases. Chicago: Heinemann Library, 2001. Patten, J. M. Acids and Bases. Vero Beach, FL: Rourke Book Company, 1995. Walters, Derek. Chemistry. Illustrated by Denis Bishop and Jim Robins. New York: F. Watts, 1982.
“Acids and Bases Frequently Asked Questions.” General Chemistry Online (Web site). (June 7, 2001).
Zumdahl, Steven S. Introductory Chemistry A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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ACID-BASE REACTIONS
CONCEPT To an extent, acids and bases can be defined in terms of factors that are apparent to the senses: edible acids taste sour, for instance, while bases are bitter-tasting and slippery to the touch. The best way to understand these two types of substances, however, is in terms of their behavior in chemical reactions. Not only do the reactions of acids and bases result in the creation of salts and water, but acids and bases can be defined by the ways in which they participate in a reaction—for instance, by donating or accepting electron pairs. The reaction of acids and bases to form water and salts is called neutralization, and it has a wide range of applications, including the promotion of plant growth in soil and the treatment of heartburn in the human stomach. Neutralization also makes it possible to test substances for their pH level, a measure of the degree to which the substance is acidic or alkaline.
HOW IT WORKS
Acids are fairly easy to understand on the phenomenological level: the name comes from the Latin term acidus, or “sour,” and many sour substances from daily life—lemons, for instance, or vinegar—are indeed highly acidic. In fact, lemons and most citrus fruits contain citric acid (C6H8O7), while the acidic quality of vinegar comes from acetic acid (CH3COOH). In addition, acids produce characteristic colors in certain vegetable dyes, such as those used in making litmus paper. The word “base,” as it is used in this context, may be a bit more difficult to appreciate on a sensory level. It helps, perhaps, if the older term “alkali” is used, though even so, people tend to think of alkaline substances primarily in contrast to acids. “Alkali,” which serves to indicate the basic quality of both the alkali metal and alkaline earth metal families of elements, comes from the Arabic al-qili. The latter refers to the ashes of the seawort plant, which usually grows in marshy areas and, in the past, was often burned to produce soda ash for making soap.
Before studying the reactions of acids and bases, it is necessary to define exactly what each is. This is not as easy as it sounds, and the Acids and Bases essay discusses in detail a subject covered more briefly here: the arduous task chemists faced in developing a workable distinction. Let us start with the phenomenological differences between the two—that is, aspects relating to things that can readily be observed without referring to the molecule properties and behaviors of acids and bases.
The reason chemists of today use the word “base” instead of “alkali” is that the latter term has a narrower meaning: all alkalies are bases, but not all bases are alkalies. Originally referring only to the ashes of burned plants containing either sodium or potassium, alkali was eventually used to designate the soluble hydroxides of the alkali and alkaline earth metals. Among these are sodium hydroxide or lye; magnesium hydroxide (found in milk of magnesia); potassium hydroxide, which appears in soaps; and other compounds. Because these represent only a few of the substances that react with acids in the ways discussed in this essay, the term “base” is preferred.
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of his time: only in 1884 did his countryman Svante Arrhenius (1859-1927) introduce the concept of the ion. This, in turn, enabled Arrhenius to formulate the first structural distinction between acids and bases.
Acid-Base Reactions
The Arrhenius Acid-Base Theory Arrhenius acid-base theory defines the two substances with regard to their behavior in an aqueous solution: an acid is any compound that produces hydrogen ions (H+), and a base is one that produces hydroxide ions (OH–) when dissolved in water. This occurred, for instance, in the reaction discussed above: the hydrochloric acid produced a hydrogen ion, while the sodium hydroxide produced a hydroxide ion, and these two ions bonded to form water.
GILBERT N. LEWIS.
T H E F O R M AT I O N O F SA LT S . As chemistry evolved, and physical scientists became aware of the atomic and molecular substructures that make up the material world, they developed more fundamental distinctions between acids and bases. By the early twentieth century, chemists had applied structural distinctions between acids and bases—that is, definitions based on the molecular structures and behaviors of those substances.
An important intermediary step occurred as chemists came to the conclusion that reactions of acids and bases form salts and water. For instance, in an aqueous solution, hydrochloric acid or HCl(aq) reacts with the base sodium hydroxide, designated as NaOH(aq), to form sodium chloride, or common table salt (NaCl[aq]) and H2O. What happens is that the sodium (Na) ion (an atom with an electric charge) in sodium hydroxide switches places with the hydrogen ion in hydrochloric acid, resulting in the creation of NaCl and water. Ions themselves had yet to be defined in 1803, when the great Swedish chemist Jons Berzelius (1779-1848) added another piece to the foundation for a structural definition. Acids and bases, he suggested, have opposite electric charges. In this, he was about eight decades ahead
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Though it was a good start, Arrhenius’s theory was limited to reactions in aqueous solutions. In addition, it confined its definition of acids and bases only to those ionic compounds, such as hydrochloric acid or sodium hydroxide, that produced either hydrogen or hydroxide ions. But ammonia, or NH3, acts like a base in aqueous solutions, even though it does not produce the hydroxide ion. These shortcomings pointed to the need for a more comprehensive theory, which came with the formulation of the BrønstedLowry definition.
The Brønsted-Lowry AcidBase Theory Developed by English chemist Thomas Lowry (1874-1936) and Danish chemist J. N. Brønsted (1879-1947), the Brønsted-Lowry acid-base theory defines an acid as a proton (H+) donor, and a base as a proton acceptor, in a chemical reaction. Protons are represented by the symbol H+, a cation (positively charged ion) of hydrogen. Elemental hydrogen, called protium to distinguish it from its isotopes, has just one proton and one electron—no neutrons. Therefore, the hydrogen cation, which has to lose its sole electron to gain a positive charge, is essentially nothing but a proton. It is thus at once an atom, an ion, and a proton, but the ionization of hydrogen constitutes the only case in which this is possible. Thus when the term “proton donor” or “proton acceptor” is used, it does not mean that a proton is splitting off from an atom or joining
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another, as in a nuclear reaction. Rather, when an acid behaves as a proton donor, this means that the hydrogen proton/ion/atom is separating from an acidic compound; conversely, when a base acts as a proton acceptor, the positively charged hydrogen ion is bonding with the basic compound. REACTIONS IN LOWRY ACID-BASE
BRØNSTEDT H E O R Y. In
representing Brønsted-Lowry acids and bases, the symbols HA and A–, respectively, are used. These appear in the equation representing the most fundamental type of Brønsted-Lowry acidbase reaction: HA(aq) + H2O(l) 4H3O+(aq) + A–(aq). The symbols (aq), (l), and 4are explained in the Chemical Reactions essay. In plain English, this equation states that when an acid in an aqueous solution reacts with liquid water, the result is the creation of H3O+, known as the hydronium ion, along with a base. Both products of the reaction are dissolved in an aqueous solution. Because water molecules are polar, the negative charges tend to congregate on one end of the molecule with the oxygen atom, while the positive charges remain on the other end with the hydrogen atoms. The Brønsted-Lowry model emphasizes the role played by water, which pulls the proton from the acid, resulting in the creation of the hydronium ion. The hydronium ion, in this equation, is an example of a conjugate acid, an acid formed when a base accepts a proton. At the same time, the acid has lost its proton, becoming A–, a conjugate base—that is, the base formed when an acid releases a proton. These two products of the reaction are called a conjugate acid-base pair, a term that refers to two substances related to one another by the donating of a proton. Brønsted and Lowry’s definition includes all Arrhenius acids and bases, as well as other chemical species not encompassed in Arrhenius theory. As mentioned earlier, ammonia is a base, yet it does not produce OH– ions; however, it does accept a proton from a water molecule. Water can serve either as an acid or base; in this instance, it is an acid, and in reaction with ammonia, it produces the conjugate acid-base pair of NH4+ (an ammonium ion) and OH–. Ammonia did not produce the hydroxide ion here; rather, OH– is the conjugate base that resulted when the water molecule lost its H+ atom (i.e., a proton.)
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The Lewis Acid-Base Theory The Brønsted-Lowry model still had its limitations, in that it only described compounds containing hydrogen. American chemist Gilbert N. Lewis (1875-1946), however, developed a theory of acids and bases that makes no reference to the presence of hydrogen. Instead, it relates to something much more fundamental: the fact that chemical bonding always involves pairs of electrons.
Acid-Base Reactions
Lewis acid-base theory defines an acid as the reactant that accepts an electron pair from another reactant in a chemical reaction, while a base is the reactant that donates an electron pair to another reactant. Note that, as with the Brønsted-Lowry definition, the Lewis definition is reaction-dependant. Instead of defining a compound as an acid or base in its own right, it identifies these in terms of how the compound reacts with another. The Lewis definition encompasses all the situations covered by the others, as well as many other reactions not described in the theories of either Arrhenius or Brønsted-Lowry. In particular, Lewis theory can be used to differentiate the acid and base in chemical reactions where ions are not produced, something that takes it far beyond the scope of Arrhenius theory. Also, Lewis theory addresses situations in which there is no proton donor or acceptor, thus offering an improvement over Brønsted-Lowry. When boron trifluoride (BF3) and ammonia (NH3), both in the gas phases, react to produce boron trifluoride ammonia complex (F3BNH3), boron trifluoride accepts an electron pair. Therefore, it is a Lewis acid, while ammonia—which donates the electron pair—can be defined as a Lewis base. This particular reaction involves hydrogen, but since the operative factor in Lewis theory relates to electron pairs and not hydrogen, the theory can be used to address reactions in which that element is not present.
REAL-LIFE A P P L I C AT I O N S Dissociation Dissociation is the separation of a molecule into ions, and it is a key factor for evaluating the “strength” of acids and bases. The more a substance is prone to dissociation, the better it can
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conduct an electric current, because the separation of charges provides a “pathway” for the current’s flow. A substance that dissociates completely, or almost completely, is called a strong electrolyte, whereas one that dissociates only slightly (or not at all) is designated as a weak electrolyte. The terms “weak” and “strong” are also applied to acids and bases. For instance, vinegar is a weak acid, because it dissociates only slightly, and therefore conducts little electric current. By contrast, hydrochloric acid (HCl) is a strong acid, because it dissociates almost completely into positively charged hydrogen ions and negatively charged chlorine ones. Represented symbolically, this is: HCl 4H+ + Cl–. A R E A C T I O N I N V O LV I N G A S T R O N G AC I D . It may seem a bit back-
ward that a strong acid or base is one that “falls apart,” while the weak one stays together. To understand the difference better, let us return to the reaction described earlier, in which an acid in aqueous solution reacts with water to produce a base in aqueous solution, along with hydronium: HA(aq) + H2O(l) 4H3O+(aq) + A–(aq). Instead of using the generic symbols HA and A–, however, let us substitute hydrochloric acid (HCl) and chloride (Cl–) respectively. The reaction HCl(aq) + H2O(l) 4H3O+(aq) is a reversible one, and for that reason, + the symbol for chemical equilibrium (!) can be inserted in place of the arrow pointing to the right. In other words, the substances on the right can just as easily react, producing the substances on the left. In this reverse reaction, the reactants of the forward reaction would become products, and the products of the forward reaction serve as the reactants. Cl–(aq)
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hydrogen ions join the water (a stronger base) to form hydronium. The chloride, incidentally, is the conjugate base of the hydrochloric acid, and this illustrates another principal regarding the “strength” of electrolytes: a strong acid produces a relatively weak conjugate base. Likewise, a strong base produces a relatively weak conjugate acid. THE STRONG ACIDS AND B AS E S . There are only a few strong acids and
bases, which are listed below: Strong Acids • • • • • •
Hydrobromic acid (HBr) Hydrochloric acid (HCl) Hydroiodic acid (HI) Nitric acid (HNO3) Perchloric acid (HClO4) Sulfuric acid (H2SO4) Strong Bases
Barium hydroxide (Ba[OH]2) Calcium hydroxide (Ca[OH]2) Lithium hydroxide (LiOH) Potassium hydroxide (KOH) Sodium hydroxide (NaOH) Strontium hydroxide (Sr[OH]2) Virtually all others are weak acids or bases, meaning that only a small percentage of molecules in these substances ionize by dissociation. The concentrations of the chemical species involved in the dissociation of weak acids and bases are mathematically governed by the equilibrium constant K.. • • • • • •
Neutralization
However, the reaction described here is not perfectly reversible, and in fact the most proper chemical symbolism would show a longer arrow pointing to the right, with a shorter arrow pointing to the left. Due to the presence of a strong electrolyte, there is more forward “thrust” to this reaction.
Neutralization is the process whereby an acid and base react with one another to form a salt and water. The simplest example of this occurs in the reaction discussed earlier, in which hydrochloric acid or HCl(aq) reacts with the base sodium hydroxide, designated as NaOH(aq), in an aqueous solution. The result is sodium chloride, or common table salt (NaCl[aq]) and H2O. This equation is written thus: HCl(aq) + NaOH(aq) 4NaCl(aq) + H2O.
Because it is a strong acid, the hydrogen chloride in solution is not a set of molecules, but a collection of H+ and Cl– ions. In the reaction, the weak Cl– ions to the right side of the equilibrium symbol exert very little attraction for the H+ ions. Instead of bonding with the chloride, these
The human stomach produces hydrochloric acid, commonly known as “stomach acid.” It is generated in the digestion process, but when a person eats something requiring the stomach to work overtime in digesting it—say, a pizza—the stomach may generate excess hydrochloric acid,
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and the result is “heartburn.” When this happens, people often take antacids, which contain a base such as aluminum hydroxide (Al[OH]3) or magnesium hydroxide (Mg[OH]2). When a person takes an antacid, the reaction leads to the creation of a salt, but not the salt with which most people are familiar—NaCl. As shown above, that particular salt is the product of a reaction between hydrochloric acid and sodium hydroxide, but a person who ingested sodium hydroxide (a substance used to unclog drains and clean ovens) would have much worse heartburn than before! In any case, the antacid reacts with the stomach acid to produce a salt, as well as water, and thus the acid is neutralized. When land formerly used for mining is reclaimed, the acidic water in the area must be neutralized, and the use of calcium oxide (CaO) as a base is one means of doing so. Acidic soil, too, can be neutralized by the introduction of calcium carbonate (CaCO3) or limestone, along with magnesium carbonate (MgCO3). If soil is too basic, as for instance in areas where there has been too little precipitation, acid-like substances such as calcium sulfate or gypsum (SaSO4) can be used. In either case, neutralization promotes plant growth. T I T RAT I O N A N D p H . One of the most important applications of neutralization is in titration, the use of a chemical reaction to determine the amount of a chemical substance in a sample of unknown purity. In a typical form of neutralization titration, a measured amount of an acid is added to a solution containing an unknown amount of a base. Once enough of the acid has been added to neutralize the base, it is possible to determine how much base exists in the solution.
Titration can also be used to measure pH (“power of hydrogen”) level by using an acidbase indicator. The pH scale assigns values ranging from 0 (a virtually pure acid) to 14 (a virtually pure base), with 7 indicating a neutral substance. An acid-base indicator such as litmus paper changes color when it neutralizes the solution.
from red to yellow across a pH range of 4.4 to 6.2, so it is most useful for testing a substance suspected of being moderately acidic.
Acid-Base Reactions
BUFFERED SOLUTIONS. A buffered solution is one that resists a change in pH even when a strong acid or base is added to it. This buffering results from the presence of a weak acid and a strong conjugate base, and it can be very important to organisms whose cells can endure changes only within a limited range of pH values. Human blood, for instance, contains buffering systems, because it needs to be at pH levels between 7.35 and 7.45.
The carbonic acid-bicarbonate buffer system is used to control the pH of blood. The most important chemical equilibria (that is, reactions involving chemical equilibrium) for this system are: H+ + HCO3– ! H2CO3 ! H20 + CO2. In other words, the hydrogen ion (H+) reacts with the hydrogen carbonate ion (HCO3– ) to produce carbonic acid (H2CO3). The latter is in equilibrium with the first set of reactants, as well as with water and carbon dioxide in the forward reaction. The controls the pH level by changing the concentration of carbon dioxide by exhalation. In accordance with Le Châtelier’s principle, this shifts the equilibrium to the right, consuming H+ ions. In normal blood plasma, the concentration of HCO3– is about 20 times as great as that of H2CO3, and this large concentration of hydrogen carbonate gives the buffer a high capacity to neutralize additional acid. The buffer has a much lower capacity to neutralize bases because of the much smaller concentration of carbonic acid.
Water: Both Acid and Base Water is an amphoteric substance; in other words, it can serve either as an acid or a base. When water experiences ionization, one water molecule serves as a Brønsted-Lowry acid, donating a proton to another water molecule— the Brønsted-Lowry base. This results in the production of a hydroxide ion and a hydronium ion: H2O(l) + H2O(l) ! H3O+(aq) + OH–(aq).
The transition interval (the pH at which the color of an indicator changes) is different for different types of indicators, and thus various indicators are used to measure substances in specific pH ranges. For instance, methyl red changes
This equilibrium equation is actually one in which the tendency toward the reverse reaction is much greater; therefore the equilibrium symbol, if rendered in its most proper form, would show a much shorter arrow pointing toward the right. In water purified by distillation, the concentra-
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Acid-Base Reactions
KEY TERMS A substance that in its edible
acids they produce salts and water. Bases
form is sour to the taste, and in non-edible
and acids are most properly defined, how-
forms is often capable of dissolving metals.
ever, not in these phenomenological terms,
Acids and bases react to form salts and
but by the three structural definitions of
water. These are all phenomenological def-
acids and bases—the Arrhenius, Brønsted-
initions, however, in contrast to the three
Lowry, and Lewis acid-base theories.
ACID:
structural definitions of acids and bases— the Arrhenius, Brønsted-Lowry, and Lewis acid-base theories. ALKALI:
BASIC:
In the context of acids and
bases, the word is the counterpart to “acidic,” identifying the base-like quality of
A term referring to the soluble
a substance.
hydroxides of the alkali and alkaline earth metals. Once “alkali” was used for the class
BRØNSTED-LOWRY ACID-BASE THE-
of substances that react with acids to form
ORY:
salts; today, however, the more general term base is preferred.
The second of three structural
definitions of acids and bases. Formulated by English chemist Thomas Lowry (18741936) and Danish chemist J. N. Brønsted
ALKALINITY:
An adjectival term used
(1879-1947),
defines an acid as a proton
displays the properties of a base.
a base as a proton acceptor.
AMPHOTERIC:
A term describing a
substance that can serve either as an acid or a base. Water is the most significant amphoteric substance. AQUEOUS SOLUTION:
CHEMICAL SPECIES:
A substance
large number of chemical reactions take place in an aqueous solution.
theory
donor, and
A generic term
used for any substance studied in chemistry—whether it be an element, comso forth. CONJUGATE ACID:
The first of three structural definitions of acids and bases. Formulated by Swedish chemist Svante Arrhenius (1859-1927), the Arrhenius theory defines acids and bases according to the ions they produce in an aqueous solution an acid produces hydrogen ions (H+), and a base hydroxide ions (OH–).
ACID-BASE
donates a single proton to a base. In the reaction that produces this pair, the acid and base switch identities. By donating a proton, the acid becomes a conjugate base, and by receiving the proton, the base becomes a conjugate acid. A base formed
when an acid releases a proton.
form is bitter to the taste. Bases tend to be
DISSOCIATION:
slippery to the touch, and in reaction with
molecules into ions.
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PAIR:
The acid and base produced when an acid
CONJUGATE BASE:
A substance that in its edible
An acid formed
when a base accepts a proton (H+). CONJUGATE
ARRHENIUS ACID-BASE THEORY:
BASE:
(H+)
pound, mixture, atom, molecule, ion, and
in which water constitutes the solvent. A
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Brønsted-Lowry
to identify the degree to which a substance
The separation of
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Acid-Base Reactions
KEY TERMS ION:
An atom or atoms that has lost or
CONTINUED
A substance that interacts
REACTANT:
gained one or more electrons, and thus has
with another substance in a chemical reac-
a net electric charge. There are two types of
tion, resulting in the creation of a product.
ions: anions and cations.
SALTS:
Ionic compounds formed by
A form of chemical
the reaction between an acid and a base. In
bonding that results from attractions
this reaction, one or more of the hydrogen
between ions with opposite electric
ions of an acid is replaced with another
charges.
positive ion. In addition to producing salts,
IONIC BONDING:
IONIC COMPOUND:
A compound in
acid-base reactions produce water. A homogeneous mixture
which ions are present. Ionic compounds
SOLUTION:
contain at least one metal and nonmetal
in which one or more substances (the
joined by an ionic bond.
solute) is dissolved in another substance (the solvent)—for example, sugar dis-
LEWIS ACID-BASE THEORY:
The
solved in water.
third of three structural definitions of acids and bases. Formulated by American chemist Gilbert N. Lewis (1875-1946),
SOLVENT:
A substance that dissolves
another, called a solute, in a solution.
Lewis theory defines an acid as the reactant
STRONG ELECTROLYTE:
that accepts an electron pair from another
highly prone to dissociation. The terms
reactant in a chemical reaction, and a base
“strong acid” or “strong base” refers to those
as the reactant that donates an electron
acids or bases which readily dissociate.
pair to another reactant.
A substance
A term describing sci-
STRUCTURAL:
process
entific definitions based on aspects of
whereby an acid and base react with one
molecular structure and behavior rather
another to form a salt and water.
than purely phenomenological data.
NEUTRALIZATION:
PH SCALE:
The
A logarithmic scale for
TITRATION:
The use of a chemical
determining the acidity or alkalinity of a
reaction to determine the amount of a
substance, from 0 (virtually pure acid) to 7
chemical substance in a sample of
(neutral) to 14 (virtually pure base).
unknown purity. Testing pH levels is an example of titration.
PHENOMENOLOGICAL:
A
term
describing scientific definitions based purely on experimental phenomena. These only convey part of the picture, however—
TRANSITION INTERVAL:
The pH
level at which the color of an acid-base indicator changes.
primarily, the part a chemist can perceive
WEAK ELECTROLYTE:
either through measurement or through
that experiences little or no dissociation.
the senses, such as sight. A structural defi-
The terms “weak acid” or “weak base” re-
nition is therefore usually preferable to a
fer to those acids or bases not prone to
phenomenological one.
dissociation.
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A substance
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tions of hydronium (H3O+) and hydroxide (OH–) ions are equal. When multiplied by one another, these yield the constant figure 1.0 • 10–14, which is the equilibrium constant for water. In fact, this constant—denoted as Kw—is called the ion-product constant for water.
WHERE TO LEARN MORE “Acids and Bases.” Vision Learning (Web site). (June 7, 2001). “Acids, Bases, and Chemical Reactions” Open Access College (Web site). (June 7, 2001). “Acids, Bases, pH.” About.com (Web site).
Because the product of these two concentrations is always the same, this means that if one of them goes up, the other one must go down in order to yield the same constant. This explains the fact, noted earlier, that water can serve either as an acid or base—or, if the concentrations of hydronium and hydroxide ions are equal—as a neutral substance. In situations where the concentration of hydronium is higher, and the hydroxide concentration automatically decreases, water serves as an acid. Conversely, when the hydroxide concentration is high, the hydronium concentration decreases correspondingly, and the water is a base.
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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“Acids, Bases, and Salts” (Web site). (June 7, 2001). “Junior Part: Acids, Bases, and Salts” (Web site). (June 7, 2001). Knapp, Brian J. Acids, Bases, and Salts. Danbury, CT: Grolier Educational, 1998. Moje, Steven W. Cool Chemistry: Great Experiments with Simple Stuff. New York: Sterling Publishing Company, 1999. Walters, Derek. Chemistry. Illustrated by Denis Bishop and Jim Robins. New York: F. Watts, 1982.
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S C I E N C E O F E V E RY DAY T H I N G S r e a l - l i f e CHEMISTRY
S O LU T I O N S A N D MIXTURES MIXTURES SOLUTIONS OSMOSIS D I S T I L L A T I O N A N D F I LT R A T I O N
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Mixtures
CONCEPT Elements and compounds are pure substances, but much of the material around us—including air, wood, soil, and even (in most cases) water— appears in the form of a mixture. Unlike a pure substance, a mixture has variable composition: in other words, it cannot be reduced to a single type of atom or molecule. Mixtures can be either homogeneous—that is, uniform in appearance, and having only one phase—or heterogeneous, meaning that the mixture is separated into various regions with differing properties. Most homogeneous mixtures are also known as solutions, and examples of these include air, coffee, and even metal alloys. As for heterogeneous mixtures, these occur, for instance, when sand or oil are placed in water. Oil can, however, be dispersed in water as an emulsion, with the aid of a surfactant or emulsifier, and the result is an almost homogeneous mixture. Another interesting example of a heterogeneous mixture occurs when colloids are suspended in fluid, whether that fluid be air or water.
HOW IT WORKS Mixtures and Pure Substances A mixture is a substance with a variable composition, meaning that it is composed of molecules or atoms of differing types. These may have intermolecular bonds, or bonds between molecules, but such bonds are not nearly as strong as those formed when elements bond to form a compound.
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MIXTURES
Examples of mixtures include milk, coffee, tea, and soft drinks—indeed, they include virtually any drink except for pure water, which is a rarity, because water is highly soluble and tends to contain minerals and other impurities. Air, too, is a mixture, because it contains oxygen, nitrogen, noble gases, carbon dioxide, and water vapor. Likewise metal alloys such as bronze, brass, and steel are mixtures. S T R U C T U RA L A N D P H E N O M E N O LO G I CA L D I S T I N C T I O N S . Be-
fore chemists accepted the atomic theory of matter, it was often difficult to distinguish a mixture, such as air or steel, from pure substances, which have the same composition throughout. Pure substances are either elements such as oxygen or iron, or compounds—for example, carbon dioxide or iron oxide. An element is made up of only one type of atom, while a compound can be reduced to one type of bonded chemical species—usually either a molecule or a formation of ions. A distinction between mixtures and pure substances based on atomic and molecular structures is called, fittingly enough, a structural definition. Prior to the development of atomic theory by English chemist John Dalton (1766-1844), and the subsequent identification of molecules by Italian physicist Amedeo Avogadro (17761856), chemists defined compounds and mixtures on the basis of phenomenological data garnered through observation and measurement. This could and did lead to incorrect suppositions. P R O U S T A N D T H E D E B AT E O V E R C O N S TA N T C O M P O S I T I O N .
Around the time of Dalton and Avogadro, French
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Mixtures
THE
WONDROUS INVENTION KNOWN AS SOAP IS A MIXTURE WITH SURFACTANT QUALITIES. (Chad Weckler/Corbis. Reproduced
by permission.)
chemist Antoine Lavoisier (1743-1794) correctly identified an element as a substance that could not be broken down into a simpler substance. Later, his countryman Joseph-Louis Proust (1754-1826) clarified the definition of a compound, stating it in much the same terms that we have used: the composition of a compound is the same throughout. But with the very rudimentary knowledge of atoms and molecules that chemists of the early nineteenth century possessed, the distinctions between compounds and mixtures remained elusive. Proust’s contemporary and intellectual rival Claude Louis Berthollet (1748-1822) observed that when metals such as iron are heated, they form oxides in which the percentage of oxygen increases with temperature. If constant composition is a fact, he challenged Proust, then how is this possible? Proust maintained that the proportions of elements in a compound are always the same, a hypothesis Berthollet countered by observing that metals can form variable alloys. Bronze, for instance, is an alloy of tin and copper at a ratio of about 25:75, but if the ratio were changed to, say, 30:70, it would still be called bronze.
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not exist whereby Berthollet’s assertions could be successfully proven wrong. Indeed, Berthollet, a student of Lavoisier who contributed to progress in the study of acids and reactants, was no antiscientific villain: he was simply responding to the evidence as he saw it. Only with the discovery of subatomic particles in the late nineteenth and early twentieth centuries, discoveries that changed the entire character of chemistry as a discipline, did it truly become possible to answer Berthollet’s challenges. Chemists now understand that the oxide formed on the surface of a metal is a compound separate from the metal itself, and that alloys (discussed later in this essay) are not compounds at all: they are mixtures.
Mixtures and Compounds
At the time, the equipment—both in terms of knowledge and tools for analysis—simply did
With our modern knowledge of atomic and molecular properties, we can more fully distinguish between a compound and a mixture. First, a mixture can exist in virtually any proportion among its constituent parts, whereas a compound has a definite and constant composition. Coffee, whether weak or strong, is still coffee, but if a second oxygen atom chemically bonds to the oxygen in carbon monoxide (CO), the resulting
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Mixtures
BRONZE—AN
ALLOY OF TIN AND COPPER—WAS ONE OF THE MOST IMPORTANT INVENTIONS IN HUMAN HISTORY.
STONE CARVING IS FROM THE PERIOD KNOWN AS THE
THIS
BRONZE AGE. (Kevin Schafer/Corbis. Reproduced by permission.)
compound is not simply “strong carbon monoxide” or even “oxygenated carbon monoxide”: it is carbon dioxide (CO2), an entirely different substance. The difference is enormous: carbon dioxide is a part of the interactions between plant and animal life that sustains the natural environment, whereas carbon monoxide is a toxic gas produced, for instance, by automobiles. Second, the parts of a mixture retain most of their properties when they join together, but elements lose their elemental characteristics once they form a compound. Sugar is still sweet, regardless of the substance into which it is dissolved. In coffee or another drink, it may no longer be dry and granular, though it could be returned to that state by evaporating the coffee. In any case, dryness and granularity are physical properties, whereas sweetness is a chemical one. On the other hand, when elemental carbon bonds with hydrogen and oxygen to form sugar itself, the resulting compound is nothing like the elements from which it is made.
much higher temperatures. On the other hand, the formation of a compound involves a chemical reaction, a vastly more complex interaction than the one required to create a mixture. Carbon, a black solid found in coal, can be mixed with hydrogen and oxygen—both colorless and odorless gases—and the resulting mess would be something; but it would not be sugar. Only the chemical reaction between the three elements, in specific proportions and under specific conditions, results in their chemical bonding to form table sugar, known to chemists as sucrose.
Homogeneous and Heterogeneous Mixtures HOMOGENEOUS MIXTURES A N D S O LU T I O N S . As we have seen, the
Third, a mixture can usually be created simply by the physical act of stirring items together, and/or by applying heat. As discussed below, relatively high temperatures are sometimes needed to dissolve sugar in tea, for instance; likewise, alloys are usually formed by heating metals to
composition of a mixture is variable. Coffee, for instance, can be weak or strong, and milk can be “whole” or low-fat. Beer can be light or dark in color, as well as “light” in terms of calorie content; furthermore, its alcohol content can be varied, as with all alcoholic drinks. Though their molecular composition is variable, each of the mixtures described here is the same throughout: in other words, there is no difference between one region and another in a glass of beer. Such a mixture is described as homogeneous.
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A homogeneous mixture is one that is the same throughout, but this is not the same as saying that a compound has a constant composition. Rather, when we say that a homogeneous mixture is the same in every region, we are speaking phenomenologically rather than structurally. From the standpoint of ordinary observation, a glass of milk is uniform, but as we shall see, milk is actually a type of emulsion, in which one substance is dispersed in another. There are no milk “molecules,” and structural analysis would reveal that milk does not have a constant molecular composition. Coffee is an example of a solution, a specific type of homogeneous mixture. Actually, most homogeneous mixtures can be considered solutions, but since a solution is properly defined as a homogeneous mixture in which one or more substances is dissolved in another substance, a 50:50 homogeneous mixture is technically not a solution. When particles are perfectly dissolved in a solution, the composition is uniform, but again, this is not a compound, because that composition can always be varied.
atoms of element y in such-and-such a structure), there is less of a sharp dividing line between homogeneous and heterogeneous solutions. When too much of a solute is added to the solvent, the solvent becomes saturated, and is no longer truly homogeneous. Such is the case when the sugar drifts to the bottom of the tea, or when coffee grounds form in the bottom of a coffee pot containing an otherwise uniform mixture of coffee and water. Milk comes to us as a homogeneous substance, thanks to the process of homogenization, but when it comes out of the cow, it is a more heterogeneous mixture of milk fat and water. In fact, milk is an example of an emulsion, the result of a process whereby two substances that would otherwise form a heterogeneous mixture are made to form a homogeneous one.
REAL-LIFE A P P L I C AT I O N S Colloids
HETEROGENEOUS MIXTURES.
Anyone who has ever made iced tea has observed that it is easy to sweeten when it is hot, because temperature affects the ability of a solvent such as water—in this case, water with particles from tea leaves filtered into it—to dissolve a solute, such as sugar. Cold tea, on the other hand, is much harder to sweeten with ordinary sugar. Usually what happens is that, instead of obtaining a homogeneous mixture, the result is heterogeneous.
FROM HOMOGENEOUS TO HETEROGENEOUS AND BACK AGA I N . The distinction between homoge-
What Brown had observed was the suspension of a colloid—a particle intermediate in size between a molecule and a speck of dust—in the water. When placed in water or another fluid (both liquids and gases are called “fluids” in the physical sciences), a colloid forms a mixture similar both to a solution and a suspension. As with a solution, the composition remains homogeneous—the particles never settle to the bottom of the container. At the same time, however, the particles remain suspended rather than dissolved, rendering a cloudy appearance to the dispersion.
neous and heterogeneous solutions only serves to further highlight the difference between compounds and mixtures. Whereas the composition of a compound is definite and quantitative (so many atoms of element x bonded with so many
Almost everyone, especially as a child, has been fascinated by the colloidal dispersion of dust particles in a beam of sunlight. They seem to be continually in motion, as indeed they are, and this movement is called “Brownian motion” in
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Whereas every region within a homogeneous mixture is more or less the same as every other region, heterogeneous mixtures contain regions that differ from one another. In the example we have used, a glass of cold tea with undissolved sugar at the bottom is a heterogeneous mixture: the tea at the top is unsweetened or even bitter, whereas at the bottom, there is an overly sweet sludge of tea and sugar.
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In 1827, Scottish naturalist Robert Brown (17731858) was studying pollen grains under a microscope when he noticed that the grains underwent a curious zigzagging motion in the water. At first, he assumed that the motion had a biological explanation—in other words, that it resulted from life processes within the pollen—but later, he discovered that even pollen from long-dead plants behaved in the same way.
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honor of the man who first observed it. Yet Brown did not understand what he was seeing; only later did scientists recognize that Brownian motion is the result of movement on the part of molecules in a fluid. Even though the molecules are much smaller than the colloid, there are enough of them producing enough collisions to cause the colloid to be in constant motion. Another remarkable aspect of dust particles floating in sunlight is the way that they cause a column of sunlight to become visible. This phenomenon, called the Tyndall effect after English physicist John Tyndall (1820-1893), makes it seem as though we are actually seeing a beam of light. In fact, what we are seeing is the reflection of light off the colloidal dispersion. Another example of a colloidal dispersion occurs when a puff of smoke hangs in the air; furthermore, as we shall see, milk is a substance made up of colloids—in this case, particles of fat and protein suspended in water.
Emulsions Miscibility is a qualitative term identifying the relative ability of two substances to dissolve in one another. Generally, water and water-based substances have high miscibility with regard to one another, as do oil and oil-based substances with one another. Oil and water, on the other hand (or substances based in either) have very low miscibility. The reason is that water molecules are polar, meaning that the positive electric charge is in one region of the molecule, while the negative charge is in another region. Oil, on the other hand, is nonpolar, meaning that charges are more evenly distributed throughout the molecule. Trying to mix oil and water is thus rather like attempting to use a magnet to attract a nonmagnetic metal such as gold.
All liquids have a certain degree of surface tension. This is what causes water on a hard surface to bead up instead of lying flat. (Mercury has an extremely high surface tension.) Surfactants break down this surface tension, enabling the marriage of two formerly immiscible liquids.
Mixtures
In an emulsion, millions of surfactants surround the dispersed droplets (known as the internal phase), shielding them from the other liquid (the external phase). Supposing oil is the internal phase, then the oil-soluble end of the surfactant points toward the oils, while the water-soluble side joins with the water of the external phase. P H Y S I CA L C H A RAC T E R I S T I CS O F A N E M U L S I O N . The resulting emul-
sion has physical (as opposed to chemical) properties different from those of the substances that make it up. Water and most oils are transparent, whereas emulsions are typically opaque and may have a lustrous, pearly gleam. Oil and water flow freely, but emulsions can be made to form thick, non-flowing creams. Emulsions are inherently unstable: they are, as it were, only temporarily homogeneous. A good example of this is an oil-and-vinegar salad dressing, which has to be shaken before putting it on salad; otherwise, what comes out of the bottle is likely to be mainly oil, which floats to the top of the water-based vinegar. It is characteristic of emulsions that eventually gravity pulls them apart, so that the lighter substances float to the top. This process may take only a few minutes, as with the salad dressing; on the other hand, it can take thousands of years.
H O W S U R FAC TA N T S A I D T H E E M U L S I O N P R O C E SS . An emulsion is
A P P L I CAT I O N S . Surfactants themselves are often used in laundry or dish detergent, because most stains on plates or clothes are oilbased, whereas the detergent itself is applied to the clothes in an aqueous solution. As for emulsions, these are found in a wide variety of products, from cosmetics to paint to milk.
a mixture of two immiscible liquids such as oil and water—we will use these simple terms, with the idea that these stand for all oil- and watersoluble substances—by dispersing microscopic droplets of one liquid in another. In order to achieve this dispersion, there needs to be a “middle man,” known as an emulsifier or surfactant. The surfactant, made up of molecules that are both water- and oil-soluble, acts as an agent for joining other substances in an emulsion.
In the pharmaceutical industry, for instance, emulsions are used as a means of delivering the active ingredients of drugs, many of which are not water soluble, in a medium that is. Pharmaceutical manufacturers also use emulsions to make medicines more palatable (easier to take); to control dosage and improve effectiveness; and to improve the usefulness of topical drugs such as ointments, which must contend with both oily and water-soluble substances on the skin.
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The oils and other conditioning agents used in hair-care products would leave hair limp and sticky if applied by themselves. Instead, these products are applied in emulsions that dilute the oils in other materials. Emulsions are also used in color photography, as well as in the production of pesticides and fungicides. Paints and inks, too, are typically emulsified substances, and these sometimes come in the form of dispersions akin to those of colloids. As we have seen, in a dispersion fine particles of solids are suspended in a liquid. Surfactants are used to bond the particles to the liquid, though paint must be shaken, usually with the aid of a high-speed machine, before it is consistent enough to apply. As mentioned earlier, milk is a form of emulsion that contains particles of milk fat or cream dispersed in water. Light strikes the microscopic fat and protein colloids, resulting in the familiar white color. Other examples of emulsified foods include not only salad dressings, but gravies and various sauces, peanut butter, ice cream, and other items. Not only does emulsion affect the physical properties of foods, but it may enhance the taste by coating the tongue with emulsified oils.
Soap The wondrous invention called soap, which has made the world a cleaner place, exhibits several of the properties we have discussed. It is a mixture with surfactant qualities, and in powdered form, it can form something close to a true solution with water. Discovered probably by the Phoenicians around 600 B.C., it was made in ancient times by boiling animal fat (tallow) or vegetable oils with an alkali or base of wood ashes. This was a costly process, and for many centuries, only the wealthy could afford soap—a fact that contributed to the notorious lack of personal hygiene that prevailed among Europeans of the Middle Ages. In fact, the situation did not change until late in the eighteenth century, when the work of two French chemists yielded a more economical manufacturing method. In 1790, Nicholas Leblanc (1742-1806) developed a process for creating sodium hydroxide (called caustic soda at the time) from sodium chloride, or ordinary table salt. This made for an inexpensive base or alkali, with which soap manufacturers could combine natural fats and oils.
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Then in 1823, Michel Eugène Chevreul (17861889) showed that fat is a compound of glycerol with organic acids, a breakthrough that led to the use of fatty acids in producing soaps. THE
CHEMISTRY
OF
S O A P.
Soap as it is made today comes from a salt of an alkali metal, such as sodium or potassium, combined with a mixture of carboxylic acids (“fatty acids”). These carboxylic acids are the result of a reaction called saponification, involving triglycerides and a base, such as sodium hydroxide. Saponification breaks the triglycerides into their component fatty acids; then, the base neutralizes these to salts. This reaction produces glycerin, a hydrocarbon bonded to a hydroxyl (-OH) group. (Hydrocarbons are discussed in the essays on Organic Chemistry; Polymers.) In general, the formula for soap is RCOOX, where X stands for the alkali metals, and R for the hydrocarbon chain. Because it is a salt (meaning that it is formed from the reaction of an acid with a base), soap partially separates into its component ions in water. The active ion is RCOO-, whose two ends behave in different fashions, making it a surfactant. The hydrocarbon end (R-) is said to be lipophilic, or “oil-loving,” which is appropriate, since most oils are hydrocarbons. On the other hand, the carboxylate end (-COO-) is hydrophilic, or “water-loving.” As a result, soap can dissolve in water, but can also clean greasy stains. When soap is mixed with water, it does not form a true homogeneous mixture or solution due to the presence of hydrocarbons. These attract one another, forming spherical aggregates called micelles. The lipophilic “tails” of the hydrocarbons are turned toward the interior of the micelle, while the hydrophilic heads remain facing toward the water that forms the external phase.
Alloys We have primarily discussed liquid mixtures, but in fact mixtures can be gaseous or even solid—as for example in the case of an alloy, a mixture of two or more metals. Alloys are usually created by melting the component metals, then mixing them together in specific proportions, but an alloy can also be created by bonding metal powders. The structure of an elemental metal includes tight “electron sea” bonds, which are discussed in the essay on Metals. These, combined with the
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Mixtures
KEY TERMS ALLOY:
A mixture of two or more
out; rather, it has various regions possessing different properties. An example of a
metals. A term describing a solu-
mixture is sand in a container of water.
tion in which a substance or substances are
Rather than dissolving to form a homoge-
dissolved in water.
neous mixture, as sugar would, the sand
AQUEOUS:
ATOM:
The smallest particle of an
sinks to the bottom. HOMOGENEOUS:
element. CHEMICAL SPECIES:
A generic term
used for any substance studied in chemistry—whether it be an element, compound, mixture, atom, molecule, ion, and
a mixture that is the same throughout, as for example when sugar is fully dissolved in water. A solution is a homogenous mixture. IMMISCIBLE:
so forth. A substance made up of
COMPOUND:
atoms of more than one element, which are chemically bonded and usually joined in molecules. The composition of a com-
A term describing
Possessing a negligible
value of miscibility. ION:
An atom or group of atoms that
has lost or gained one or more electrons, and thus has a net electric charge. A qualitative term iden-
pound is always the same, unless it is
MISCIBILITY:
changed chemically.
tifying the relative ability of two substances
DISPERSION:
A term describing the
distribution of particles in a fluid. ELEMENT:
A substance made up of
only one kind of atom. Unlike compounds, elements cannot be chemically broken down into other substances. EMULSIFIER: EMULSION:
A surfactant. A mixture of two immis-
to dissolve in one another. MIXTURE:
A substance with a variable
composition, meaning that it is composed of molecules or atoms of differing types. Compare with pure substance or compound. MOLECULE:
A group of atoms, usual-
ly but not always representing more than one element, joined in a structure.
cible liquids such as oil and water, made by
Compounds are typically made of up
dispersing microscopic droplets of one liq-
molecules.
uid in another. In creating an emulsion, surfactants act as bridges between the two liquids.
PHENOMENOLOGICAL:
A
term
describing scientific definitions based purely on experimental phenomena. These
A substance with the ability to
only convey part of the picture, however—
flow. In physical sciences such as chemistry
primarily, the part a chemist can perceive
and physics, “fluid” refers both to liquids
either through measurement or through
and gases.
the senses, such as sight. A structural defi-
FLUID:
HETEROGENEOUS:
A term describ-
ing a mixture that is not the same through-
S C I E N C E O F E V E RY DAY T H I N G S
nition is therefore usually preferable to a phenomenological one.
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Mixtures
KEY TERMS PURE SUBSTANCE:
A substance that
CONTINUED
STRUCTURAL:
A term describing sci-
has the same composition throughout.
entific definitions based on aspects of
Pure substances are either elements or
molecular structure rather than purely
compounds, and should not be confused
phenomenological data.
with mixtures. A homogeneous mixture is SURFACTANT:
although it has an unvarying composition,
of molecules that are both water- and oil-
it cannot be reduced to a single type of
soluble, which acts as an agent for joining
atom or molecule.
other substances in an emulsion.
SOLUTION:
A homogeneous mixture A term that refers to a
in which one or more substances is dis-
SUSPENSION:
solved in another substances—for exam-
mixture in which solid particles are sus-
ple, sugar dissolved in water.
pended in a fluid.
metal’s crystalline structure, create a situation in which internal bonding is very strong, but nondirectional. As a result, most metals form alloys, but again, this is not the same as a compound: the elemental metals retain their identity in these metal composites, forming characteristic fibers, beads, and other shapes. S O M E FA M O U S A L LOY S . One of the most important alloys in early human history was a 25:75 mixture of tin and copper that gave its name to an entire stage of technological development: the Bronze Age (c. 3300-1200 B.C.). This combination formed a metal much stronger than either copper or tin, and bronze remained dominant until the discovery of new iron-smelting methods ushered in the Iron Age in about 1200 B.C.
Another important alloy of the ancient world was brass, which is about one-third zinc to two-thirds copper. Introduced in the period c. 1400-c. 1200 B.C, brass was one of the metals that defined the world in which the Bible was written. Biblical references to it abound, as in the famous passage from I Corinthians 13 (read at many weddings), in which the Apostle Paul proclaims that “without love, I am as sounding brass.” Some biblical scholars, however, maintain that some of the references to brass in the Old Testament are actually mistranslations of “bronze.”
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A substance made up
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Tin, copper, and antimony form pewter, a soft mixture that can be molded when cold and beaten regularly without turning brittle. Though used in Roman times, it became most popular in England from the fourteenth to the eighteenth centuries, when it offered a cheap substitute for silver in plates, cups, candelabra, and pitchers. The pewter turned out by colonial American metalsmiths is still admired for its beauty and functionality. As for iron, it appears in nature as an impure ore, but even when purified, it is typically alloyed with other elements. Among the well-known forms of iron are cast iron, a variety of mixtures containing carbon and/or silicon; wrought iron, which contains small amounts of various other elements, such as nickel, cobalt, copper, chromium, and molybdenum; and steel. Steel is a mixture of iron with manganese and chromium, purified with a blast of hot air. Steel is also sometimes alloyed with aluminum in a one-third/twothirds mixture to make duraluminum, developed for the superstructures of German zeppelins during World War I. WHERE TO LEARN MORE “All About Colloids.” Synthashield (Web site). (June 6, 2001). Carona, Phillip B. Magic Mixtures: Alloys and Plastics. Englewood Cliffs, NJ: Prentice Hall, 1963.
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ChemLab. Danbury, CT: Grolier Educational, 1998. “Corrosion of Alloys.” Corrosion Doctors (Web site). (June 6, 2001). “Emulsions.” Pharmweb (Web site). (June 6, 2001). Hauser, Jill Frankel. Super Science Concoctions: 50 Mysterious Mixtures for Fabulous Fun. Charlotte, VT: Williamson Publishing, 1996.
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Knapp, Brian J. Elements, Compounds, and Mixtures. Danbury, CT: Grolier Educational, 1998.
Mixtures
Maton, Anthea. Exploring Physical Science. Upper Saddle River, NJ: Prentice Hall, 1997. Patten, J. M. Elements, Compounds, and Mixtures. Vero Beach, FL: Rourke Book Company, 1995. The Soap and Detergent Association (Web site). (June 6, 2001).
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S O LU T I O N S Solutions
CONCEPT We are most accustomed to thinking of solutions as mixtures of a substance dissolved in water, but in fact the meaning of the term is broader than that. Certainly there is a special place in chemistry for solutions in which water—”the universal solvent”—provides the solvent medium. This is also true in daily life. Coffee, tea, soft drinks, and even water itself (since it seldom appears in pure form) are solutions, but the meaning of the term is not limited to solutions involving water. Indeed, solutions do not have to be liquid; they can be gaseous or solid as well. One of the most important solutions in the world, in fact, is the air we breathe, a combination of nitrogen, oxygen, noble gases, carbon dioxide, and water vapor. Nonetheless, aqueous or water-based substances are the focal point of study where solutions are concerned, and reactions that take place in an aqueous solution provide an important area of study.
HOW IT WORKS Mixtures Solutions belong to the category of substances identified as mixtures, substances with variable composition. This may seem a bit confusing, since among the defining characteristics of a solution are its uniformity and consistency. But this definition of a solution involves external qualities—the things we can observe with our senses—whereas a mixture can be distinguished from a pure substance not only in terms of external characteristics, but also because of its internal and structural properties.
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At one time, chemists had a hard time differentiating between mixtures and pure substances (which are either elements or compounds), primarily because they had little or no knowledge of those “internal and structural properties.” Externally, a mixture and compound can be difficult to distinguish, but the “variable composition” mentioned above is a key factor. Coffee can be almost as weak as water, or so strong it seems to galvanize the throat as it goes down—yet in both cases, though its composition has varied, it is still coffee. By contrast, if a compound is altered by the variation of just one atom in its molecular structure, it becomes something else entirely. When an oxygen atom bonds with a carbon and oxygen atom, carbon monoxide—a poisonous gas produced by the burning of fossil fuels—is turned into carbon dioxide, an essential component of the interaction between plants and animals in the natural environment. MIXTURES VS. COMPOUNDS: T H R E E D I S T I N C T I O N S . Air (a mix-
ture) can be distinguished from a compound, such as carbon dioxide, in three ways. First, a mixture can exist in virtually any proportions among its constituent parts, whereas a compound has a definite and constant composition. Air can be oxygen-rich or oxygen-poor, but if we vary the numbers of oxygen atoms chemically bonded to form a compound, the result is an entirely different substance. Second, the parts of a mixture retain most of their properties when they join together, but elements—once they form a compound—lose their elemental characteristics. If pieces of carbon were floating in the air, their character would be quite
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Solutions
WATER
AND OIL DROPLETS EXPOSED TO POLARIZED LIGHT.
WATER
AND OIL HAVE VERY LITTLE MISCIBILITY WITH
REGARD TO ONE ANOTHER, MEANING THAT THEY TEND TO REMAIN SEPARATE WHEN COMBINED. (Science Pictures
Limited/Corbis. Reproduced by permission.)
different from that of the carbon in carbon dioxide. Carbon, in its natural form, is much like coal or graphite (graphite is pure carbon, and coal an impure form of the element), but when a carbon atom combines with an oxygen atom, the two form a gas. Pieces of carbon in the air, on the other hand, would be solid, as carbon itself is. Third, a mixture can usually be created simply by the physical act of stirring items together, and/or by applying heat. Certainly this is true of many solutions, such as brewed coffee. On the other hand, a compound such as carbon dioxide can only be formed by the chemical reaction of atoms in specific proportions and at specific temperatures. Some such reactions consume heat, whereas others produce it. These interactions of heat are highly complex; on the other hand, in making coffee, heat is simply produced by an external source (the coffee maker) and transferred to the coffee in the brewing process.
said to be the same throughout. It is thus a heterogeneous mixture. The same is true of cold tea when table sugar (sucrose) is added to it: the sugar drifts to the bottom, and as a result, the first sip of tea from the glass is not nearly as sweet as the last. Wood is a mixture that typically appears in heterogeneous form, a fact that can be easily confirmed by studying wood paneling. There are knots, for instance—areas where branches once grew, and where the concentrations of sap are higher. Striations of color run through the boards of paneling, indicating complex variations in the composition of the wood. Much the same is true of soil, with a given sample varying widely depending on a huge array of factors: the concentrations of sand, rock, or decayed vegetation, for instance, or the activities of earthworms and other organisms in processing the soil.
basic types of mixtures. One of these occurs, for instance, when sand is added to a beaker of water: the sand sinks to the bottom, and the composition of the sand-water mixture cannot be
In a homogeneous mixture, by contrast, there is no difference between one area of the mixture and another. If coffee has been brewed properly, and there are no grounds at the bottom of the pot, it is homogeneous. If sweetener is added to tea while it is hot, it too should yield a homogeneous mixture.
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HETEROGENEOUS AND HOMOGENEOUS MIXTURES. There are two
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MISCIBILITY
Solutions
AND
S O LU B I L I -
T Y. Miscibility is a term describing the relative
ability of two substances to dissolve in one another. Generally, water and water-based substances have high miscibility with regard to one another, as do oil and oil-based substances. Oil and water, on the other hand (or substances based in either) have very low miscibility. The reasons for this will be discussed below. Miscibility is a qualitative term like “fast” or “slow”; on the other hand, solubility—the maximum amount of a substance that dissolves in a given amount of solvent at a specific temperature—can be either qualitative or quantitative. In a general sense, the word is qualitative, referring to the property of being soluble, or able to dissolve in a solution.
WATER
COMPLETELY MISCIBLE, 99% WATER AND 1% ETHANOL, 50% OF BOTH, OR 99% ETHANOL AND 1% WATER. SHOWN HERE IS A GLASS OF BEER—AN EXAMPLE OF A WATER -ETHANOL SOLUTION. (Owen AND
ETHANOL
ARE
WHETHER THE SOLUTION BE
Franken/Corbis. Reproduced by permission.)
Solutions and Solubility Virtually all varieties of homogeneous mixtures can be classified as a solution—that is, a homogeneous mixture in which one or more substances is dissolved in another substance. If two or more substances were combined in exactly equal proportions, this would technically not be a solution; hence the distinction between solutions and the larger class of homogeneous mixtures. A solution is made up of two parts: the solute, the substance or substances that are dissolved; and the solvent, the substance that dissolves the solute. The solvent typically determines the physical state of the solution: in other words, if the solvent is a liquid, the solution will most likely be a liquid. Likewise if the solvent is a solid such as a metal, melted at high temperatures to form a metallic solution called an alloy, then when the solution is cooled to its normal temperature, it will be solid again.
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At some points in this essay, “solubility” will be used in this qualitative sense; however, within the realm of chemistry, it also has a quantitative meaning. In other words, instead of involving an imprecise quality such as “fast” or “slow,” solubility in this sense relates to precise quantities more along the lines of “100 MPH (160.9 km/h).” Solubility is usually expressed in grams (g) (0.0022 lb) of solute per 100 g (0.22 lb) of solvent. O T H E R Q UA N T I TAT I V E T E R M S .
Another quantitative means of describing a solution is in terms of mass percent: the mass of the solute divided by the mass of the solution, and multiplied by 100%. If there are 25 g of solute in a solution of 200 g, for instance, 25 would be divided by 200 and multiplied by 100% to yield a 12.5% figure of solution composition. Molarity also provides a quantitative means of showing the concentration of solute to solution. Whereas mass percent is, as its name indicates, a comparison of the mass of the solute to that of the solvent, molarity shows the amount of solute in a given volume of solution. This is measured in moles of solute per liter of solution, abbreviated mol/l.
REAL-LIFE A P P L I C AT I O N S Saturation and Dilution The quantitative terms for describing solubility that we have reviewed are useful to a professional chemist, or to anyone performing work in a laboratory. For the most part, however, qualita-
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tive expressions will suffice for the present discussion. Among the most useful qualitative terms is saturation. When it is possible to dissolve solute in a solvent, the solution is said to be unsaturated— rather like a sponge that has not been filled to capacity with liquid. By contrast, a solution that contains as much solute as it can at a given temperature is like a sponge that has been filled with all the liquid it can possibly contain. It can no longer absorb more of the liquid; rather, it can only push liquid particles along, and the sponge is said to be saturated. In the same way, if tea is hot, it is easier to introduce sugar to it, but when the temperature is low, sugar will not dissolve as easily. SAT U RAT I O N A N D T E M P E RA T U R E . With tea and many other substances,
higher temperatures mean that a greater amount of solute can be added before the solution is fully saturated. The reason for this relationship between saturation and temperature, according to generally accepted theory, is that heated solvent particles move more quickly than cold ones, and as a result, create more space into which the solvent can fit. Indeed, “space” is a prerequisite for a solution: the molecules of solute need to find a “hole” between the molecules of solvent into which they can fit. Thus the molecules in a solution can be compared to a packed crowd: if a crowd is suddenly dispersed, it is easier to walk through it. Not all substances respond to rises in temperature in the manner described, however. As a rule, gases (with the exception of helium) are more soluble at lower temperatures than at higher ones. Higher temperatures mean an increase in kinetic energy, with more molecules colliding with one another, and this makes it easier for the gases to escape the liquid in which they are dissolved. Carbonated soft drinks get their “fizz” from carbon dioxide gas dissolved, along with sugar and other flavorings, in a solution of water. When the soft-drink container is opened, much of the carbon dioxide quickly departs, while a certain proportion stays dissolved in the cola. The remaining carbon dioxide will eventually escape as well, but it will do so more quickly if left in a warm environment rather than a cold one, such as the inside of a refrigerator.
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D I LU T I O N A N D C O N C E N T RA T I O N . Another useful set of qualitative terms
Solutions
for solutions also relates to the relative amount of solute that has been dissolved. But whereas saturation is an absolute condition at a certain temperature (in other words, the solution is definitely saturated at such-and-such a temperature), concentration and dilution are much more relative terms. When a solution contains a relatively small amount of solute, it is said to be dilute; on the other hand, a solution with a relatively large amount of solute is said to be concentrated. For instance, hydrogen peroxide (H2O2) as sold over the counter in drug stores, to be used in homes as a disinfectant of bleaching agent, is a dilute 3% solution in water. In higher concentrations, hydrogen peroxide can cause burns to human skin, and is used to power rockets. Chemists often keep on hand in their laboratories concentrated versions of various frequently used solutions. Maintaining them in concentrated form saves space; when more of a solution is needed, the chemist dilutes it in water according to desired molarity values. To do so, the chemist determines how much water needs to be added to a particular “stock solution” (as these concentrated solutions in a laboratory are called) to create a solution of a particular concentration. In the dilution with water, the number of moles of the solute does not change; rather, the particles of solute are dispersed over a larger volume.
“Like Dissolves Like” In the molecules of a compound, the atoms are held together by powerful attractions. The molecules within a compound, however, also have an intermolecular attraction, but this is much weaker than the interatomic bonds in a molecule. It is thus quite possible for the molecules in a solution to exert a greater attractive force than the one holding the molecules of solute together with one another. When this happens, the solute dissolves. A useful rule of thumb when studying solutions is “like dissolves like.” In other words, water dissolves water-based solutes, whereas oil dissolves oily substances. Or to put it another way, water and water-based substances are miscible with one another, as are oil and oil-based substances. Water and oil together, however, are largely immiscible.
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P O L A R W AT E R , N O N P O L A R O I L . Water and oil and immiscible due to their
respective molecule structures, and hence their inherent characteristics of intermolecular bonding. Water molecules are polar, meaning that the positive electric charge is at one end of the molecule, while the negative charge is at the other end. Oil, on the other hand, is nonpolar—charges are more evenly distributed throughout the molecule. The oxygen atom in a water molecule has a much greater electronegativity than the hydrogen atoms, so it pulls negatively charged electrons to its end of the molecule. Conversely, most oils are composed of carbon and hydrogen, which have similar values of electronegativity. As a result, positive and negative charges are distributed evenly throughout the oil molecule. Whereas a water molecule is like a magnet with a north and south pole, an oil molecule is like a nonmagnetic metal. Thus, as most people know, “oil and water don’t mix.” The immiscible quality of oil and water in relation to one another explains a number of phenomena from the everyday world. It is easy enough to wash mud from your hands under running water, because the water and the mud (which, of course, contains water) are highly miscible. But motor oil or oil-based paint will leave a film on the hands, as these substances bond to oily molecules in the skin itself, and no amount of water will wash the film off. To remove it, one needs mineral spirits, paint thinner, or soap manufactured to bond with the oils. Everyone has had the experience of eating spicy foods and then trying to cool down the mouth with cold water—and just about everyone has discovered that this does not work. This is because most spicy substances contain emulsified oils that coat the tongue, and these oils are not attracted to water. A much better “solution” (in more ways than one) is milk, and in particular, whole milk. Though a great deal of milk is composed of water, it also contains tiny droplets of fats and proteins that join with the oils in spicy substances, thus cooling down the mouth.
How does the soap manage to “connect” both with oils and water? Likewise, how does milk—which is water-soluble and capable of dilution in water—wash away the oils associated with spicy food? To answer these questions, we need to briefly consider a subject examined in more depth within the Mixtures essay: emulsions, or mixtures of two immiscible liquids. E M U L S I F I E R S A N D S U R FAC TA N T S . The dispersion of two substances in
an emulsion is achieved through the use of an emulsifier or surfactant. Made up of molecules that are both water- and oil-soluble, an emulsifier or surfactant acts as an agent for joining other substances in an emulsion. The two words are virtually synonymous, but “emulsifier” is used typically in reference to foods, whereas “surfactant” most often refers to an ingredient in detergents and related products. In an emulsion, millions of surfactants surround the dispersed droplets of solute, known as the internal phase, shielding them from the solvent, or external phase. Surfactants themselves are often used in laundry or dish detergent, because most stains on plates or clothes are oilbased, whereas the detergent itself is applied to the clothes in a water-based external phase. The emulsifiers in milk help to bond oily particles of milk fat (cream) and protein to the external phase of water that comprises the majority of milk’s volume.
The active ingredient in a dry-cleaning chemical usually has nonpolar molecules, because the toughest stains are made by oils and greases. But
As for soap, it is a mixture of an acid and a base—specifically, carboxylic acids joined with a base such as sodium hydroxide. Carboxylic acids, chains of hydrogen and carbon atoms, are just some of many hydrocarbons that form the chemical backbone of a vast array of organic substances. Because it is a salt, meaning that it is formed from the reaction of an acid with a base, soap partially separates into its component ions in water. The active ion is RCOO- (R stands for
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what about ordinary soap, which we use in water to wash both water- and oil-based substances from our bodies? Though, as noted earlier, certain kinds of oil stains require special cleaning solutions, ordinary soap is fine for washing off the natural oils secreted by the skin. Likewise, it can wash off small concentrations of oil that come from the environment and attach to the skin—for instance, from working over a deep fryer in a fast-food restaurant.
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the hydrocarbon chain), whose two ends behave in different fashions, making it a surfactant. The hydrocarbon end (R-) is said to be lipophilic, or “oil-loving”; on the other hand, the carboxylate end (-COO-) is hydrophilic, or “water-loving.” As a result, soap can dissolve in water, but can also clean greasy stains. When soap is mixed with water, it does not form a true solution, due to the presence of the hydrocarbons, which attract one another to form spherical aggregates called micelles. The lipophilic “tails” of the hydrocarbons are turned toward the interior of the micelle, while the hydrophilic “heads” remain facing toward the water that forms the external phase. E T H A N O L . When a hydrocarbon joins with other substances in one of the hydrocarbon functional groups, these form numerous hydrocarbon derivatives. Among the hydrocarbon derivatives is alcohol, and within this grouping is ethyl alcohol or ethanol, which includes a hydrocarbon bonded to the –OH functional group. The formula for ethanol is C2H6O, though this is sometimes rendered as C2H5OH to show that the alcohol functional group (–OH) is bonded to the hydroxyl radical (C2H5).
Ethanol, the same alcohol found in alcoholic beverages, is obviously miscible with water. Beer, after all, is mostly water, and if ethanol and water were not miscible, it would be impossible to mix alcohol with water or a water-based substance to make Scotch and water or a Bloody Mary (vodka and tomato juice.) In fact, water and ethanol are completely miscible, whether the solution be 99% water and 1% ethanol, 50% of both, or 99% ethanol and 1% water. How can this be, given the fact that ethanol is a hydrocarbon derivative—in other words, a cousin of petroleum? The addition of the term “derivative” gives us a clue: note that ethanol contains oxygen, just as water does. As in water, the oxygen and hydrogen form a polar bond, giving that portion of the ethanol molecule a high affinity for water. Molecules of water and the alcohol functional group are joined through an intermolecular force called hydrogen bonding.
reactions in aqueous solutions—though we can only touch on them briefly here—constitute a large and significant body of reactions studied by chemists. Most of the solutions we have discussed up to this point are aqueous. We have referred, at least in an external or phenomenological way, to the means by which sugar dissolves in an aqueous solution, such as tea. Now let us consider, from a molecular or structural standpoint, the means by which salt does so as well. SA LT WAT E R. Salt is formed of positively charged sodium ions, firmly bonded to negatively charged chlorine ions. To break these ionic bonds and dissolve the sodium chloride, water must exert a strong attraction. However, salt is not really composed of molecules but simply repeating series of sodium and chlorine atoms joined together in a simple face-centered cubic lattice which has each each sodium ion (Na+) surrounded by six chlorine ions (Cl–); at the same time, each chlorine ion is surrounded by six sodium ions.
In dissolving the salt, water molecules surround ions that make up the salt, holding them in place through the electrical attraction of opposite charges. Due to the differences in electronegativity that give the water molecule its high polarity, the hydrogen atoms are more positively charged, and thus these attract the negatively charged chlorine ion. Similarly, the negatively charged oxygen end of the water molecule attracts the positively charged sodium ion. As a result, the salt is “surrounded” or dissolved. P LAS M A A N D AQ U E O U S - S O LUTION REACTIONS IN THE B O DY. Whereas saltwater is an aqueous solu-
tion that can eventually kill someone who drinks it, plasma is an essential component of the life process—and in fact, it contains a small quantity of sodium chloride. Not to be confused with the phase of matter also called plasma, this plasma is the liquid portion of blood. Blood itself is about 55% plasma, with red and white blood cells and platelets suspended in it.
The term aqueous refers to water, and because water has extraordinary solvent qualities (discussed in the Osmosis essay) it serves as the medium for numerous solutions. Furthermore,
Plasma is in turn approximately 90% water, with a variety of other substances suspended or dissolved in it. Prominent among these substances are proteins, of which there are about 60 in plasma, and these serve numerous important functions—for instance, as antibodies. Plasma
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Aqueous Solutions
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Solutions
KEY TERMS A term describing a solu-
out; rather, it has various regions possess-
tion in which a substance or substances are
ing different properties. One example of
dissolved in water.
this is sand in a container of water. Rather
AQUEOUS:
A substance made up of
than dissolving to form a homogeneous
atoms of more than one element, which are
mixture as sugar does, the sand sinks to the
chemically bonded and usually joined in
bottom.
COMPOUND:
molecules. The composition of a com-
HOMOGENEOUS:
A term describing
pound is always the same, unless it is
a mixture that is the same throughout, as
changed chemically.
for example when sugar is fully dissolved
CONCENTRATED:
A qualitative term
describing a solution with a relatively large
in water. A solution is a homogenous mixture.
ratio of solute to solvent. IMMISCIBLE: DILUTE:
A qualitative term describing
Possessing a negligible
value of miscibility.
a solution with a relatively small ratio of MASS
solute to solvent. A surfactant. (Usually
EMULSIFIER:
the term “emulsifier” is applied to foods, and “surfactant” to detergents and other inedible products.)
A quantitative
means of measuring solubility in terms of the mass of the solute divided by the mass of the solution, multiplied by 100%. MISCIBILITY:
A term identifying the
A mixture of two immis-
relative ability of two substances to dissolve
cible liquids, such as oil and water, made by
in one another. Miscibility is qualitative,
dispersing microscopic droplets of one liq-
like “fast” or “slow”; solubility, on the other
uid in another. In creating an emulsion,
hand, can be a quantitative term.
EMULSION:
surfactants act as bridges between the two liquids. HETEROGENEOUS:
MIXTURE:
A substance with a variable
composition, composed of molecules or A term describ-
ing a mixture that is not the same through-
also contains ions, which prevent red blood cells from taking up excess water in osmosis. Prominent among these ions are those of salt, or sodium chloride. Plasma also transports nutrients such as amino acids, glucose, and fatty acids, as well as waste products such as urea and uric acid, which it passes on to the kidneys for excretion. Much of the activity that sustains life in the body of a living organism can be characterized as a chemical reaction in an aqueous solution. When we breathe in oxygen, it is taken to the lungs and fed into the bloodstream, where it
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atoms of differing types. Compare with pure substance.
associates with the iron-containing hemoglobin in red blood cells and is transported to the organs. In the stomach, various aqueous-solution reactions process food, turning part of it into fuel that the blood carries to the cells, where the oxygen engages in complex reactions with nutrients.
A Miscellany of Solutions Aqueous-solution reactions can lead to the formation of a solid, as when a solution of potassi-
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Solutions
KEY TERMS
CONTINUED
A quantitative means of
apply the word in a quantitative sense, to
showing the concentration of solute to
indicate the maximum amount of a sub-
solution. This is measured in moles of
stance that dissolves in a given amount of
solute per liter of solution, abbreviated
solvent at a specific temperature. Solubility
mol/L.
is usually expressed in grams of solute per
MOLARITY:
PURE SUBSTANCE:
A substance—
100 g of solvent.
either an element or compound—that has
SOLUBLE:
an unvarying composition. This means
solvent.
that by changing the proportions of atoms,
SOLUTE:
Capable of dissolving in a
The substance or substances
the result would be an entirely different
that are dissolved in a solvent to form a
substance. Compare with mixture.
solution.
Involving a compari-
QUALITATIVE:
A homogeneous mixture
SOLUTION:
son between qualities that are not precisely
in which one or more substances (the
defined, such as “fast” and “slow” or
solute) is dissolved in a solvent—for exam-
“warm” and “cold.”
ple, sugar dissolved in water. Involving a compari-
QUANTITATIVE:
SOLVENT:
The substance or sub-
son between precise quantities—for
stances that dissolve a solute to form a
instance, 10 lb vs. 100 lb, or 50 MPH vs. 120
solution.
MPH. SURFACTANT:
term
of molecules that are both water- and oil-
describing a solution that contains as
soluble, which acts as an agent for joining
much solute as it can dissolve at a given
other substances in an emulsion.
SATURATED:
A
qualitative
A substance made up
temperature. UNSATURATED:
A term describing a
In a broad, qualitative
solution that is capable of dissolving
sense, solubility refers to the property of
additional solute, if that solute is intro-
being soluble. Chemists, however, usually
duced to it.
SOLUBILITY:
um chromate (K2CrO4) is added to an aqueous solution of barium nitrate (Ba[NO3]2 to form solid barium chromate (BaCrO4) and a solution of potassium nitrate (KNO3). This reaction is described in the essay on Chemical Reactions.
ments (those in which two atoms join to form a molecule of a single element); monatomic elements (those elements that exist as single atoms); one element in a triatomic molecule; and two compounds.
We have primarily discussed liquid solutions, and in particular aqueous solutions. It should be stressed, however, that solutions can also exist in the gaseous or solid phases. The air we breathe is a solution, not a compound: in other words, there is no such thing as an “air molecule.” Instead, it is made up of diatomic ele-
The “solvent” in air is nitrogen, a diatomic element that accounts for 78% of Earth’s atmosphere. Oxygen, also diatomic, constitutes an additional 21%. Argon, which like all noble gases is monatomic, ranks a distant third, with 0.93%. The remaining 0.07% is made up of traces of other noble gases; the two compounds men-
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tioned, carbon dioxide and water (in vapor form); and, high in the atmosphere, the triatomic form of oxygen known as ozone (O3). The most significant solid solutions are alloys of metals, discussed in the essay on Mixtures, as well as in essays on various metal families, particularly the Transition Metals. Some well-known alloys include bronze (three-quarters copper, one-quarter tin); brass (two-thirds copper, one-third zinc); pewter (a mixture of tin and copper with traces of antimony); and numerous alloys of iron—particularly steel—as well as alloys involving other metals. WHERE TO LEARN MORE
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Hauser, Jill Frankel. Super Science Concoctions: 50 Mysterious Mixtures for Fabulous Fun. Charlotte, VT: Williamson Publishing, 1996. “Introduction to Solutions” (Web site). (June 6, 2001). Knapp, Brian J. Air and Water Chemistry. Illustrated by David Woodroffe. Danbury, CT: Grolier Educational, 1998. Seller, Mick. Elements, Mixtures, and Reactions. New York: Shooting Star Press, 1995. “Solubility.” Spark Notes (Web site). (June 6, 2001). “Solutions and Solubility” (Web site). (June 6, 2001).
“Aqueous Solutions” (Web site). (June 6, 2001).
Watson, Philip. Liquid Magic. Illustrated by Elizabeth Wood and Ronald Fenton. New York: Lothrop, Lee, and Shepard Books, 1982.
Gibson, Gary. Making Things Change. Brookfield, CT: Copper Beech Books, 1995.
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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Osmosis
CONCEPT The term osmosis describes the movement of a solvent through a semipermeable membrane from a less concentrated solution to a more concentrated one. Water is sometimes called “the perfect solvent,” and living tissue (for example, a human being’s cell walls) is the best example of a semipermeable membrane. Osmosis has a number of life-preserving functions: it assists plants in receiving water, it helps in the preservation of fruit and meat, and is even used in kidney dialysis. In addition, osmosis can be reversed to remove salt and other impurities from water.
HOW IT WORKS If you were to insert a hollow tube of a certain diameter into a beaker of water, the water would rise inside the tube and reach the same level as the water outside it. But suppose you sealed the bottom end of the tube with a semipermeable membrane, then half-filled the tube with salt water and again inserted it into the beaker. Over a period of time, the relative levels of the salt water in the tube and the regular water in the beaker would change, with the fresh water gradually rising into the beaker. This is osmosis at work; however, before investigating the process, it is necessary to understand at least three terms. A solvent is a liquid capable of dissolving or dispersing one or more other substances. A solute is the substance that is dissolved, and a solution is the resulting mixture of solvent and solute. Hence, when you mix a packet of sugar into a cup of hot coffee, the coffee—which is mostly water—acts as a solvent for the sugar, a solute, and the resulting sweetened coffee is a solution. (Indeed, people who need a
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cup of coffee in the morning might say that it is a “solution” in more ways than one!) The relative amount of solute in the solution determines whether it can be described as more or less concentrated.
Water and Oil: Molecular Differences In the illustrations involving the beaker and the hollow tube, water plays one of its leading roles, as a solvent. It is possible to use a number of other solvents for osmosis, but most of the ones that will be discussed here are water-based substances. In fact, virtually everything people drink is either made with water as its central component (soft drinks, coffee, tea, beer and spirits), or comes from a water-based plant or animal life form (fruit juices, wine, milk.) Then of course there is water itself, still the world’s most popular drink. By contrast, people are likely to drink an oily product only in extreme circumstances: for instance, to relieve constipation, holistic-health practitioners often recommend a mixture of olive oil and other compounds for this purpose. Oil, unlike water, has a tendency to pass straight through a person’s system, without large amounts of it being absorbed through osmosis. In fact, oil and water differ significantly at the molecular level. Water is the best example of a polar molecule, sometimes called a dipole. As everyone knows, water is a name for the chemical H2O, in which two relatively small hydrogen atoms bond with a large atom of oxygen. You can visualize a water molecule by imagining oxygen as a basketball with hydrogen as two baseballs fused to the
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A
SEMIPERMEABLE MEMBRANE PERMITS ONLY CERTAIN COMPONENTS OF SOLUTIONS, USUALLY THE SOLVENT, TO PASS
THROUGH.
basketball’s surface. Bonded together as they are, the oxygen tends to pull electrons from the hydrogen atoms, giving it a slight negative charge and the hydrogen a slight positive charge. As a result, one end of a water molecule has a positive electrical charge, and the other end a negative charge. This in turn causes the positive end of one molecule to attract the negative side of its neighbor, and vice versa. Though the electromagnetic force is weak, even in relative terms, it is enough to bond water molecules tightly to one another.
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across the surface of the molecule. Hence, the bond between oil molecules is much less tight than for water molecules. Clean motor oil in a car’s crankshaft behaves as though it were made of millions of tiny ball-bearings, each rolling through the engine without sticking. Water, on the other hand, has a tendency to stick to surfaces, since its molecules are so tightly bonded to one another.
By contrast, oily substances—whether the oil is animal-, vegetable-, or petroleum-based— are typically nonpolar, meaning that the positive and negative charges are distributed evenly
This tight bond gives water highly unusual properties compared to other substances close to its molecular weight. Among these are its high boiling point, its surprisingly low density when frozen, and the characteristics that make osmosis possible. Thanks to its intermolecular structure, water is not only an ideal solvent, but its closely
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Osmosis
OSMOSIS
EQUALIZES CONCENTRATION.
packed structure enables easy movement, as, for instance, from an area of low concentration to an area of high concentration. In the beaker illustration, the “pure” water is almost pure solvent. (Actually, because of its solvent qualities, water seldom appears in a pure state unless one distills it: even water flowing through a “pure” mountain stream carries all sorts of impurities, including microscopic particles of the rocks over which it flows.) In any case, the fact that the water in the beaker is almost pure makes it easy for it to flow through the semipermeable membrane in the bottom of the tube. By contrast, the solute particles in the saltwater solution have a much harder time passing through, and are much more likely to block the openings in the membrane. As a result, the movement is all in one direction: water in the beaker moves through the membrane, and into the tube. A few points of clarification are in order here. A semipermeable membrane is anything with a structure somewhere between that of, say, plastic on the one hand and cotton on the other. Were the tube in the beaker covered with Saran wrap, for instance, no water would pass through. On the other hand, if one used a piece of cotton in the bottom of the tube, the water would pass straight through without osmosis taking place. In contrast to cotton, Gore-tex is a fabric containing
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a very thin layer of plastic with billions of tiny pores which let water vapor flow out without allowing liquid water to seep in. This accounts for the popularity of Gore-tex for outdoor gear—it keeps a person dry without holding in their sweat. So Gore-tex would work well as a semipermeable membrane. Also, it is important to consider the possibilities of what can happen during the process of osmosis. If the tube were filled with pure salt, or salt with only a little water in it, osmosis would reach a point and then stop due to osmotic pressure within the substance. Osmotic pressure results when a relatively concentrated substance takes in a solvent, thus increasing its pressure until it reaches a point at which the solution will not allow any more solvent to enter.
REAL-LIFE A P P L I C AT I O N S Cell Behavior and Salt Water Cells in the human body and in the bodies of all living things behave like microscopic bags of solution housed in a semipermeable membrane. The health and indeed the very survival of a person, animal, or plant depends on the ability of
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IN
THIS
1966
PHOTO, A GIRL IS UNDERGOING KIDNEY DIALYSIS, A CRUCIAL MODERN MEDICAL APPLICATION THAT
RELIES ON OSMOSIS. (Bettmann/Corbis. Reproduced by permission.)
the cells to maintain their concentration of solutes. Two illustrations involving salt water demonstrate how osmosis can produce disastrous effects in living things. If you put a carrot in salty water, the salt water will “draw” the water from inside the carrot—which, like the human body and most other forms of life, is mostly made up of water. Within a few hours, the carrot will be limp, its cells shriveled. Worse still is the process that occurs when a person drinks salt water. The body can handle a little bit, but if you were to consume nothing but salt water for a period of a few days, as in the case of being stranded on the proverbial desert island, the osmotic pressure would begin drawing water from other parts of your body. Since a human body ranges from 60% water (in an adult male) to 85% in a baby, there would be a great deal of water available—but just as clearly, water is the essential ingredient in the human body. If you continued to ingest salt water, you would eventually experience dehydration and die.
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for them, salt water is an isotonic solution, or one that has the same concentration of solute—and hence the same osmotic pressure—as in their own cells.
Osmosis in Plants Plants depend on osmosis to move water from their roots to their leaves. The further toward the edge or the top of the plant, the greater the solute concentration, which creates a difference in osmotic pressure. This is known as osmotic potential, which draws water upward. In addition, osmosis protects leaves against losing water through evaporation. Crucial to the operation of osmosis in plants are “guard cells,” specialized cells dispersed along the surface of the leaves. Each pair of guard cells surrounds a stoma, or pore, controlling its ability to open and thus release moisture.
How, then, do fish and other forms of marine life survive in a salt-water environment? In most cases, a creature whose natural habitat is the ocean has a much higher solute concentration in its cells than does a land animal. Hence,
In some situations, external stimuli such as sunlight may cause the guard cells to draw in potassium from other cells. This leads to an increase in osmotic potential: the guard cell becomes like a person who has eaten a dry biscuit, and is now desperate for a drink of water to wash it down. As a result of its increased osmotic potential, the guard cell eventually takes on
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water through osmosis. The guard cells then swell with water, opening the stomata and increasing the rate of gas exchange through them. The outcome of this action is an increase in the rate of photosynthesis and plant growth. When there is a water shortage, however, other cells transmit signals to the guard cells that cause them to release their potassium. This decreases their osmotic potential, and water passes out of the guard cells to the thirsty cells around them. At the same time, the resultant shrinkage in the guard cells closes the stomata, decreasing the rate at which water transpires through them and preventing the plant from wilting.
Osmosis and Medicine Osmosis has several implications where medical care is concerned, particularly in the case of the storage of vitally important red blood cells. These are normally kept in a plasma solution which is isotonic to the cells when it contains specific proportions of salts and proteins. However, if red blood cells are placed in a hypotonic solution, or one with a lower solute concentration than in the cells themselves, this can be highly detrimental. Hence water, a life-giving and life-preserving substance in most cases, is a killer in this context. If red blood cells were stored in pure water, osmosis would draw the water into the cells, causing them to swell and eventually burst. Similarly, if the cells were placed in a solution with a higher solute concentration, or hypertonic solution, osmosis would draw water out of the cells until they shriveled. In fact, the plasma solution used by most hospitals for storing red blood cells is slightly hypertonic relative to the cells, to prevent them from drawing in water and bursting. Physicians use a similar solution when injecting a drug intravenously into a patient. The active ingredient of the drug has to be suspended in some kind of medium, but water would be detrimental for the reasons discussed above, so instead the doctor uses a saline solution that is slightly hypertonic to the patient’s red blood cells. One vital process closely linked to osmosis is dialysis, which is critical to the survival of many victims of kidney diseases. Dialysis is the process by which an artificial kidney machine removes waste products from a patients’ blood—performing the role of a healthy, normally function-
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ing kidney. The openings in the dialyzing membrane are such that not only water, but salts and other waste dissolved in the blood, pass through to a surrounding tank of distilled water. The red blood cells, on the other hand, are too large to enter the dialyzing membrane, so they return to the patient’s body.
Osmosis
Preserving Fruits and Meats Osmosis is also used for preserving fruits and meats, though the process is quite different for the two. In the case of fruit, osmosis is used to dehydrate it, whereas in the preservation of meat, osmosis draws salt into it, thus preventing the intrusion of bacteria. Most fruits are about 75% water, and this makes them highly susceptible to spoilage. To preserve fruit, it must be dehydrated, which—as in the case of the salt in the meat— presents bacteria with a less-than-hospitable environment. Over the years, people have tried a variety of methods for drying fruit, but most of these have a tendency to shrink and harden the fruit. The reason for this is that most drying methods, such as heat from the Sun, are relatively quick and drastic; osmosis, on the other hand, is slower, more moderate—and closer to the behavior of nature. Osmotic dehydration techniques, in fact, result in fruit that can be stored longer than fruit dehydrated by other methods. This in turn makes it possible to provide consumers with a wider variety of fruit throughout the year. Also, the fruit itself tends to maintain more of its flavor and nutritional qualities while keeping out microorganisms. Because osmosis alone can only remove about 50% of the water in most ripe fruits, however, the dehydration process involves a secondary method as well. First the fruit is blanched, or placed briefly in scalding water to stop enzymatic action. Next it is subjected to osmotic dehydration by dipping it in, or spreading it with, a specially made variety of syrup whose sugar draws out the water in the fruit. After this, air drying or vacuum drying completes the process. The resulting product is ready to eat; can be preserved on a shelf under most climatic conditions; and may even be powdered for making confectionery items. Whereas osmotic dehydration of fruit is currently used in many parts of the world, the salt-
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Osmosis
KEY TERMS HYPERTONIC:
Of higher osmotic
pressure. HYPOTONIC:
Of
lower
osmotic
pressure. ISOTONIC:
Of equal osmotic pressure.
The movement of a solvent through a semipermeable membrane from a less concentrated solution to a more concentrated one.
OSMOSIS:
A difference in osmotic pressure that draws water from an area of less osmotic pressure to an area of greater osmotic pressure. OSMOTIC POTENTIAL:
The pressure that builds in a substance as it experiences osmosis, and eventually stops that process. OSMOTIC PRESSURE:
A liquid capable of dissolving or dispersing one or more other substances. SOLVENT:
SOLUTE: A substance capable of being dissolved in a solvent. SOLUTION:
A mixture of solvent and
solute.
curing of meat in brine is largely a thing of the past, due to the introduction of refrigeration. Many poorer families, even in the industrialized world, however, remained without electricity long after it spread throughout most of Europe and North America. John Steinbeck’s Grapes of Wrath (1939) offers a memorable scene in which a contemporary family, the Joads, kill and cure a pig before leaving Oklahoma for California. And a Web site for Walton Feed, an Idaho company specializing in dehydrated foods, offers reminiscences by Canadians whose families were still salt-curing meats in the middle of the twentieth century. Verla Cress of southern Alberta, for instance, offered a recipe from which the following details are drawn.
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First a barrel is filled with a solution containing 2 gal (7.57 l) of hot water and 8 oz (.2268 kg) of salt, or 32 parts hot water to one part salt, as well as a small quantity of vinegar. The pig or cow, which would have just been slaughtered, should then be cut up into what Cress called “ham-sized pieces (about 10-15 lb [5-7 kg]) each.” The pieces are then soaked in the brine barrel for six days, after which the meat is removed, dried, “and put... in flour or gunny sacks to keep the flies away. Then hang it up in a cool dry place to dry. It will keep like this for perhaps six weeks if stored in a cool place during the Summer. Of course, it will keep much longer in the Winter. If it goes bad, you’ll know it!” Cress offered another method, one still used on ham today. Instead of salt, sugar is used in a mixture of 32 oz (.94 l) to 3 gal (11.36 l) of water. After being removed, the meat is smoked—that is, exposed to smoke from a typically aromatic wood such as hickory, in an enclosed barn—for three days. Smoking the meat tends to make it last much longer: four months in the summer, according to Cress. The Walton Feeds Web page included another brine-curing recipe, this one used by the women of the Stirling, Alberta, Church of the Latter-Day Saints in 1973. Also included were reminiscences by Glenn Adamson (born 1915): “...When we butchered a pig, Dad filled a wooden 45-gal (170.34 l) barrel with salt brine. We cut up the pig into maybe eight pieces and put it in the brine barrel. The pork soaked in the barrel for several days, then the meat was taken out, and the water was thrown away.... In the hot summer days after they [the pieces of meat] had dried, they were put in the root cellar to keep them cool. The meat was good for eating two or three months this way.” For thousands of years, people used salt to cure and preserve meat: for instance, the sailing ships that first came to the New World carried on board barrels full of cured meat, which fed sailors on the voyage over. Meat was not the only type of food preserved through the use of salt or brine, which is hypertonic—and thus lethal—to bacteria cells. Among other items packed in brine were fish, olives, and vegetables. Even today, some types of canned fish come to the consumer still packed in brine, as do olives. Another method that survives is the use of
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sugar—which can be just as effective as salt for keeping out bacteria—to preserve fruit in jam.
Reverse Osmosis Given the many ways osmosis is used for preserving food, not to mention its many interactions with water, it should not be surprising to discover that osmosis can also be used for desalination, or turning salt water into drinking water. Actually, it is not osmosis, strictly speaking, but rather reverse osmosis that turns salt water from the ocean—97% of Earth’s water supply—into water that can be used for bathing, agriculture, and in some cases even drinking. When you mix a teaspoon of sugar into a cup of coffee, as mentioned in an earlier illustration, this is a non-reversible process. Short of some highly complicated undertaking—for instance, using ultrasonic sound waves— it would be impossible to separate solute and solvent. Osmosis, on the other hand, can be reversed. This is done by using a controlled external pressure of approximately 60 atmospheres, an atmosphere being equal to the air pressure at sea level—14.7 pounds-per-square-inch (1.013 ⫻ 105 Pa.) In reverse osmosis, this pressure is applied to the area of higher solute concentration—in this case, the seawater. As a result, the pressure in the seawater pushes water molecules into a reservoir of pure water. If performed by someone with a few rudimentary tools and a knowledge of how to provide just the right amount of pressure, it is possible that reverse osmosis could save the life of a shipwreck victim stranded in a location without a fresh water supply. On the other hand, a person in such a situation may be able to absorb sufficient water from fruits and plant life, as Tom Hanks’s character did in the 2001 film Cast Away.
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Companies such as Reverse Osmosis Systems in Atlanta, Georgia, offer a small unit for home or business use, which actually performs the reverse-osmosis process on a small scale. The unit makes use of a process called crossflow, which continually cleans the semipermeable membrane of impurities that have been removed from the water. A small pump provides the pressure necessary to push the water through the membrane. In addition to an under-the-sink model, a reverse osmosis water cooler is also available.
Osmosis
Not only is reverse osmosis used for making water safe, it is also applied to metals in a variety of capacities, not least of which is its use in treating wastewater from electroplating. But there are other metallurgical methods of reverse osmosis that have little to do with water treatment: metal finishing, as well as recycling of metals and chemicals. These processes are highly complicated, but they involve the same principle of removing impurities that governs reverse osmosis. WHERE TO LEARN MORE Francis, Frederick J., editor-in-chief. Encyclopedia of Food Science and Technology. New York: Wiley, 2000. Gardner, Robert. Science Project Ideas About Kitchen Chemistry. Berkeley, N.J.: Enslow Publishers, 2002. Laschish, Uri. “Osmosis, Reverse Osmosis, and Osmotic Pressure: What They Are” (Web site). (February 20, 2001). “Lesson 5: Osmosis” (Web site). (February 20, 2001). Rosenfeld, Sam. Science Experiments with Water. Illustrated by John J. Floherty, Jr. Irvington-on-Hudson, NY: Harvey House, 1965. “Salt-Curing Meat in Brine.” Walton Feed (Web site). (February 20, 2001).
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D I S T I L L AT I O N A N D F I LT R A T I O N Distillation and Filtration
CONCEPT When most people think of chemistry, they think about joining substances together. Certainly, the bonding of elements to form compounds through chemical reactions is an integral component of the chemist’s study; but chemists are also concerned with the separation of substances. Some forms of separation, in which compounds are returned to their elemental form, or in which atoms split off from molecules to yield a compound and a separated element, are complex phenomena that require chemical reactions. But chemists also use simpler physical methods, distillation and filtration, to separate mixtures. Distillation can be used to purify water, make alcohols, or separate petroleum into various components that range from natural gas to gasoline to tar. Filtration also makes possible the separation of gases or liquids from solids, and sewage treatment—a form of filtration—separates liquids, solids, and gases through a series of chemical and physical processes.
HOW IT WORKS Mixtures: Homogeneous and Heterogeneous In contrast to a pure substance, a class that includes only elements and compounds, mixtures constitute a much broader category. Usually, a mixture consists of many compounds mixed together, but it is possible to have a mixture (air is an example) in which elemental substances are combined with compounds. Elements alone can be combined in a mixture, as when copper and zinc are alloyed to make brass. It is also possible to have a mixture of mixtures, as for example
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when milk (a particular type of mixture called an emulsion) is added to coffee. It is sometimes difficult, without studying the chemical aspects involved, to recognize the difference between a mixture and a pure substance. A mixture, however, can be defined as a substance with a variable composition, meaning that if more of one component is added, it does not change the essential character of the mixture. People unconsciously recognize this when they joke, “Would you like a little coffee with your milk?” This comment, made when someone puts a great quantity of milk into a cup of coffee, implies that we generally regard coffee and milk as a solution in which the coffee dissolves the milk. But even if someone made a cup of coffee that was half milk, so that the resulting substance had a vanilla-like color, we would still call it coffee. If the components of a pure substance are altered, however, it becomes something entirely different. Two hydrogen atoms bonded to an oxygen atom create water, but when two hydrogen atoms bond to two oxygen atoms, this is hydrogen peroxide, an altogether different substance. Water at ordinary temperatures does not bubble, whereas hydrogen peroxide does. Hydrogen peroxide boils at a temperature more than 1.5 times the boiling point of water, and potatoes boiled in hydrogen peroxide would be nothing like potatoes boiled in water. Eating them, in fact, could very well be fatal. HOMOGENEOUS VS. HETEROG E N E O U S . Unlike a compound or element,
a mixture can never be broken down to a single type of molecule or atom, yet there are mixtures
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that appear to be the same throughout. These are called homogeneous mixtures, in which the properties and characteristics are the same throughout the mixture. In a heterogeneous mixture, on the other hand, the composition is not the same throughout, and in fact the mixture is separated into regions with varying properties. Chemists of the past sometimes had difficulty distinguishing between homogeneous mixtures—virtually all of which can be described as solutions—and pure substances. Air, for example, appears to be a pure substance; yet there is no such thing as an “air molecule.” Instead, air is composed primarily of nitrogen and oxygen, which appear in molecular rather than atomic form, along with separated atoms of noble gases and two important compounds: carbon dioxide and water. (Water exists in air as a vapor.) There is less probability of confusing a heterogeneous mixture with a pure substance, because one of the defining aspects of a heterogeneous substance is the fact that it is clearly a mixture. When sand is added to a container of water, and the sand sinks to the bottom, it is obvious that there is no “sand-and-water” molecule pervading the entire mixture. Clearly, the upper portion of the container is mostly water, and the lower portion mostly sand.
Distillation may seem like a chemical process, but in fact it is purely physical, because the composition of neither compound—salt or water—has been changed. As for filtration, it is clearly a physical process, just as heterogeneous mixtures are more obviously mixtures and not compounds. Suppose we wanted to separate the heterogeneous mixture we described earlier, of sand in water: all we would need would be a mesh screen through which the liquid could be strained, leaving behind the sand. Despite the apparent simplicity of filtration, it can become rather complicated, as we shall see, in the treatment of sewage to turn it into water that poses no threat to the environment. Furthermore, it should be noted that sometimes these processes—distillation and filtration—are used in tandem. Suppose we had a mixture of sand and salt water taken from the beach, and we wanted to separate the mixture. The first step would involve the simpler process of filtration, separating the sand from the salt water. This would be followed by the separation of pure water and salt through the distillation process.
REAL-LIFE A P P L I C AT I O N S
Separating Mixtures
Distillation
There are two basic processes for separating mixtures, distillation and filtration. In general, these are applied for the separation of homogeneous and heterogeneous mixtures, respectively. Distillation is the use of heat to separate the components of a liquid and/or gas, while filtration is the separation of solids from a fluid (either a gas or a liquid) by allowing the fluid to pass through a filter.
In distillation, the more volatile component of the mixture—that is, the part that is more easily vaporized—is separated from the less volatile portion. With regard to the illustration used above, of separating water from salt, clearly the water is the more volatile portion: its boiling point is much, much lower than that of salt, and the heat required to vaporize the salt is so great that the water would be long since vaporized by the time the salt was affected.
In a solution such as salt water, there are two components: the solvent (the water) and the solute (the salt). These can be separated by distillation in a laboratory using a burner placed under a beaker containing the salt water. As the water is heated, it passes out of the beaker in the form of steam, and travels through a tube cooled by a continual flow of cold water. Inside the tube, the steam condenses to form liquid water, which passes into a second beaker. Eventually, all of the solvent will be distilled from the first beaker, leaving behind the salt that constituted the solute of the original solution.
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Distillation and Filtration
Once the volatile portion has been vaporized, or turned into distillate, it experiences condensation—the cooling of a gas to form a liquid, after which the liquid or condensate is collected. Note that in all these stages of distillation, heat is the agent of separation. This is especially important in the process of fractional distillation, discussed below. The process of removing water vapor from salt water, described earlier, is an example of what is called “single-stage differential distillation.” Sometimes, however—especially when a
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A
WATER FILTRATION PLANT IN
CONTRA COSTA COUNTY, CALIFORNIA. (James A. Sugar/Corbis. Reproduced by permission.)
high level of purity in the resulting condensate is desired—it may be necessary to subject the condensate to multiple processes of distillation to remove additional impurities. This process is called rectification. PU R I F I E D WAT E R A N D E T H A N O L . If distillation can be used to separate
water from salt, obviously it can also be used to separate water from microbes and other impurities through a more detailed process of rectification. Distilled water, purchased for drinking and other purposes, is just one of the more common applications of the distillation process. Another well-known use of this process is the production of ethyl alcohol, made famous (or perhaps infamous) by stories of bootleggers producing
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homemade whiskey from “stills” or distilleries in the woods. Ethanol, the alcohol in alcoholic beverages, is produced by the fermentation of glucose, a sugar found in various natural substances. The choice of substances is a function of the desired product: grapes for wine; barley and hops for beer; juniper berries for gin; potatoes for vodka, and so on. Glucose reacts with yeast, fermenting to yield ethanol, and this reaction is catalyzed by enzymes in the yeast. The reaction continues until the alcohol content reaches a point equal to about 13%. After that point, the yeast enzymes can no longer survive, and this is where the production of beer or wine usually ends. Fortified wine or
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FEW
INDUSTRIES EMPLOY DISTILLATION TO A GREATER DEGREE THAN DOES THE PETROLEUM INDUSTRY.
SHOWN
HERE
IS AN OIL REFINERY. (Mark L. Stephenson/Corbis. Reproduced by permission.)
malt liquor—variations of wine and beer, respectively, that are more than 13% alcohol, or 26 proof—are exceptions. These two products are the result of mixtures between undistilled beer and wine and products of distillation having a higher alcohol content. Distillation constitutes the second stage in the production of alcohol. Often, the fermentation products are subjected to a multistage rectification process, which yields a mixture of up to 95% ethanol and 5% water. This mixture is called an azeotrope, meaning that it will not change composition when distilled further. Usually the production of whiskey or other liquor stops well below the point of yielding an azeotrope, but in
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some states, brands of grain alcohol at 190 proof (95%) are sold. INDUSTRIAL
D I S T I L L AT I O N .
In contrast to ethanol, methanol or “wood alcohol” is a highly toxic substance whose ingestion can lead to blindness or death. It is widely used in industry for applications in adhesives, plastics, and other products, and was once produced by the distillation of wood. In this old production method, wood was heated in the absence of air, such that it did not burn, but rather decomposed into a number of chemicals, a fraction of which were methanol and other alcohols. The distillation of wood alcohol was abandoned for a number of reasons, not least of which was the environmental concern: thou-
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sands of trees had to be cut down for use in an inefficient process yielding only small portions of the desired product. Today, methanol is produced from synthesis gas, itself a product of coal gasification; nonetheless, numerous industrial processes use distillation. Distillation is employed, for instance, to separate the hydrocarbons benzene and toluene, as well as acetone from acetic acid. In nuclear power plants that require quantities of the hydrogen isotope deuterium, the lighter protium isotope, or plain hydrogen, is separated from the heavier deuterium by means of distillation. Few industries, however, employ distillation to a greater degree than the petroleum industry. Through a process known as fractional distillation, oil companies separate hydrocarbons from petroleum, allowing those of lower molecular mass to boil off and be collected first. For instance, at temperatures below 96.8°F (36°C), natural gas separates from petroleum. Other substances, including petroleum ether and naphtha, separate before the petroleum reaches the 156.2°F-165.2°F (69°C-74°C) range, at which point gasoline separates. Fractional distillation continues, with the separation of other substances, all the way up to 959°F (515°C), above which tar becomes the last item to be separated. Petroleum and petroleumproduct companies account for a large portion of the more than 40,000 distillation units in operation across the country. About 95% of all industrial separation processes involve distillation, which consumes large amounts of energy; for that reason, ever more efficient forms of distillation are continually being researched.
Filtration In the simplest form of filtration, described earlier, a suspension (solid particles floating in a liquid) is allowed to pass through filter paper supported in a glass funnel. The filter paper traps the solid particles, allowing a clear solution (the filtrate) to pass through the funnel and into a receiving container.
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An example of the latter occurs in sewage treatment. Here the solid left behind is feces—as undesirable as gold is desirable. Filtration can further be classified as either gaseous or liquid, depending on which of the fluids constitutes the filtrate. Furthermore, the force that moves the fluid through the filter—whether gravity, a vacuum, or pressure—is another defining factor. The type of filter used can also serve to distinguish varieties of filtration. L I Q U I D F I LT RAT I O N . In liquid filtration, such as that applied in sewage treatment, a liquid can be pulled through the filter by gravitational force, as in the examples given. On the other hand, some sort of applied pressure, or a pressure differential created by the existence of a vacuum, can force the liquid through the filter.
Water filtration for purification purposes is often performed by means of gravitation. Usually, water is allowed to run down through a thick layer of granular material such as sand, gravel, or charcoal, which removes impurities. These layers may be several feet thick, in which case the filter is known as a deep-bed filter. Water purification plants may include fine particles of charcoal, known as activated carbon, in the deep-bed filter to absorb unpleasant-smelling gases. For separating smaller volumes of solution, a positive-pressure system—one that uses external pressure to push the liquid through the filter—may be used. Fluid may be introduced under pressure at one end of a horizontal tank, then forced through a series of vertical plates covered with thick filtering cloths that collect solids. In a vacuum filter, a vacuum (an area virtually devoid of matter, including air) is created beneath the solution to be filtered, and as a result, atmospheric pressure pushes the liquid through the filter. When the liquid is virtually freed of impurities, it may be passed through a second variety of filter, known as a clarifying filter. This type of filter is constructed of extremely fine-mesh wires or fibers designed to remove the smallest particles suspended in the liquid. Clarifying filters may also use diatomaceous earth, a finely powdered material produced from the decay of marine organisms.
There are two basic purposes for filtration: either to capture the solid material suspended in the fluid, or to clarify the fluid in which the solid is suspended. An example of the former occurs, for instance, when panning for gold: the water is allowed to pass through a sieve, leaving behind rocks that—the prospector hopes—contain gold.
GAS F I LT RAT I O N . Gas filtration is used in a common appliance, the vacuum cleaner, which passes a stream of dust-filled air
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Distillation and Filtration
KEY TERMS A solution that has been
AZEOTROPE:
subjected through distillation and is still
ing different properties. An example is sand in a container of water.
not fully separated, but cannot be separat-
HOMOGENEOUS:
ed any further by means of distillation. An
a mixture that is the same throughout, as
example is ethanol, which cannot be dis-
for example when sugar is fully dissolved
tilled beyond the point at which it reaches
in water. A solution is a homogenous
a 95% concentration with water.
mixture.
CONDENSATE:
The liquid product
that results from distillation. The cooling of a
CONDENSATION:
gas to form a liquid or condensate. DISTILLATE:
The vapor collected from
the volatile material or materials in distillation. This vapor is then subjected to condensation.
MIXTURE:
A term describing
A substance with a variable
composition, composed of molecules or atoms of differing types. Compare with pure substance. PURE SUBSTANCE:
A substance—
either an element or compound—that has an unvarying composition. This means that by changing the proportions of atoms, the result would be an entirely different
DISTILLATION:
The use of heat to
separate the components of a liquid and/or
substance. Compare with mixture. SOLUTE:
The substance or substances
gas. Generally, distillation is used to sepa-
that are dissolved in a solvent to form a
rate mixtures that are homogeneous.
solution.
FILTRATE:
The liquid or gas separated
from a solid by means of filtration. FILTRATION:
The separation of solids
SOLUTION:
A homogeneous mixture
in which one or more substances is dissolved in an another substance—for exam-
from a fluid (either gas or liquid) by allow-
ple, sugar dissolved in water.
ing the fluid to pass through a filter. Gen-
SOLVENT:
erally, filtration is used to separate mix-
a solute to form a solution.
tures that are heterogeneous.
SUSPENSION:
HETEROGENEOUS:
A term describ-
The substance that dissolves A term that refers to a
mixture in which solid particles are sus-
ing a mixture that is not the same through-
pended in a fluid.
out; rather, it has various regions possess-
VOLATILE:
Easily vaporized.
through a filtering bag inside the machine. The bag traps solid particles, while allowing clean air to pass back out into the room. This is essentially the same principle applied in air filters and even air conditioning and heating systems, which, in addition to regulating temperature, also remove dust, pollen, and other impurities from the air.
Various industries use gas filtration, not only to purify the products released into the atmosphere, but also to filter the air in the workplace, as for instance in a factory room where fine airborne particles are a hazard of production. The gases from power plants that burn coal and oil are often purified by passing them through filtering systems that collect particles.
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Sewage Treatment Distillation and Filtration
Sewage treatment is a complex, multistage process whereby waste water is freed of harmful contents and rendered safe, so that it can be returned to the environment. This is a critical part of modern life, because when people congregate in cities, they generate huge amounts of wastes that contain disease-causing bacteria, viruses, and other microorganisms. Lack of proper waste management in ancient and medieval times led to devastating plagues in cities such as Athens, Rome, and Constantinople. Indeed, one of the factors contributing to the end of the Athenian golden age of the fifth century B.C. was a plague, caused by lack of proper sewage-disposal methods, that felled many of the city’s greatest figures. The horrors created by improper waste management reached their apogee in 1347-51, when microorganisms carried by rats brought about the Black Death, in which Europe’s population was reduced by one-third. AEROBIC AND ANAEROBIC D E CAY. Small amounts of sewage can be dealt
with through aerobic (oxygen-consuming) decay, in which microorganisms such as bacteria and fungi process the toxins in human waste. With larger amounts of waste, however, oxygen is depleted and the decay mechanism must be anaerobic, or carried out in the absence of oxygen. For people who are not connected to a municipal sewage system, and therefore must rely on a septic tank for waste disposal, waste products pass through a tank in which they are subjected to anaerobic decay by varieties of microorganisms that do not require oxygen to survive. From there, the waste goes through the drain field, a network of pipes that allow the water to seep into a deep-bed filter. In the drain field, the waste is subjected to aerobic decay by oxygen-dependant microorganisms before it either filters through the drain pipes into the ground, or is evaporated. M U N I C I PA L WASTE T R E AT M E N T. Municipal waste treatment is a much
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described in the most general terms here. Essentially, large-scale sewage treatment requires the separation of larger particles first, followed by the separation of smaller particles, as the process continues. Along the way, the sewage is chemically treated as well. The separation of smaller solid particles is aided by aluminum sulfate, which causes these particles to settle to the bottom more rapidly. Through continual processing by filtration, water is eventually clarified of biosolids (that is, feces), but it is still far from being safe. At that point, all the removed biosolids are dried and incinerated; or they may be subjected to additional processes to create fertilizer. The water, or effluent, is further clarified by filtration in a deep-bed filter, and additional air may be introduced to the water to facilitate aerobic decay— for instance, by using algae. Through a long series of such processes, the water is rendered safe to be released back into the environment. However, wastes containing extremely high levels of toxins may require additional or different forms of treatment. WHERE TO LEARN MORE “Case Study: Petroleum Distillation” (Web site). (June 6, 2001). “Classification of Matter” (Web site). _98/smith/smith2. ht ml (June 6, 2001). “Fractional Distillation” (Web site). (June 6, 2001). “Introduction to Distillation” (Web site). (June 6, 2001). Kellert, Stephen B. and Matthew Black. The Encyclopedia of the Environment. New York: Franklin Watts, 1999. Oxlade, Chris. Chemistry. Illustrated by Chris Fairclough. Austin, TX: Raintree Steck-Vaughn, 1999. Seuling, Barbara. Drip! Drop! How Water Gets to Your Tap. Illustrated by Nancy Tobin. New York: Holiday House, 2000. “Sewage Treatment” (Web site). (June 6, 2001).
more involved process, and will only be
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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S C I E N C E O F E V E RY DAY T H I N G S r e a l - l i f e CHEMISTRY
ORGANIC CHEMISTRY ORGANIC CHEMISTRY P O LY M E R S
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ORGANIC CHEMISTRY
CONCEPT There was once a time when chemists thought “organic” referred only to things that were living, and that life was the result of a spiritual “life force.” While there is nothing wrong with viewing life as having a spiritual component, spiritual matters are simply outside the realm of science, and to mix up the two is as silly as using mathematics to explain love (or vice versa). In fact, the “life force” has a name: carbon, the common denominator in all living things. Not everything that has carbon is living, nor are all the areas studied in organic chemistry—the branch of chemistry devoted to the study of carbon and its compounds—always concerned with living things. Organic chemistry addresses an array of subjects as vast as the number of possible compounds that can be made by strings of carbon atoms. We can thank organic chemistry for much of what makes life easier in the modern age: fuel for cars, for instance, or the plastics found in many of the products used in an average day.
HOW IT WORKS Introduction to Carbon As the element essential to all of life, and hence the basis for a vast field of study, carbon is addressed in its own essay. The Carbon essay, in addition to examining the chemical properties of carbon (discussed below), approaches a number of subjects, such as the allotropes of carbon. These include three crystalline forms (graphite, diamond, and buckminsterfullerene), as well as amorphous carbon. In addition, two oxides of carbon—carbon dioxide and carbon monoxide—are important, in the case of the former, to
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the natural carbon cycle, and in the case of the latter, to industry. Both also pose environmental dangers. The purpose of this summary of the carbon essay is to provide a hint of the complexities involved with this sixth element on the periodic table, the 14th most abundant element on Earth. In the human body, carbon is second only to oxygen in abundance, and accounts for 18% of the body’s mass. Capable of combining in seemingly endless ways, carbon, along with hydrogen, is at the center of huge families of compounds. These are the hydrocarbons, present in deposits of fossil fuels: natural gas, petroleum, and coal. A PROPENSITY FOR LIMITL E SS B O N D I N G . Carbon has a valence
electron configuration of 2s22p2. Likewise all the members of Group 4 on the periodic table (Group 14 in the IUPAC version of the table)— sometimes known as the “carbon family”—have configurations of ns2np2, where n is the number of the period or row the element occupies on the table. There are two elements noted for their ability to form long strings of atoms and seemingly endless varieties of molecules: one is carbon, and the other is silicon, directly below it on the periodic table. Just as carbon is at the center of a vast network of organic compounds, silicon holds the same function in the inorganic realm. It is found in virtually all types of rocks, except the calcium carbonates—which, as their name implies, contain carbon. In terms of known elemental mass, silicon is second only to oxygen in abundance on Earth. Silicon atoms are about one and a half times as large as those of carbon; thus not even silicon can compete with carbon’s ability to form
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Organic Chemistry
“I
JUST WANT TO SAY ONE WORD TO YOU...PLASTICS.”
THESE WORDS WERE UTTERED TO
DUSTIN HOFFMAN’S
SIGNIFYING
THAT PLASTICS WERE THE WAVE OF THE FUTURE,
CHARACTER IN THE
1967
FILM
THE GRADUATE. (The Kobal
Collection. Reproduced by permission.)
an almost limitless array of molecules in various shapes and sizes, and with various chemical properties.
Electronegativity Carbon is further distinguished by its high value of electronegativity, the relative ability of an atom to attract valence electrons. To mention a few basic aspects of chemical bonding, developed at considerably greater length in the Chemical Bonding essay, if two atoms have an electric charge and thus are ions, they form strong ionic bonds. Ionic bonding occurs when a metal bonds with a nonmetal. The other principal type of bond is a covalent bond, in which two uncharged atoms share eight valence electrons. If the electronegativity values of the two elements involved are equal, then they share the electrons equally; but if one element has a higher electronegativity value, the electrons will be more drawn to that element.
364
reactive and most of which have high electronegativity values. If one ignores the noble gases, which are virtually unreactive and occupy the extreme right-hand side of the periodic table, electronegativity values are highest in the upper right-hand side of the table—the location of fluorine—and lowest in the lower left. In other words, the value increases with group or column number (again, leaving out the noble gases in Group 8), and decreases with period or row number.
The electronegativity of carbon is certainly not the highest on the periodic table. That distinction belongs to fluorine, with an electronegativity value of 4.0, which makes it the most reactive of all elements. Fluorine is at the head of Group 7, the halogens, all of which are highly
With an electronegativity of 2.5, carbon ties with sulfur and iodine (a halogen) for sixth place, behind only fluorine; oxygen (3.5); nitrogen and chlorine (3.0); and bromine (2.8). Thus its electronegativity is high, without being too high. Fluorine is not likely to form the long chains for which is carbon is known, simply because its electronegativity is so high, it overpowers other elements with which it comes into contact. In addition, with four valence electrons, carbon is ideally suited to find other elements (or other carbon atoms) for forming covalent bonds according to the octet rule, whereby most elements bond so that they have eight valence electrons.
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Carbon’s Multiple Bonds Carbon—with its four valence electrons—happens to be tetravalent, or capable of bonding to four other atoms at once. It is not necessarily the case that an element has the ability to bond with as many other elements as it has valence electrons; in fact, this is rarely the case. Additionally, carbon is capable of forming not only a single bond, with one pair of shared valence electrons, but a double bond (two pairs) or even a triple bond (three pairs.) Another special property of carbon is its ability to bond in long chains that constitute strings of carbons and other atoms. Furthermore, though sometimes carbon forms a typical molecule (for example, carbon dioxide, or CO2, is just one carbon atom with two oxygens), it is also capable of forming “molecules” that are really not molecules in the way that the word is typically used in chemistry. Graphite, for instance, is just a series of “sheets” of carbon atoms bonded tightly in a hexagonal, or six-sided, pattern, while a diamond is simply a huge “molecule” composed of carbon atoms strung together by covalent bonds.
Organic Chemistry
IT IS VIRTUALLY IMPOSSIBLE FOR AMERICA TO SPEND AN ENTIRE
A PERSON IN MODERN DAY WITHOUT COMING
INTO CONTACT WITH AT LEAST ONE, AND MORE LIKELY
Organic Chemistry
DOZENS, OF PLASTIC PRODUCTS, ALL MADE POSSIBLE BY ORGANIC CHEMISTRY.
Organic chemistry is the study of carbon, its compounds, and their properties. The only major carbon compounds considered inorganic are carbonates (for instance, calcium carbonate, alluded to above, which is one of the major forms of mineral on Earth) and oxides, such as carbon dioxide and carbon monoxide. This leaves a huge array of compounds to be studied, as we shall see. The term “organic” in everyday language connotes “living,” but organic chemistry is involved with plenty of compounds not part of living organisms: petroleum, for instance, is an organic compound that ultimately comes from the decayed bodies of organisms that once were alive. It should be stressed that organic compounds do not have to be produced by living things, or even by things that once were alive; they can be produced artificially in a laboratory. The breakthrough event in organic chemistry came in 1828, when German chemist Friedrich Wöhler (1800-1882) heated a sample of ammonium cyanate (NH4OCN) and converted it to urea (H2N-CO-NH2). Ammonium cyanite is an inorganic material, whereas urea, a waste product in the urine of mammals, is an organic one. “Without benefit of a kidney, a bladder, or a
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HERE, A FASHION MODEL PVC. (Reuters NewMedia
PARADES A DRESS MADE OF
Inc./Corbis. Reproduced by permission.)
dog,” as Wöhler later said, he had managed to transform an inorganic substance into an organic one. Ammonium cyanate and urea are isomers: substances having the same formula, but possessing different chemical properties. Thus they have exactly the same numbers and proportions of atoms, yet these atoms are arranged in different ways. In urea, the carbon forms an organic chain, and in ammonium cyanate, it does not. Thus, to reduce the specifics of organic chemistry even further, this discipline can be said to constitute the study of carbon chains, and ways to rearrange them to create new substances.
REAL-LIFE A P P L I C AT I O N S Organic Chemistry and Modern Life At first glance, the term “organic chemistry” might sound like something removed from
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Organic Chemistry
ANOTHER
BYPRODUCT OF ORGANIC CHEMISTRY: PETROLEUM JELLY. (Laura Dwight/Corbis. Reproduced by permission.)
everyday life, but this could not be further from the truth. The reality of the role played by organic chemistry in modern existence is summed up in a famous advertising slogan used by E. I. du Pont de Nemours and Company (usually referred to as “du Pont”): “Better Things for Better Living Through Chemistry.” Often rendered simply as “Better Living Through Chemistry,” the advertising campaign made its debut in 1938, just as du Pont introduced a revolutionary product of organic chemistry: nylon, the creation of a brilliant young chemist named Wallace Carothers (1896-1937). Nylon, an example of a polymer (discussed below), started a revolution in plastics that was still unfolding three decades later, in 1967. That was the year of the film The Graduate, which included a famous interchange between the character of Benjamin Braddock (Dustin Hoffman) and an adult named Mr. McGuire (Walter Brooke): • Mr. McGuire: I just want to say one word to you... just one word. • Benjamin Braddock: Yes, sir. • Mr. McGuire: Are you listening? • Benjamin Braddock: Yes, sir, I am. • Mr. McGuire: Plastics.
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The meaning of this interchange was that plastics were the wave of the future, and that an intelligent young man such as Ben should invest his energies in this promising new field. Instead, Ben puts his attention into other things, quite removed from “plastics,” and much of the plot revolves around his revolt against what he perceives as the “plastic” (that is, artificial) character of modern life. In this way, The Graduate spoke for a whole generation that had become ambivalent concerning “better living through chemistry,” a phrase that eventually was perceived as ironic in view of concerns about the environment and the many artificial products that make up modern life. Responding to this ambivalence, du Pont dropped the slogan in the late 1970s; yet the reality is that people truly do enjoy “better living through chemistry”—particularly organic chemistry. A P P L I CAT I O N S O F O R GA N I C C H E M I S T RY. What would the world be like
without the fruits of organic chemistry? First, it would be necessary to take away all the various forms of rubber, vitamins, cloth, and paper made from organically based compounds. Aspirins and all types of other drugs; preservatives that keep food from spoiling; perfumes and toiletries; dyes
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and flavorings—all these things would have to go as well. Synthetic fibers such as nylon—used in everything from toothbrushes to parachutes— would be out of the picture if it were not for the enormous progress made by organic chemistry. The same is true of plastics or polymers in general, which have literally hundreds upon hundreds of applications. Indeed, it is virtually impossible for a person in twenty-first century America to spend an entire day without coming into contact with at least one, and more likely dozens, of plastic products. Car parts, toys, computer housings, Velcro fasteners, PVC (polyvinyl chloride) plumbing pipes, and many more fixtures of modern life are all made possible by plastics and polymers. Then there is the vast array of petrochemicals that power modern civilization. Best-known among these is gasoline, but there is also coal, still one of the most significant fuels used in electrical power plants, as well as natural gas and various other forms of oil used either directly or indirectly in providing heat, light, and electric power to homes. But the influence of petrochemicals extends far beyond their applications for fuel. For instance, the roofing materials and tar that (quite literally) keep a roof over people’s heads, protecting them from sun and rain, are the product of petrochemicals—and ultimately, of organic chemistry.
Hydrocarbons Carbon, together with other elements, forms so many millions of organic compounds that even introductory textbooks on organic chemistry consist of many hundreds of pages. Fortunately, it is possible to classify broad groupings of organic compounds. The largest and most significant is that class of organic compounds known as hydrocarbons—chemical compounds whose molecules are made up of nothing but carbon and hydrogen atoms.
Theoretically, there is no limit to the number of possible hydrocarbons. Not only does carbon form itself into apparently limitless molecular shapes, but hydrogen is a particularly good partner. It has the smallest atom of any element on the periodic table, and therefore it can bond to one of carbon’s valence electrons without getting in the way of the other three.
Organic Chemistry
There are two basic varieties of hydrocarbon, distinguished by shape: aliphatic and aromatic. The first of these forms straight or branched chains, as well as rings, while the second forms only benzene rings, discussed below. Within the aliphatic hydrocarbons are three varieties: those that form single bonds (alkanes), double bonds (alkenes), and triple bonds (alkynes.) A L KA N E S . The alkanes are also known as saturated hydrocarbons, because all the bonds not used to make the skeleton itself are filled to their capacity (that is, saturated) with hydrogen atoms. The formula for any alkane is CnH2n+2, where n is the number of carbon atoms. In the case of a linear, unbranched alkane, every carbon atom has two hydrogen atoms attached, but the two end carbon atoms each have an extra hydrogen.
What follows are the names and formulas for the first eight normal, or unbranched, alkanes. Note that the first four of these received common names before their structures were known; from C5 onward, however, they were given names with Greek roots indicating the number of carbon atoms (e.g., octane, a reference to “eight.”)
Every molecule in a hydrocarbon is built upon a “skeleton” composed of carbon atoms, either in closed rings or in long chains. The chains may be straight or branched, but in each case—rings or chains, straight chains or branched ones—the carbon bonds not used in tying the carbon atoms together are taken up by hydrogen atoms.
Methane (CH4) Ethane (C2H6) Propane (C3H8) Butane (C4H10) Pentane (C5H12) Hexane (C6H14) Heptane (C7H16) Octane (C8H18) The reader will undoubtedly notice a number of familiar names on this list. The first four, being the lowest in molecular mass, are gases at room temperature, while the heavier ones are oily liquids. Alkanes even heavier than those on this list tend to be waxy solids, an example being paraffin wax, for making candles. It should be noted that from butane on up, the alkanes have numerous structural isomers, depending on
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whether they are straight or branched, and these isomers have differing chemical properties. Branched alkanes are named by indicating the branch attached to the principal chain. Branches, known as substituents, are named by taking the name of an alkane and replacing the suffix with yl—for example, methyl, ethyl, and so on. The general term for an alkane which functions as a substituent is alkyl. Cycloalkanes are alkanes joined in a closed loop to form a ring-shaped molecule. They are named by using the names above, with cyclo- as a prefix. These start with propane, or rather cyclopropane, which has the minimum number of carbon atoms to form a closed shape: three atoms, forming a triangle. A L K E N E S A N D A L KY N E S . The names of the alkenes, hydrocarbons that contain one or more double bonds per molecule, are parallel to those of the alkanes, but the family ending is -ene. Likewise they have a common formula: CnH2n. Both alkenes and alkynes, discussed below, are unsaturated—in other words, some of the carbon atoms in them are free to form other bonds. Alkenes with more than one double bond are referred to as being polyunsaturated.
As with the alkenes, the names of alkynes (hydrocarbons containing one or more triple bonds per molecule) are parallel to those of the alkanes, only with the replacement of the suffix -yne in place of -ane. The formula for alkenes is CnH2n-2. Among the members of this group are acetylene, or C2H2, used for welding steel. Plastic polystyrene is another important product from this division of the hydrocarbon family. A R O M AT I C
HYDROCARBONS.
Aromatic hydrocarbons, despite their name, do not necessarily have distinctive smells. In fact the name is a traditional one, and today these compounds are defined by the fact that they have benzene rings in the middle. Benzene has a formula C6H6, and a benzene ring is usually represented as a hexagon (the six carbon atoms and their attached hydrogen atoms) surrounding a circle, which represents all the bonding electrons as though they were everywhere in the molecule at once.
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the vast hydrocarbon network is trinitrotoluene, or TNT. Naphthalene is derived from coal tar, and used in the synthesis of other compounds. A crystalline solid with a powerful odor, it is found in mothballs and various deodorantdisinfectants. P E T R O C H E M I CA L S . As for petrochemicals, these are simply derivatives of petroleum, itself a mixture of alkanes with some alkenes, as well as aromatic hydrocarbons. Through a process known as fractional distillation, the petrochemicals of the lowest molecular mass boil off first, and those having higher mass separate at higher temperatures.
Among the products derived from the fractional distillation of petroleum are the following, listed from the lowest temperature range (that is, the first material to be separated) to the highest: natural gas; petroleum ether, a solvent; naphtha, a solvent (used for example in paint thinner); gasoline; kerosene; fuel for heating and diesel fuel; lubricating oils; petroleum jelly; paraffin wax; and pitch, or tar. A host of other organic chemicals, including various drugs, plastics, paints, adhesives, fibers, detergents, synthetic rubber, and agricultural chemicals, owe their existence to petrochemicals. Obviously, petroleum is not just for making gasoline, though of course this is the first product people think of when they hear the word “petroleum.” Not all hydrocarbons in gasoline are desirable. Straight-chain or normal heptane, for instance, does not fire smoothly in an internal-combustion engine, and therefore disrupts the engine’s rhythm. For this reason, it is given a rating of zero on a scale of desirability, while octane has a rating of 100. This is why gas stations list octane ratings at the pump: the higher the presence of octane, the better the gas is for one’s automobile.
Hydrocarbon Derivatives
In this group are products such as naphthalene, toluene, and dimethyl benzene. These last two are used as solvents, as well as in the synthesis of drugs, dyes, and plastics. One of the more famous (or infamous) products in this part of
With carbon and hydrogen as the backbone, the hydrocarbons are capable of forming a vast array of hydrocarbon derivatives by combining with other elements. These other elements are arranged in functional groups—an atom or group of atoms whose presence identifies a specific family of compounds. Below we will briefly discuss some of the principal hydrocarbon deriv-
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atives, which are basically hydrocarbons with the addition of other molecules or single atoms. Alcohols are oxygen-hydrogen molecules wedded to hydrocarbons. The two most important commercial types of alcohol are methanol, or wood alcohol; and ethanol, which is found in alcoholic beverages, such as beer, wine, and liquor. Though methanol is still known as “wood alcohol,” it is no longer obtained by heating wood, but rather by the industrial hydrogenation of carbon monoxide. Used in adhesives, fibers, and plastics, it can also be applied as a fuel. Ethanol, too, can be burned in an internalcombustion engine, when combined with gasoline to make gasohol. Another significant alcohol is cholesterol, found in most living organisms. Though biochemically important, cholesterol can pose a risk to human health. Aldehydes and ketones both involve a double-bonded carbon-oxygen molecule, known as a carbonyl group. In a ketone, the carbonyl group bonds to two hydrocarbons, while in an aldehyde, the carbonyl group is always at the end of a hydrocarbon chain. Therefore, instead of two hydrocarbons, there is always a hydrocarbon and at least one other hydrogen bonded to the carbon atom in the carbonyl. One prominent example of a ketone is acetone, used in nail polish remover. Aldehydes often appear in nature—for instance, as vanillin, which gives vanilla beans their pleasing aroma. The ketones carvone and camphor impart the characteristic flavors of spearmint leaves and caraway seeds. CA R B OX Y L I C AC I D S A N D E S T E R S . Carboxylic acids all have in common
what is known as a carboxyl group, designated by the symbol -COOH. This consists of a carbon atom with a double bond to an oxygen atom, and a single bond to another oxygen atom that is, in turn, wedded to a hydrogen. All carboxylic acids can be generally symbolized by RCOOH, with R as the standard designation of any hydrocarbon. Lactic acid, generated by the human body, is a carboxylic acid: when a person overexerts, the muscles generate lactic acid, resulting in a feeling of fatigue until the body converts the acid to water and carbon dioxide. Another example of a carboxylic acid is butyric acid, responsible in part for the smells of rancid butter and human sweat. When a carboxylic acid reacts with an alcohol, it forms an ester. An ester has a structure similar to that described for a carboxylic acid,
S C I E N C E O F E V E RY DAY T H I N G S
with a few key differences. In addition to its bonds (one double, one single) with the oxygen atoms, the carbon atom is also attached to a hydrocarbon, which comes from the carboxylic acid. Furthermore, the single-bonded oxygen atom is attached not to a hydrogen, but to a second hydrocarbon, this one from the alcohol. One well-known ester is acetylsalicylic acid—better known as aspirin. Esters, which are a key factor in the aroma of various types of fruit, are often noted for their pleasant smell.
Organic Chemistry
Polymers Polymers are long, stringy molecules made of smaller molecules called monomers. They appear in nature, but thanks to Carothers—a tragic figure, who committed suicide a year before Nylon made its public debut—as well as other scientists and inventors, synthetic polymers are a fundamental part of daily life. The structure of even the simplest polymer, polyethylene, is far too complicated to discuss in ordinary language, but must be represented by chemical symbolism. Indeed, polymers are a subject unto themselves, but it is worth noting here just how many products used today involve polymers in some form or another. Polyethylene, for instance, is the plastic used in garbage bags, electrical insulation, bottles, and a host of other applications. A variation on polyethylene is Teflon, used not only in nonstick cookware, but also in a number of other devices, such as bearings for low-temperature use. Polymers of various kinds are found in siding for houses, tire tread, toys, carpets and fabrics, and a variety of other products far too lengthy to enumerate. WHERE TO LEARN MORE Blashfield, Jean F. Carbon. Austin, TX: Raintree SteckVaughn, 1999. “Carbon.” Xrefer (Web site). (May 30, 2001). Chemistry Help Online for Students (Web site). May 30, 2001). Knapp, Brian J. Carbon Chemistry. Illustrated by David Woodroffe. Danbury, CT: Grolier Educational, 1998. Loudon, G. Marc. Organic Chemistry. Menlo Park, CA: Benjamin/Cummings, 1988.
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Organic Chemistry
KEY TERMS Hydrocarbons that form single bonds. Alkanes are also called saturated hydrocarbons.
ALKANES:
ALKENES:
Hydrocarbons that form
double bonds. A general term for an alkane that functions as a substituent.
ALKYL:
ALKYNES:
Hydrocarbons that form
triple bonds. Different versions of the same element, distinguished by molecular structure.
ALLOTROPES:
AMORPHOUS:
Having no definite
structure. A type of chemical bonding in which two atoms share valence electrons.
COVALENT BONDING:
A term describing the distribution of valence electrons that takes place in chemical bonding for most elements, which end up with eight valence electrons. OCTET RULE:
The study of carbon, its compounds, and their properties. (Some carbon-containing compounds, most notably oxides and carbonates, are not considered organic.)
ORGANIC CHEMISTRY:
A term describing a hydrocarbon in which each carbon is already bound to four other atoms. Alkanes are saturated hydrocarbons. SATURATED:
A form of bonding in which two atoms share one pair of valence electrons. Carbon is also capable of double bonds and triple bonds.
SINGLE BOND:
A term describing a type of solid in which the constituent parts have a simple and definite geometric arrangement repeated in all directions.
SUBSTITUENTS:
A form of bonding in which two atoms share two pairs of valence electrons. Carbon is also capable of single bonds and triple bonds.
TETRAVALENT:
CRYSTALLINE:
DOUBLE BOND:
The relative ability of an atom to attract valence electrons. ELECTRONEGATIVITY:
An atom or group of atoms whose presence identifies a specific family of compounds. FUNCTIONAL GROUPS:
Any chemical compound whose molecules are made up of nothing but carbon and hydrogen atoms. HYDROCARBON:
Families of compounds formed by the joining of hydrocarbons with various functional groups. HYDROCARBON DERIVATIVES:
Substances having the same chemical formula, but that are different
ISOMERS:
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chemically due to disparities in the arrangement of atoms.
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Branches of alkanes, named by taking the name of an alkane and replacing the suffix with yl—for example, methyl, ethyl, and so on.
Capable of bonding to four other elements. A form of bonding in which two atoms share three pairs of valence electrons. Carbon is also capable of single bonds and double bonds.
TRIPLE BOND:
A term describing a hydrocarbon in which the carbons involved in a multiple bond (a double bond or triple bond) are free to bond with other atoms. Alkenes and alkynes are both unsaturated. UNSATURATED:
Electrons that occupy the highest principal energy level in an atom. These are the electrons involved in chemical bonding.
VALENCE ELECTRONS:
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“Organic Chemistry” (Web site). (May 30, 2001). “Organic Chemistry.” Frostburg State University Chemistry Helper (Web site). (May 30, 2001).
S C I E N C E O F E V E RY DAY T H I N G S
Sparrow, Giles. Carbon. New York: Benchmark Books, 1999.
Organic Chemistry
Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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P O LY M E R S Polymers
CONCEPT Formed from hydrocarbons, hydrocarbon derivatives, or sometimes from silicon, polymers are the basis not only for numerous natural materials, but also for most of the synthetic plastics that one encounters every day. Polymers consist of extremely large, chain-like molecules that are, in turn, made up of numerous smaller, repeating units called monomers. Chains of polymers can be compared to paper clips linked together in long strands, and sometimes cross-linked to form even more durable chains. Polymers can be composed of more than one type of monomer, and they can be altered in other ways. Likewise they are created by two different chemical processes, and thus are divided into addition and condensation polymers. Among the natural polymers are wool, hair, silk, rubber, and sand, while the many synthetic polymers include nylon, synthetic rubber, Teflon, Formica, Dacron, and so forth. It is very difficult to spend a day without encountering a natural polymer—even if hair is removed from the list—but in the twenty-first century, it is probably even harder to avoid synthetic polymers, which have collectively revolutionized human existence.
HOW IT WORKS
The similarities between these two are so great, in fact, that some chemists speak of Group 4 (Group 14 in the IUPAC system) on the periodic table as the “carbon family.” Both carbon and silicon have the ability to form long chains of atoms that include bonds with other elements. The heavier elements of this “family,” however (most notably lead), are made of atoms too big to form the vast array of chains and compounds for which silicon and carbon are noted. Indeed, not even silicon—though it is at the center of an enormous range of inorganic compounds—can compete with carbon in its ability to form arrangements of atoms in various shapes and sizes, and hence to participate in an almost limitless array of compounds. The reason, in large part, is that carbon atoms are much smaller than those of silicon, and thus can bond to one another and still leave room for other bonds.
Polymers can be defined as large, typically chainlike molecules composed of numerous smaller, repeating units known as monomers. There are numerous varieties of monomers, and since these can be combined in different ways to form polymers, there are even more of the latter.
Carbon is such an important element that an entire essay in this book is devoted to it, while a second essay discusses organic chemistry, the study of compounds containing carbon. In the present context, there will be occasional references to non-carbon (that is, silicon) polymers, but the majority of our attention will be devoted to hydrocarbon and hydrocarbon-derivative polymers, which most of us know simply as “plastics.”
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Polymers of Silicon and Carbon
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The name “polymer” does not, in itself, define the materials that polymers contain. A handful of polymers, such as natural sand or synthetic silicone oils and rubbers, are built around silicon. However, the vast majority of polymers center around an element that occupies a position just above silicon on the periodic table: carbon.
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Polymers
COTTON
IS AN EXAMPLE OF A NATURAL POLYMER. (Carl Corey/Corbis. Reproduced by permission.)
Organic Chemistry As explained in the essay on Organic Chemistry, chemists once defined the term “organic” as relating only to living organisms; the materials that make them up; materials derived from them; and substances that come from formerly living organisms. This definition, which more or less represents the everyday meaning of “organic,” includes a huge array of life forms and materials: humans, all other animals, insects, plants, microorganisms, and viruses; all substances that make up their structures (for example, blood, DNA, and proteins); all products that come from them (a list diverse enough to encompass everything from urine to honey); and all materials derived from the bodies of organisms that were once alive (paper, for instance, or fossil fuels). As broad as this definition is, it is not broad enough to represent all the substances addressed by organic chemistry—the study of carbon, its compounds, and their properties. All living or once-living things do contain carbon; however, organic chemistry is also concerned with carboncontaining materials—for instance, the synthetic plastics we will discuss in this essay—that have never been part of a living organism.
carbon itself is found in other compounds not considered organic: oxides such as carbon dioxide and monoxide, as well as carbonates, most notably calcium carbonate or limestone. In other words, as broad as the meaning of “organic” is, it still does not encompass all substances containing carbon.
Hydrocarbons As for hydrocarbons, these are chemical compounds whose molecules are made up of nothing but carbon and hydrogen atoms. Every molecule in a hydrocarbon is built upon a “skeleton” of carbon atoms, either in closed rings or in long chains, which are sometimes straight and sometimes branched. Theoretically, there is no limit to the number of possible hydrocarbons: not only does carbon form itself into seemingly limitless molecular shapes, but hydrogen is a particularly good partner. It is the smallest atom of any element on the periodic table, and therefore it can bond to one of carbon’s four valence electrons without getting in the way of the other three.
It should be noted that while organic chemistry involves only materials that contain carbon,
There are many, many varieties of hydrocarbon, classified generally as aliphatic hydrocarbons (alkanes, alkenes, and alkynes) and aromatic hydrocarbons, the latter being those that con-
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Polymers
MODERN
APPLIANCES CONTAIN NUMEROUS EXAMPLES OF SYNTHETIC POLYMERS, FROM THE FLOORING TO THE COUN-
TERTOPS TO VIRTUALLY ALL APPLIANCES. (Scott Roper/Corbis. Reproduced by permission.)
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tain a benzene ring. By means of a basic alteration in the shape or structure of a hydrocarbon, it is possible to create new varieties. Thus, as noted above, the number of possible hydrocarbons is essentially unlimited.
REAL-LIFE A P P L I C AT I O N S
Certain hydrocarbons are particularly useful, one example being petroleum, a term that refers to a wide array of hydrocarbons. Among these is an alkane that goes by the name of octane (C8H18), a preferred ingredient in gasoline. Hydrocarbons can be combined with various functional groups (an atom or group of atoms whose presence identifies a specific family of compounds) to form hydrocarbon derivatives such as alcohols and esters.
Many polymers exist in nature. Among these are silk, cotton, starch, sand, and asbestos, as well as the incredibly complex polymers known as RNA (ribonucleic acid) and DNA (deoxyribonucleic acid), which hold genetic codes. The polymers discussed in this essay, however, are primarily of the synthetic kind. Artificial polymers include such plastics (defined below) as polyethylene, styrofoam, and Saran wrap; fibers such as nylon, Dacron (polyester), and rayon; and other materials such as Formica, Teflon, and PVC pipe.
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Types of Polymers and Polymerization
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As noted earlier, most polymers are formed from monomers either of hydrocarbon or hydrocarbon derivatives. The most basic synthetic monomer is ethylene (C2H4), a name whose -ene ending identifies it as an alkene, a hydrocarbon formed by double bonds between carbon atoms. Another alkene hydrocarbon monomer is butadiene, whose formula is C4H6. This is an example of the fact that the formula of a compound does not tell the whole story: on paper, the difference between these two appears to be merely a matter of two extra atoms each of carbon and hydrogen. In fact, butadiene’s structure is much more complex. Still more complex is styrene, which includes a benzene ring. Several other monomers involve other elements: chloride, in vinyl chloride; nitrogen, in acrylonitrile; and fluorine, in tetrafluoroethylene. It is not necessary, in the present context, to keep track of all of these substances, which in any case represent just some of the more prominent among a wide variety of synthetic monomers. A good high-school or college chemistry textbook (either general chemistry or organic chemistry) should provide structural representations of these common monomers. Such representations will show, for instance, the vast differences between purely hydrocarbon monomers such as ethylene, propylene, styrene, and butadiene. When combined into polymers, the monomers above form the basis for a variety of useful and familiar products. Once the carbon double bonds in tetrafluoroethylene (C2F4) are broken, they form the polymer known as Teflon, used in the coatings of cooking utensils, as well as in electrical insulation and bearings. Vinyl chloride breaks its double bonds to form polyvinyl chloride, better known as PVC, a material used for everything from plumbing pipe to toys to Saran wrap. Styrene, after breaking its double bonds, forms polystyrene, used in containers and thermal insulation. P O LY M E R I Z AT I O N . Note that several times in the preceding paragraph, there was a reference to the breaking of carbon double bonds. This is often part of one variety of polymerization, the process whereby monomers join to form polymers. If monomers of a single type join, the resulting polymer is called a homopolymer, but if the polymer consists of more than one type of monomer, it is known as a copolymer. This joining may take place by one of two
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Polymers
A
SYNTHETIC POLYMER KNOWN AS KEVLAR IS USED IN
THE CONSTRUCTION OF BULLETPROOF VESTS FOR LAWENFORCEMENT OFFICERS. (Anna Clopet/Corbis. Reproduced by
permission.)
processes. The first of these, addition polymerization, is fairly simple: monomers add themselves to one another, usually breaking double bonds in the process. This results in the creation of a polymer and no other products. Much more complex is the process known as condensation polymerization, in which a small molecule called a dimer is formed as monomers join. The specifics are too complicated to discuss in any detail, but a few things can be said here about condensation polymerization. The monomers in condensation polymerization must be bifunctional, meaning that they have a functional group at each end. When characteristic structures at the ends of the monomers react to one another by forming a bond, they create a dimer, which splits off from the polymer. The products of condensation polymerization are thus not only the polymer itself, but also a dimer, which may be water, hydrochloric acid (HCl), or some other substance.
A Plastic World A DAY I N T H E L I F E . Though “plastic” has a number of meanings in everyday life,
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and in society at large (as we shall see), the scientific definition is much more specific. Plastics are materials, usually organic, that can be caused to flow under certain conditions of heat and pressure, and thus to assume a desired shape when the pressure and temperature conditions are withdrawn. Most plastics are made of polymers. Every day, a person comes into contact with dozens, if not hundreds, of plastics and polymers. Consider a day in the life of a hypothetical teenage girl. She gets up in the morning, brushes her teeth with a toothbrush made of nylon, then opens a shower door—which is likely to be plastic rather than glass—and steps into a molded plastic shower or bathtub. When she gets out of the shower, she dries off with a towel containing a polymer such as rayon, perhaps while standing on tile that contains plastics, or polymers. She puts on makeup (containing polymers) that comes in plastic containers, and later blowdries her hair with a handheld hair dryer made of insulated plastic. Her clothes, too, are likely to contain synthetic materials made of polymers. When she goes to the kitchen for breakfast, she will almost certainly walk on flooring with a plastic coating. The countertops may be of formica, a condensation polymer, while it is likely that virtually every appliance in the room will contain plastic. If she opens the refrigerator to get out a milk container, it too will be made of plastic, or of paper with a thin plastic coating. Much of the packaging on the food she eats, as well as sandwich bags and containers for storing food, is also made of plastic. And so it goes throughout the day. The phone she uses to call a friend, the computer she sits at to check her e-mail, and the stereo in her room all contain electrical components housed in plastic. If she goes to the gym, she may work out in Gore-tex, a fabric containing a very thin layer of plastic with billions of tiny pores, so that it lets through water vapor (that is, perspiration) without allowing the passage of liquid water. On the way to the health club, she will ride in a car that contains numerous plastic molds in the steering wheel and dashboard. If she plays a compact disc—itself a thin wafer of plastic coated with metal—she will pull it out of a plastic jewel case. Finally, at night, chances are she will sleep in sheets, and with a pillow, containing synthetic polymers.
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A S I L E N T R E V O LU T I O N . The scenario described above—a world surrounded by polymers, plastics, and synthetic materials— represents a very recent phenomenon. “Before the 1930s,” wrote John Steele Gordon in an article about plastics for American Heritage, “almost everything people saw or handled was made of materials that had been around since ancient times: wood, stone, metal, and animal and plant fibers.” All of that changed in the era just before World War II, thanks in large part to a brilliant young American chemist named Wallace Carothers (1896-1937).
By developing nylon for E. I. du Pont de Nemours and Company (known simply as “DuPont” or “du Pont”), Carothers and his colleagues virtually laid the foundation for modern polymer chemistry—a field that employs more chemists than any other. These men created what Gordon called a “materials revolution” by introducing the world to polymers and plastics, which are typically made of polymers. Yet as Gordon went on to note, “It has been a curiously silent revolution.... When we think of the scientific triumphs of [the twentieth century], we think of nuclear physics, medicine, space exploration, and the computer. But all these developments would have been much impeded, in some cases impossible, without... plastics. And yet ‘plastic’ remains, as often as not, a term of opprobrium.” A M B I VA L E N C E T O WA R D P LAS T I CS . Gordon was alluding to a cultural atti-
tude discussed in the essay on Organic Chemistry: the association of plastics, a physical material developed by chemical processes, with the condition—spiritual, moral, and intellectual—of being “plastic” or inauthentic. This was symbolized in a famous piece of dialogue about plastics from the 1967 movie The Graduate, in which a nonplussed Ben Braddock (Dustin Hoffman) listens as one of his parents’ friends advises him to invest his future in plastics. As Gordon noted, “however intergenerationally challenged that half-drunk friend of Dustin Hoffman’s parents may have been... he was right about the importance of the materials revolution in the twentieth century.” One aspect of society’s ambivalence over plastics relates to very genuine concerns about the environment. Most synthetic polymers are made from petroleum, a nonrenewable resource;
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but this is not the greatest environmental danger that plastics present. Most plastics are not biodegradable: though made of organic materials, they do not contain materials that will decompose and eventually return to the ground. Nor is there anything in plastics to attract microorganisms, which, by assisting in the decomposition of organic materials, help to facilitate the balance of decay and regeneration necessary for life on Earth. Efforts are underway among organic chemists in the research laboratories of corporations and other institutions to develop biodegradable plastics that will speed up the decomposition of materials in the polymers—a process that normally takes decades. Until such replacement polymers are developed, however, the most environmentally friendly solution to the problem of plastics is recycling. Today only about 1% of plastics are recycled, while the rest goes into waste dumps, where they account for 30% of the volume of trash. Long before environmental concerns came to the forefront, however, people had begun almost to fear plastics as a depersonalizing aspect of modern life. It seemed that in a given day, a person touched fewer and fewer things that came directly from the natural environment: the “wood, stone, metal, and animal and plant fibers” to which Gordon alluded. Plastics seemed to have made human life emptier; yet the truth of the matter—including the fact that plastics add more than they take away from the landscape of our world—is much more complex.
The Plastics Revolution
developed from cellulose, a substance found in the cell walls of plants—a much less appealing name, “Parkesine.” Hyatt, who used celluloid to make smooth, hard, round billiard balls (thereby winning the contest) took out a patent for the process involved in making the material he had dubbed “Celluloid,” with a capital C.
Polymers
Though the Celluloid made by Hyatt’s process was flammable (as was Parkesine), it proved highly successful as a product when he introduced it in 1869. He marketed it successfully for use in items such as combs and baby rattles, and Celluloid sales received a powerful boost after photography pioneer George Eastman (1854-1932) chose the material for use in the development of film. Eventually, Celluloid would be applied in motion-picture film, and even today, the adjective “celluloid” is sometimes used in relation to the movies. Actually, Celluloid (which can be explosive in large quantities) was phased out in favor of “safety film,” or cellulose acetate, beginning in 1924. Two important developments in the creation of synthetic polymers occurred at the turn of the century. One was the development of Galalith, an ivory-like substance made from formaldehyde and milk, by German chemist Adolf Spitteler. An even more important innovation happened in 1907, when Belgian-American chemist Leo Baekeland (1863-1944) introduced Bakelite. The latter, created in a reaction between phenol and formaldehyde, was a hard, black plastic that proved an excellent insulator. It soon found application in making telephones and household appliances, and by the 1920s, chemists had figured out how to add pigments to Bakelite, thus introducing the public to colored plastics.
Though the introduction of plastics is typically associated with the twentieth century, in fact the “materials revolution” surrounding plastics began in 1865. That was the year when English chemist Alexander Parkes (1813-1890) produced the first plastic material, celluloid. Parkes could have become a rich man from his invention, but he was not a successful marketer. Instead, the man who enjoyed the first commercial success in plastics was—not surprisingly—an American, inventor John Wesley Hyatt (1837-1920).
S Y N T H E T I C R U B B E R. Throughout these developments, chemists had only a vague understanding of polymers, but by the 1930s, they had come to accept the model of polymers as large, flexible, chain-like molecules. One of the most promising figures in the emerging field of polymer chemistry was Carothers, who in 1926 left a teaching post at Harvard University to accept a position as director of the polymer research laboratory at DuPont.
Responding to a contest in which a billiardball manufacturer offered $10,000 to anyone who could create a substitute for ivory, which was extremely costly, Hyatt turned to Parkes’s celluloid. Actually, Parkes had given his creation—
Among the first problems Carothers tackled was the development of synthetic rubber. Natural rubber had been known for many centuries when English chemist Joseph Priestley (17331804) gave it its name because he used it to rub
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out pencil marks. In 1839, American inventor Charles Goodyear (1800-1860) accidentally discovered a method for making rubber more durable, after he spilled a mixture of rubber and sulfur onto a hot stove. Rather than melting, the rubber bonded with the sulfur to form a much stronger but still elastic product, and Goodyear soon patented this process under the name vulcanization. Natural rubber, nonetheless, had many undesirable properties, and hence DuPont put Carothers to the task of developing a substitute. The result was neoprene, which he created by adding a chlorine atom to an acetylene derivative. Neoprene was stronger, more durable, and less likely to become brittle in cold weather than natural rubber. It would later prove an enormous boost to the Allied war effort, after the Japanese seized the rubber plantations of Southeast Asia in 1941. N Y LO N . Had neoprene, which Carothers developed in 1931, been the extent of his achievements, he would still be remembered by science historians. However, his greatest creation still lay ahead of him. Studying the properties of silk, he became convinced that he could develop a more durable compound that could replicate the properties of silk at a much lower cost.
Carothers was not alone in his efforts, as Gordon showed in his account of events at the DuPont laboratories: One day, an assistant, Julian Hill, noticed that when he stuck a glass stirring rod into a gooey mass at the bottom of a beaker the researchers had been investigating, he could draw out threads from it, the polymers forming spontaneously as he pulled. When Carothers was absent one day, Hill and his colleagues decided to see how far they could go with pulling threads out of goo by having one man hold the beaker while another ran down the hall with the glass rod. A very long, silk-like thread was produced. Realizing what they had on their hands, DuPont devoted $27 million to the research efforts of Carothers and his associates at the lab, and in 1937, Carothers presented his boss with the results, saying “Here is your synthetic textile fabric.” DuPont introduced the material, nylon, to the American public the following year with one of the most famous advertising campaigns of all time: “Better Things for Better Living Through Chemistry.”
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The product got an additional boost through exposure at the 1939 World’s Fair. When DuPont put 4,000 pairs of nylon stockings on the market, they sold in a matter of hours. A few months later, four million pairs sold in New York City in a single day. Women stood in line to buy stockings of nylon, a much better (and less expensive) material for that purpose than silk—but they did not have long to enjoy it. During World War II, all nylon went into making war materials such as parachutes, and nylon did not become commercially available again until 1946. As Gordon noted, Carothers would surely have won the Nobel Prize in chemistry for his work—“but Nobel prizes go only to living recipients....” Carothers had married in 1936, and by early 1937, his wife Helen was pregnant. (Presumably, he was unaware of the fact that he was about to become a father.) Though highly enthusiastic about his work, Carothers was always shy and withdrawn, and in Gordon’s words, “he had few outlets other than work.” He was, however, a talented singer, as was his closest sibling, Isobel, a radio celebrity. Her death in January 1937 sent him into a bout of depression, and on April 29, he killed himself with a dose of cyanide. Seven months later, on November 27, Helen gave birth to a daughter, Jane. H O W P LAS T I CS H AV E E N H A N C E D L I F E . Despite his tragic end,
Carothers had brought much good to the world by sparking enormous interest in polymer research and plastics. Over the years that followed, polymer chemists developed numerous products that had applications in a wide variety of areas. Some, such as polyester—a copolymer of terephthalic acid and ethylene—seemed to fit the idea of “plastics” as ugly, inauthentic, and even dehumanizing. During the 1970s, clothes of polyester became fashionable, but by the early 1980s, there was a public backlash against synthetics, and in favor of natural materials. Yet even as the public rejected synthetic fabrics for everyday wear, Gore-tex and other synthetics became popular for outdoor and workout clothing. At the same time, the polyester that many regarded as grotesque when used in clothing was applied in making safer beverage bottles. The American Plastics Council dramatized this in a 1990s commercial that showed a few seconds in the life of a mother. Her child takes a soft-
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KEY TERMS ADDITION
form
of
POLYMERIZATION:
polymerization
in
A
which
monomers having at least one double bond or triple bond simply add to one another, forming a polymer and no other products. Compare to condensation polymerization. Hydrocarbons that contain
ALKENES:
double bonds. COPOLYMER:
tional groups. MONOMERS:
Small, individual sub-
units, often built of hydrocarbons, that join together to form polymers. ORGANIC:
A term referring to any
compound that contains carbon, except for oxides such as carbon dioxide, or car-
A polymer composed of
more than one type of monomer. DIMER:
joining of hydrocarbons with various func-
bonates such as calcium carbonate (i.e., limestone).
A molecule formed by the ORGANIC CHEMISTRY:
joining of two monomers. DOUBLE BOND:
The study
of carbon, its compounds, and their
A form of bonding
properties.
in which two atoms share two pairs of valence electrons. Carbon is noted for its ability to form double bonds, as for instance in many hydrocarbons. FUNCTIONAL GROUPS:
An atom or
group of atoms whose presence identifies a specific family of compounds. When combined with hydrocarbons, various
PLASTICS:
Materials, usually organic,
that can be caused to flow under certain conditions of heat and pressure, and thus to assume a desired shape when the pressure and temperature conditions are withdrawn. Plastics are usually made up of polymers. The
process
functional groups form hydrocarbon
POLYMERIZATION:
derivatives.
whereby monomers join to form polymers.
HOMOPOLYMER:
A polymer that
consists of only one type of monomer. HYDROCARBON:
Any chemical com-
POLYMERS:
Large, typically chain-like
molecules composed of numerous smaller, repeating units known as monomers.
pound whose molecules are made up of
VALENCE ELECTRONS:
nothing but carbon and hydrogen atoms.
that occupy the highest principal energy
HYDROCARBON
level in an atom. These are the electrons
DERIVATIVES:
Families of compounds formed by the
drink bottle out of the refrigerator and drops it, and the mother cringes at what she thinks she is about to see next: glass shattering around her child. But she is remembering the way things were when she was a child, when soft drinks still came in glass bottles: instead, the plastic bottle bounces harmlessly.
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Electrons
involved in chemical bonding.
Of course, such dramatizations may seem a bit self-serving to critics of plastic, but the fact remains that plastics enhance—and in some cases even preserve—life. Kevlar, for instance, enhances life when it is used in making canoes for recreation; when used to make a bulletproof vest, it can save the life of a law-enforcement officer. Mylar, a form of polyester, enhances life
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when used to make a durable child’s balloon— but this highly nonreactive material also saves lives when it is applied to make replacement human blood vessels, or even replacement skin for burn victims.
Recycling As mentioned above, plastics—for all their benefits—do pose a genuine environmental threat, due to the fact that the polymers break down much more slowly than materials from living organisms. Hence the need not only to develop biodegradable plastics, but also to work on more effective means of recycling. One of the challenges in the recycling arena is the fact that plastics come in a variety of grades. Different catalysts are used to make polymers that possess different properties, with varying sizes of molecules, and in chains that may be linear, branched, or cross-linked. Long chains of 10,000 or more monomers can be packed closely to form a hard, tough plastic known as highdensity polyethylene or HDPE, used for bottles containing milk, soft drinks, liquid soap, and other products. On the other hand, shorter, branched chains of about 500 ethylene monomers each produce a much less dense plastic, low-density polyethylene or LDPE. This is used for plastic food or garment bags, spray bottles, and so forth. There are other grades of plastic as well. In some forms of recycling, plastics of all varieties are melted down together to yield a cheap, low-grade product known as “plastic lumber,” used in materials such as landscaping timbers, or in making park benches. In order to achieve higher-grade recycled plastics, the materials need to be separated, and to facilitate this, recycling codes have been developed. Many plastic materials sold today are stamped with a recycling code number between 1 and 6, identifying specific varieties of plastic. These can be melted
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or ground according to type at recycling centers, and reprocessed to make more plastics of the same grade. To meet the environmental challenges posed by plastics, polymer chemists continue to research new methods of recycling, and of using recycled plastic. One impediment to recycling, however, is the fact that most state and local governments do not make it convenient, for instance by arranging trash pickup for items that have been separated into plastic, paper, and glass products. Though ideally private recycling centers would be preferable to government-operated recycling, few private companies have the financial resources to make recycling of plastics and other materials practical. WHERE TO LEARN MORE Bortz, Alfred B. Superstuff!: Materials That Have Changed Our Lives. New York: Franklin Watts, 1990. Ebbing, Darrell D.; R. A. D. Wentworth; and James P. Birk. Introductory Chemistry. Boston: Houghton Mifflin, 1995. Galas, Judith C. Plastics: Molding the Past, Shaping the Future. San Diego, CA: Lucent Books, 1995. Gordon, John Steele. “Plastics, Chance, and the Prepared Mind.” American Heritage, July-August 1998, p. 18. Mebane, Robert C. and Thomas R. Rybolt. Plastics and Polymers. Illustrated by Anni Matsick. New York: Twenty-First Century Books, 1995. Plastics.com (Web site). (June 5, 2001). “Plastics 101.” Plastics Resource (Web site). (June 5, 2001). “Polymers.” University of Illinois, Urbana/Champaign, Materials Science and Technology Department (Web site). (June 5, 2001). “Polymers and Liquid Crystals.” Case Western Reserve University (Web site). (June 5, 2001). Zumdahl, Steven S. Introductory Chemistry: A Foundation, 4th ed. Boston: Houghton Mifflin, 2000.
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SCIENCEOF
EVERYDAY THINGS
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SCIENCEOF
EVERYDAY THINGS volume 2: REAL-LIFE PHYSICS
edited by NEIL SCHLAGER written by JUDSON KNIGHT A SCHLAGER INFORMATION GROUP BOOK
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S C I E N C E O F E V E RY DAY T H I N G S VOLUME 2
Re a l - L i f e p h y s i c s
A Schlager Information Group Book Neil Schlager, Editor Written by Judson Knight Gale Group Staff Kimberley A. McGrath, Senior Editor Maria Franklin, Permissions Manager Margaret A. Chamberlain, Permissions Specialist Shalice Shah-Caldwell, Permissions Associate Mary Beth Trimper, Manager, Composition and Electronic Prepress Evi Seoud, Assistant Manager, Composition and Electronic Prepress Dorothy Maki, Manufacturing Manager Rita Wimberley, Buyer Michelle DiMercurio, Senior Art Director Barbara J. Yarrow, Manager, Imaging and Multimedia Content Robyn V. Young, Project Manager, Imaging and Multimedia Content Leitha Etheridge-Sims, Mary K. Grimes, and David G. Oblender, Image Catalogers Pam A. Reed, Imaging Coordinator Randy Bassett, Imaging Supervisor Robert Duncan, Senior Imaging Specialist Dan Newell, Imaging Specialist While every effort has been made to ensure the reliability of the information presented in this publication, Gale Group does not guarantee the accuracy of the data contained herein. Gale accepts no payment for listing, and inclusion in the publication of any organization, agency, institution, publication, service, or individual does not imply endorsement of the editors and publisher. Errors brought to the attention of the publisher and verified to the satisfaction of the publisher will be corrected in future editions. The paper used in the publication meets the minimum requirements of American National Standard for Information Sciences—Permanence Paper for Printed Library Materials, ANSI Z39.48-1984. This publication is a creative work fully protected by all applicable copyright laws, as well as by misappropriation, trade secret, unfair competition, and other applicable laws. The authors and editors of this work have added value to the underlying factual material herein through one or more of the following: unique and original selection, coordination, expression, arrangement, and classification of the information. All rights to this publication will be vigorously defended. Copyright © 2002 Gale Group, 27500 Drake Road, Farmington Hills, Michigan 48331-3535 No part of this book may be reproduced in any form without permission in writing from the publisher, except by a reviewer who wishes to quote brief passages or entries in connection with a review written for inclusion in a magazine or newspaper. ISBN
0-7876-5631-3 (set) 0-7876-5632-1 (vol. 1) 0-7876-5633-X (vol. 2)
0-7876-5634-8 (vol. 3) 0-7876-5635-6 (vol. 4)
Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
Library of Congress Cataloging-in-Publication Data Knight, Judson. Science of everyday things / written by Judson Knight, Neil Schlager, editor. p. cm. Includes bibliographical references and indexes. Contents: v. 1. Real-life chemistry – v. 2 Real-life physics. ISBN 0-7876-5631-3 (set : hardcover) – ISBN 0-7876-5632-1 (v. 1) – ISBN 0-7876-5633-X (v. 2) 1. Science–Popular works. I. Schlager, Neil, 1966-II. Title. Q162.K678 2001 500–dc21
2001050121
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CONTENTS
Introduction.............................................v Advisory Board ......................................vii
THERMODYNAMICS Gas Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
GENERAL CONCEPTS
Molecular Dynamics. . . . . . . . . . . . . . . . . . . 192
Frame of Reference. . . . . . . . . . . . . . . . . . . . . . . 3 Kinematics and Dynamics . . . . . . . . . . . . . . . 13 Density and Volume . . . . . . . . . . . . . . . . . . . . 21 Conservation Laws . . . . . . . . . . . . . . . . . . . . . 27
Structure of Matter . . . . . . . . . . . . . . . . . . . . 203
KINEMATICS AND PARTICLE DYNAMICS Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Centripetal Force . . . . . . . . . . . . . . . . . . . . . . . 45 Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . 59 Gravity and Gravitation . . . . . . . . . . . . . . . . . 69 Projectile Motion . . . . . . . . . . . . . . . . . . . . . . . 78 Torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 FLUID MECHANICS
Thermodynamics . . . . . . . . . . . . . . . . . . . . . 216 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . 236 Thermal Expansion. . . . . . . . . . . . . . . . . . . . 245 WAVE MOTION AND OSCILLATION Wave Motion . . . . . . . . . . . . . . . . . . . . . . . . . 255 Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . 263 Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . 278 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . 286 Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 Doppler Effect . . . . . . . . . . . . . . . . . . . . . . . . 301
Fluid Mechanics. . . . . . . . . . . . . . . . . . . . . . . . 95 Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . 102 Bernoulli’s Principle . . . . . . . . . . . . . . . . . . . 112 Buoyancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
SOUND
STATICS
Ultrasonics. . . . . . . . . . . . . . . . . . . . . . . . . . . 319
Statics and Equilibrium . . . . . . . . . . . . . . . . 133 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 WORK AND ENERGY
Acoustics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
LIGHT AND ELECTROMAGNETISM Magnetism. . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Electromagnetic Spectrum . . . . . . . . . . . . . . 340 Light. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
Mechanical Advantage and Simple Machines . . . . . . . . . . . . . . . . . . 157 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
S C I E N C E O F E V E RY DAY T H I N G S
Luminescence . . . . . . . . . . . . . . . . . . . . . . . . 365 General Subject Index ......................373
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INTRODUCTION
Overview of the Series Welcome to Science of Everyday Things. Our aim is to explain how scientific phenomena can be understood by observing common, real-world events. From luminescence to echolocation to buoyancy, the series will illustrate the chief principles that underlay these phenomena and explore their application in everyday life. To encourage cross-disciplinary study, the entries will draw on applications from a wide variety of fields and endeavors. Science of Everyday Things initially comprises four volumes: Volume 1: Real-Life Chemistry Volume 2: Real-Life Physics Volume 3: Real-Life Biology Volume 4: Real-Life Earth Science Future supplements to the series will expand coverage of these four areas and explore new areas, such as mathematics.
Arrangement of Real Life Physics This volume contains 40 entries, each covering a different scientific phenomenon or principle. The entries are grouped together under common categories, with the categories arranged, in general, from the most basic to the most complex. Readers searching for a specific topic should consult the table of contents or the general subject index.
• How It Works Explains the principle or theory in straightforward, step-by-step language. • Real-Life Applications Describes how the phenomenon can be seen in everyday events. • Where to Learn More Includes books, articles, and Internet sites that contain further information about the topic. Each entry also includes a “Key Terms” section that defines important concepts discussed in the text. Finally, each volume includes numerous illustrations, graphs, tables, and photographs. In addition, readers will find the comprehensive general subject index valuable in accessing the data.
About the Editor, Author, and Advisory Board Neil Schlager and Judson Knight would like to thank the members of the advisory board for their assistance with this volume. The advisors were instrumental in defining the list of topics, and reviewed each entry in the volume for scientific accuracy and reading level. The advisors include university-level academics as well as high school teachers; their names and affiliations are listed elsewhere in the volume. N E I L S C H LAG E R is the president of
• Concept Defines the scientific principle or theory around which the entry is focused.
Schlager Information Group Inc., an editorial services company. Among his publications are When Technology Fails (Gale, 1994); How Products Are Made (Gale, 1994); the St. James Press Gay and Lesbian Almanac (St. James Press, 1998); Best Literature By and About Blacks (Gale,
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Within each entry, readers will find the following rubrics:
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2000); Contemporary Novelists, 7th ed. (St. James Press, 2000); and Science and Its Times (7 vols., Gale, 2000-2001). His publications have won numerous awards, including three RUSA awards from the American Library Association, two Reference Books Bulletin/Booklist Editors’ Choice awards, two New York Public Library Outstanding Reference awards, and a CHOICE award for best academic book. Judson Knight is a freelance writer, and author of numerous books on subjects ranging from science to history to music. His work on science titles includes Science, Technology, and Society, 2000 B.C.-A.D. 1799 (U*X*L, 2002), as well as extensive contributions to Gale’s seven-volume Science and Its Times (2000-2001). As a writer on history, Knight has published Middle Ages Reference Library (2000), Ancient
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Civilizations (1999), and a volume in U*X*L’s African American Biography series (1998). Knight’s publications in the realm of music include Parents Aren’t Supposed to Like It (2001), an overview of contemporary performers and genres, as well as Abbey Road to Zapple Records: A Beatles Encyclopedia (Taylor, 1999). His wife, Deidre Knight, is a literary agent and president of the Knight Agency. They live in Atlanta with their daughter Tyler, born in November 1998.
Comments and Suggestions Your comments on this series and suggestions for future editions are welcome. Please write: The Editor, Science of Everyday Things, Gale Group, 27500 Drake Road, Farmington Hills, MI 48331.
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ADVISORY BO T IATR LD E
William E. Acree, Jr. Professor of Chemistry, University of North Texas Russell J. Clark Research Physicist, Carnegie Mellon University Maura C. Flannery Professor of Biology, St. John’s University, New York John Goudie Science Instructor, Kalamazoo (MI) Area Mathematics and Science Center Cheryl Hach Science Instructor, Kalamazoo (MI) Area Mathematics and Science Center Michael Sinclair Physics instructor, Kalamazoo (MI) Area Mathematics and Science Center Rashmi Venkateswaran Senior Instructor and Lab Coordinator, University of Ottawa Ottawa, Ontario, Canada
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S C I E N C E O F E V E RY DAY T H I N G S real-life Physics
GENERAL CONCEPTS FRAME OF REFERENCE K I N E M AT I C S A N D D Y N A M I C S DENSITY AND VOLUME C O N S E R VAT I O N L A W S
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FRAME OF REFERENCE
CONCEPT Among the many specific concepts the student of physics must learn, perhaps none is so deceptively simple as frame of reference. On the surface, it seems obvious that in order to make observations, one must do so from a certain point in space and time. Yet, when the implications of this idea are explored, the fuller complexities begin to reveal themselves. Hence the topic occurs at least twice in most physics textbooks: early on, when the simplest principles are explained—and near the end, at the frontiers of the most intellectually challenging discoveries in science.
HOW IT WORKS There is an old story from India that aptly illustrates how frame of reference affects an understanding of physical properties, and indeed of the larger setting in which those properties are manifested. It is said that six blind men were presented with an elephant, a creature of which they had no previous knowledge, and each explained what he thought the elephant was. The first felt of the elephant’s side, and told the others that the elephant was like a wall. The second, however, grabbed the elephant’s trunk, and concluded that an elephant was like a snake. The third blind man touched the smooth surface of its tusk, and was impressed to discover that the elephant was a hard, spear-like creature. Fourth came a man who touched the elephant’s legs, and therefore decided that it was like a tree trunk. However, the fifth man, after feeling of its tail, disdainfully announced that the elephant was nothing but a frayed piece of rope. Last of all, the sixth blind man, standing beside the elephant’s slowly flapping ear, felt of the ear itself and
S C I E N C E O F E V E RY DAY T H I N G S
determined that the elephant was a sort of living fan. These six blind men went back to their city, and each acquired followers after the manner of religious teachers. Their devotees would then argue with one another, the snake school of thought competing with adherents of the fan doctrine, the rope philosophy in conflict with the tree trunk faction, and so on. The only person who did not join in these debates was a seventh blind man, much older than the others, who had visited the elephant after the other six. While the others rushed off with their separate conclusions, the seventh blind man had taken the time to pet the elephant, to walk all around it, to smell it, to feed it, and to listen to the sounds it made. When he returned to the city and found the populace in a state of uproar between the six factions, the old man laughed to himself: he was the only person in the city who was not convinced he knew exactly what an elephant was like.
Understanding Frame of Reference The story of the blind men and the elephant, within the framework of Indian philosophy and spiritual beliefs, illustrates the principle of syadvada. This is a concept in the Jain religion related to the Sanskrit word syat, which means “may be.” According to the doctrine of syadvada, no judgment is universal; it is merely a function of the circumstances in which the judgment is made. On a complex level, syadvada is an illustration of relativity, a topic that will be discussed later; more immediately, however, both syadvada and the story of the blind men beautifully illus-
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trate the ways that frame of reference affects perceptions. These are concerns of fundamental importance both in physics and philosophy, disciplines that once were closely allied until each became more fully defined and developed. Even in the modern era, long after the split between the two, each in its own way has been concerned with the relationship between subject and object. These two terms, of course, have numerous definitions. Throughout this book, for instance, the word “object” is used in a very basic sense, meaning simply “a physical object” or “a thing.” Here, however, an object may be defined as something that is perceived or observed. As soon as that definition is made, however, a flaw becomes apparent: nothing is just perceived or observed in and of itself—there has to be someone or something that actually perceives or observes. That something or someone is the subject, and the perspective from which the subject perceives or observes the object is the subject’s frame of reference. A M E R I CA A N D C H I N A : F RA M E O F R E F E R E N C E I N P RAC T I C E . An
old joke—though not as old as the story of the blind men—goes something like this: “I’m glad I wasn’t born in China, because I don’t speak Chinese.” Obviously, the humor revolves around the fact that if the speaker were born in China, then he or she would have grown up speaking Chinese, and English would be the foreign language. The difference between being born in America and speaking English on the one hand—even if one is of Chinese descent—or of being born in China and speaking Chinese on the other, is not just a contrast of countries or languages. Rather, it is a difference of worlds—a difference, that is, in frame of reference. Indeed, most people would see a huge distinction between an English-speaking American and a Chinese-speaking Chinese. Yet to a visitor from another planet—someone whose frame of reference would be, quite literally, otherworldly—the American and Chinese would have much more in common with each other than either would with the visitor.
A landing in San Francisco would create a falsely inflated impression regarding the number of Asian Americans or Americans of Pacific Island descent, who actually make up only a small portion of the national population. The same would be true if one first arrived in Arizona or New Mexico, where the Native American population is much higher than for the nation as a whole. There are numerous other examples to be made in the same vein, all relating to the visitors’ impressions of the population, economy, climate, physical features, and other aspects of a specific place. Without consulting some outside reference point—say, an almanac or an atlas—it would be impossible to get an accurate picture of the entire country. The principle is the same as that in the story of the blind men, but with an important distinction: an elephant is an example of an identifiable species, whereas the United States is a unique entity, not representative of some larger class of thing. (Perhaps the only nation remotely comparable is Brazil, also a vast land settled by outsiders and later populated by a number of groups.) Another important distinction between the blind men story and the United States example is the fact that the blind men were viewing the elephant from outside, whereas the visitor to America views it from inside. This in turn reflects a difference in frame of reference relevant to the work of a scientist: often it is possible to view a process, event, or phenomenon from outside; but sometimes one must view it from inside—which is more challenging.
Frame of Reference in Science
Now imagine that the visitor from outer space (a handy example of someone with no preconceived ideas) were to land in the United States. If
Philosophy (literally, “love of knowledge”) is the most fundamental of all disciplines: hence, most persons who complete the work for a doctorate receive a “doctor of philosophy” (Ph.D.) degree. Among the sciences, physics—a direct offspring of philosophy, as noted earlier—is the most fun-
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the visitor landed in New York City, Chicago, or Los Angeles, he or she would conclude that America is a very crowded, fast-paced country in which a number of ethnic groups live in close proximity. But if the visitor first arrived in Iowa or Nebraska, he or she might well decide that the United States is a sparsely populated land, economically dependent on agriculture and composed almost entirely of Caucasians.
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damental, and frame of reference is among its most basic concepts.
Frame of Reference
Hence, it is necessary to take a seemingly backward approach in explaining how frame of reference works, examining first the broad applications of the principle and then drawing upon its specific relation to physics. It makes little sense to discuss first the ways that physicists apply frame of reference, and only then to explain the concept in terms of everyday life. It is more meaningful to relate frame of reference first to familiar, or at least easily comprehensible, experiences—as has been done. At this point, however, it is appropriate to discuss how the concept is applied to the sciences. People use frame of reference every day— indeed, virtually every moment—of their lives, without thinking about it. Rare indeed is the person who “walks a mile in another person’s shoes”—that is, someone who tries to see events from the viewpoint of another. Physicists, on the other hand, have to be acutely aware of their frame of reference. Moreover, they must “rise above” their frame of reference in the sense that they have to take it into account in making calculations. For physicists in particular, and scientists in general, frame of reference has abundant “real-life applications.”
LINES
OF
LONGITUDE
ON
EARTH
ARE
MEASURED
AGAINST THE LINE PICTURED HERE: THE IAN” RUNNING THROUGH
“PRIME MERIDGREENWICH, ENGLAND. AN
IMAGINARY LINE DRAWN THROUGH THAT SPOT MARKS THE Y-AXIS FOR ALL VERTICAL COORDINATES ON
EARTH, 0° ALONG THE X-AXIS, WHICH IS THE EQUATOR. THE PRIME MERIDIAN, HOWEVER, IS AN ARBITRARY STANDARD THAT DEPENDS ON ONE’S FRAME OF REFERENCE. (Photograph by Dennis di Cicco/Corbis. ReproWITH A VALUE OF
duced by permission.)
REAL-LIFE A P P L I C AT I O N S Points and Graphs There is no such thing as an absolute frame of reference—that is, a frame of reference that is fixed, and not dependent on anything else. If the entire universe consisted of just two points, it would be impossible (and indeed irrelevant) to say which was to the right of the other. There would be no right and left: in order to have such a distinction, it is necessary to have a third point from which to evaluate the other two points. As long as there are just two points, there is only one dimension. The addition of a third point—as long as it does not lie along a straight line drawn through the first two points—creates two dimensions, length and width. From the frame of reference of any one point, then, it is possible to say which of the other two points is to the right. S C I E N C E O F E V E RY DAY T H I N G S
Clearly, the judgment of right or left is relative, since it changes from point to point. A more absolute judgment (but still not a completely absolute one) would only be possible from the frame of reference of a fourth point. But to constitute a new dimension, that fourth point could not lie on the same plane as the other three points—more specifically, it should not be possible to create a single plane that encompasses all four points. Assuming that condition is met, however, it then becomes easier to judge right and left. Yet right and left are never fully absolute, a fact easily illustrated by substituting people for points. One may look at two objects and judge which is to the right of the other, but if one stands on one’s head, then of course right and left become reversed. Of course, when someone is upside-down, the correct orientation of left and right is still VOLUME 2: REAL-LIFE PHYSICS
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fairly obvious. In certain situations observed by physicists and other scientists, however, orientation is not so simple. It then becomes necessary to assign values to various points, and for this, scientists use tools such as the Cartesian coordinate system. C O O R D I N AT E S
AND
AX E S .
Though it is named after the French mathematician and philosopher René Descartes (15961650), who first described its principles, the Cartesian system owes at least as much to Pierre de Fermat (1601-1665). Fermat, a brilliant French amateur mathematician—amateur in the sense that he was not trained in mathematics, nor did he earn a living from that discipline—greatly developed the Cartesian system. A coordinate is a number or set of numbers used to specify the location of a point on a line, on a surface such as a plane, or in space. In the Cartesian system, the x-axis is the horizontal line of reference, and the y-axis the vertical line of reference. Hence, the coordinate (0, 0) designates the point where the x- and y-axes meet. All numbers to the right of 0 on the x-axis, and above 0 on the y-axis, have a positive value, while those to the left of 0 on the x-axis, or below 0 on the y-axis have a negative value. This version of the Cartesian system only accounts for two dimensions, however; therefore, a z-axis, which constitutes a line of reference for the third dimension, is necessary in three-dimensional graphs. The z-axis, too, meets the x- and yaxes at (0, 0), only now that point is designated as (0, 0, 0). In the two-dimensional Cartesian system, the x-axis equates to “width” and the y-axis to “height.” The introduction of a z-axis adds the dimension of “depth”—though in fact, length, width, and height are all relative to the observer’s frame of reference. (Most representations of the three-axis system set the x- and y-axes along a horizontal plane, with the z-axis perpendicular to them.) Basic studies in physics, however, typically involve only the x- and y-axes, essential to plotting graphs, which, in turn, are integral to illustrating the behavior of physical processes. T H E T R I P L E P O I N T. For instance, there is a phenomenon known as the “triple point,” which is difficult to comprehend unless one sees it on a graph. For a chemical compound such as water or carbon dioxide, there is a point at which it is simultaneously a liquid, a solid, and
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a vapor. This, of course, seems to go against common sense, yet a graph makes it clear how this is possible. Using the x-axis to measure temperature and the y-axis pressure, a number of surprises become apparent. For instance, most people associate water as a vapor (that is, steam) with very high temperatures. Yet water can also be a vapor—for example, the mist on a winter morning—at relatively low temperatures and pressures, as the graph shows. The graph also shows that the higher the temperature of water vapor, the higher the pressure will be. This is represented by a line that curves upward to the right. Note that it is not a straight line along a 45° angle: up to about 68°F (20°C), temperature increases at a somewhat greater rate than pressure does, but as temperature gets higher, pressure increases dramatically. As everyone knows, at relatively low temperatures water is a solid—ice. Pressure, however, is relatively high: thus on a graph, the values of temperatures and pressure for ice lie above the vaporization curve, but do not extend to the right of 32°F (0°C) along the x-axis. To the right of 32°F, but above the vaporization curve, are the coordinates representing the temperature and pressure for water in its liquid state. Water has a number of unusual properties, one of which is its response to high pressures and low temperatures. If enough pressure is applied, it is possible to melt ice—thus transforming it from a solid to a liquid—at temperatures below the normal freezing point of 32°F. Thus, the line that divides solid on the left from liquid on the right is not exactly parallel to the y-axis: it slopes gradually toward the y-axis, meaning that at ultra-high pressures, water remains liquid even though it is well below the freezing point. Nonetheless, the line between solid and liquid has to intersect the vaporization curve somewhere, and it does—at a coordinate slightly above freezing, but well below normal atmospheric pressure. This is the triple point, and though “common sense” might dictate that a thing cannot possibly be solid, liquid, and vapor all at once, a graph illustrating the triple point makes it clear how this can happen.
Numbers In the above discussion—and indeed throughout this book—the existence of the decimal, or base-
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Frame of Reference
(y-axis) pressure
(liquid) (solid)
triple point
(x-axis)
THIS CARTESIAN
(vapor)
temperature
COORDINATE GRAPH SHOWS HOW A SUBSTANCE SUCH AS WATER COULD EXPERIENCE A TRIPLE
POINT—A POINT AT WHICH IT IS SIMULTANEOUSLY A LIQUID, A SOLID, AND A VAPOR.
10, numeration system is taken for granted. Yet that system is a wonder unto itself, involving a complicated interplay of arbitrary and real values. Though the value of the number 10 is absolute, the expression of it (and its use with other numbers) is relative to a frame of reference: one could just as easily use a base-12 system. Each numeration system has its own frame of reference, which is typically related to aspects of the human body. Thus throughout the course of history, some societies have developed a base2 system based on the two hands or arms of a person. Others have used the fingers on one hand (base-5) as their reference point, or all the fingers and toes (base-20). The system in use throughout most of the world today takes as its frame of reference the ten fingers used for basic counting. C O E F F I C I E N T S . Numbers, of course, provide a means of assigning relative values to a variety of physical characteristics: length, mass, force, density, volume, electrical charge, and so on. In an expression such as “10 meters,” the numeral 10 is a coefficient, a number that serves as a measure for some characteristic or property. A coefficient may also be a factor against which other values are multiplied to provide a desired result.
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For instance, the figure 3.141592, better known as pi (π), is a well-known coefficient used in formulae for measuring the circumference or area of a circle. Important examples of coefficients in physics include those for static and sliding friction for any two given materials. A coefficient is simply a number—not a value, as would be the case if the coefficient were a measure of something.
Standards of Measurement Numbers and coefficients provide a convenient lead-in to the subject of measurement, a practical example of frame of reference in all sciences— and indeed, in daily life. Measurement always requires a standard of comparison: something that is fixed, against which the value of other things can be compared. A standard may be arbitrary in its origins, but once it becomes fixed, it provides a frame of reference. Lines of longitude, for instance, are measured against an arbitrary standard: the “Prime Meridian” running through Greenwich, England. An imaginary line drawn through that spot marks the line of reference for all longitudinal measures on Earth, with a value of 0°. There is nothing special about Greenwich in any profound scientific sense; rather, its place of impor-
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tance reflects that of England itself, which ruled the seas and indeed much of the world at the time the Prime Meridian was established. The Equator, on the other hand, has a firm scientific basis as the standard against which all lines of latitude are measured. Yet today, the coordinates of a spot on Earth’s surface are given in relation to both the Equator and the Prime Meridian. C A L I B R AT I O N . Calibration is the process of checking and correcting the performance of a measuring instrument or device against the accepted standard. America’s preeminent standard for the exact time of day, for instance, is the United States Naval Observatory in Washington, D.C. Thanks to the Internet, people all over the country can easily check the exact time, and correct their clocks accordingly.
There are independent scientific laboratories responsible for the calibration of certain instruments ranging from clocks to torque wrenches, and from thermometers to laser beam power analyzers. In the United States, instruments or devices with high-precision applications—that is, those used in scientific studies, or by high-tech industries—are calibrated according to standards established by the National Institute of Standards and Technology (NIST). T H E VA L U E O F S TA N D A R D I Z AT I O N T O A S O C I E T Y. Standardiza-
tion of weights and measures has always been an important function of government. When Ch’in Shih-huang-ti (259-210 B.C.) united China for the first time, becoming its first emperor, he set about standardizing units of measure as a means of providing greater unity to the country—thus making it easier to rule.
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More importantly, it increased the cost of transporting freight from East to West. Russia also used the old Julian calendar, as opposed to the Gregorian calendar adopted throughout much of Western Europe after 1582. Thus October 25, 1917, in the Julian calendar of old Russia translated to November 7, 1917 in the Gregorian calendar used in the West. That date was not chosen arbitrarily: it was then that Communists, led by V. I. Lenin, seized power in the weakened former Russian Empire. METHODS S TA N DA R D S .
OF
DETERMINING
It is easy to understand, then, why governments want to standardize weights and measures—as the U.S. Congress did in 1901, when it established the Bureau of Standards (now NIST) as a nonregulatory agency within the Commerce Department. Today, NIST maintains a wide variety of standard definitions regarding mass, length, temperature, and so forth, against which other devices can be calibrated. Note that NIST keeps on hand definitions rather than, say, a meter stick or other physical model. When the French government established the metric system in 1799, it calibrated the value of a kilogram according to what is now known as the International Prototype Kilogram, a platinum-iridium cylinder housed near Sèvres in France. In the years since then, the trend has moved away from such physical expressions of standards, and toward standards based on a constant figure. Hence, the meter is defined as the distance light travels in a vacuum (an area of space devoid of air or other matter) during the interval of 1/299,792,458 of a second.
More than 2,000 years later, another empire—Russia—was negatively affected by its failure to adjust to the standards of technologically advanced nations. The time was the early twentieth century, when Western Europe was moving forward at a rapid pace of industrialization. Russia, by contrast, lagged behind—in part because its failure to adopt Western standards put it at a disadvantage.
M E T R I C V S . B R I T I S H . Scientists almost always use the metric system, not because it is necessarily any less arbitrary than the British or English system (pounds, feet, and so on), but because it is easier to use. So universal is the metric system within the scientific community that it is typically referred to simply as SI, an abbreviation of the French Système International d’Unités—that is, “International System of Units.”
Train travel between the West and Russia was highly problematic, because the width of railroad tracks in Russia was different than in Western Europe. Thus, adjustments had to be performed on trains making a border crossing, and this created difficulties for passenger travel.
The British system lacks any clear frame of reference for organizing units: there are 12 inches in a foot, but 3 feet in a yard, and 1,760 yards in a mile. Water freezes at 32°F instead of 0°, as it does in the Celsius scale associated with the metric system. In contrast to the English system, the
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metric system is neatly arranged according to the base-10 numerical framework: 10 millimeters to a centimeter, 100 centimeters to a meter, 1,000 meters to kilometer, and so on. The difference between the pound and the kilogram aptly illustrates the reason scientists in general, and physicists in particular, prefer the metric system. A pound is a unit of weight, meaning that its value is entirely relative to the gravitational pull of the planet on which it is measured. A kilogram, on the other hand, is a unit of mass, and does not change throughout the universe. Though the basis for a kilogram may not ultimately be any more fundamental than that for a pound, it measures a quality that—unlike weight—does not vary according to frame of reference.
Frame of Reference in Classical Physics and Astronomy Mass is a measure of inertia, the tendency of a body to maintain constant velocity. If an object is at rest, it tends to remain at rest, or if in motion, it tends to remain in motion unless acted upon by some outside force. This, as identified by the first law of motion, is inertia—and the greater the inertia, the greater the mass. Physicists sometimes speak of an “inertial frame of reference,” or one that has a constant velocity—that is, an unchanging speed and direction. Imagine if one were on a moving bus at constant velocity, regularly tossing a ball in the air and catching it. It would be no more difficult to catch the ball than if the bus were standing still, and indeed, there would be no way of determining, simply from the motion of the ball itself, that the bus was moving. But what if the inertial frame of reference suddenly became a non-inertial frame of reference—in other words, what if the bus slammed on its brakes, thus changing its velocity? While the bus was moving forward, the ball was moving along with it, and hence, there was no relative motion between them. By stopping, the bus responded to an “outside” force—that is, its brakes. The ball, on the other hand, experienced that force indirectly. Hence, it would continue to move forward as before, in accordance with its own inertia—only now it would be in motion relative to the bus.
powerful role in astronomy. At every moment, Earth is turning on its axis at about 1,000 MPH (1,600 km/h) and hurtling along its orbital path around the Sun at the rate of 67,000 MPH (107,826 km/h.) The fastest any human being— that is, the astronauts taking part in the Apollo missions during the late 1960s—has traveled is about 30% of Earth’s speed around the Sun.
Frame of Reference
Yet no one senses the speed of Earth’s movement in the way that one senses the movement of a car—or indeed the way the astronauts perceived their speed, which was relative to the Moon and Earth. Of course, everyone experiences the results of Earth’s movement—the change from night to day, the precession of the seasons—but no one experiences it directly. It is simply impossible, from the human frame of reference, to feel the movement of a body as large as Earth—not to mention larger progressions on the part of the Solar System and the universe. F R O M AS T R O N O M Y T O P H Y S I CS . The human body is in an inertial frame of
reference with regard to Earth, and hence experiences no relative motion when Earth rotates or moves through space. In the same way, if one were traveling in a train alongside another train at constant velocity, it would be impossible to perceive that either train was actually moving— unless one referred to some fixed point, such as the trees or mountains in the background. Likewise, if two trains were sitting side by side, and one of them started to move, the relative motion might cause a person in the stationary train to believe that his or her train was the one moving. For any measurement of velocity, and hence, of acceleration (a change in velocity), it is essential to establish a frame of reference. Velocity and acceleration, as well as inertia and mass, figured heavily in the work of Galileo Galilei (15641642) and Sir Isaac Newton (1642-1727), both of whom may be regarded as “founding fathers” of modern physics. Before Galileo, however, had come Nicholas Copernicus (1473-1543), the first modern astronomer to show that the Sun, and not Earth, is at the center of “the universe”— by which people of that time meant the Solar System.
A S T R O N O M Y A N D R E L AT I V E M O T I O N . The idea of relative motion plays a
In effect, Copernicus was saying that the frame of reference used by astronomers for millennia was incorrect: as long as they believed Earth to be the center, their calculations were bound to be wrong. Galileo and later Newton,
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through their studies in gravitation, were able to prove Copernicus’s claim in terms of physics. At the same time, without the understanding of a heliocentric (Sun-centered) universe that he inherited from Copernicus, it is doubtful that Newton could have developed his universal law of gravitation. If he had used Earth as the centerpoint for his calculations, the results would have been highly erratic, and no universal law would have emerged.
Relativity For centuries, the model of the universe developed by Newton stood unchallenged, and even today it identifies the basic forces at work when speeds are well below that of the speed of light. However, with regard to the behavior of light itself—which travels at 186,000 mi (299,339 km) a second—Albert Einstein (1879-1955) began to observe phenomena that did not fit with Newtonian mechanics. The result of his studies was the Special Theory of Relativity, published in 1905, and the General Theory of Relativity, published a decade later. Together these altered humanity’s view of the universe, and ultimately, of reality itself. Einstein himself once offered this charming explanation of his epochal theory: “Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. That’s relativity.” Of course, relativity is not quite as simple as that— though the mathematics involved is no more challenging than that of a high-school algebra class. The difficulty lies in comprehending how things that seem impossible in the Newtonian universe become realities near the speed of light.
Again, a full explanation—requiring reference to formulae regarding time dilation, and so on—would be a rather involved undertaking. The short answer, however, is that which was stated above: no measurement of space or time is absolute, but each depends on the relative motion of the observer and the observed. Put another way, there is no such thing as absolute motion, either in the three dimensions of space, or in the fourth dimension identified by Einstein, time. All motion is relative to a frame of reference. R E LAT I V I T Y A N D I T S I M P L I CA T I O N S . The ideas involved in relativity have
been verified numerous times, and indeed the only reason why they seem so utterly foreign to most people is that humans are accustomed to living within the Newtonian framework. Einstein simply showed that there is no universal frame of reference, and like a true scientist, he drew his conclusions entirely from what the data suggested. He did not form an opinion, and only then seek the evidence to confirm it, nor did he seek to extend the laws of relativity into any realm beyond that which they described.
An exhaustive explanation of relativity is far beyond the scope of the present discussion. What is important is the central precept: that no measurement of space or time is absolute, but depends on the relative motion of the observer (that is, the subject) and the observed (the object). Einstein further established that the movement of time itself is relative rather than absolute, a fact that would become apparent at speeds close to that of light. (His theory also showed that it is impossible to surpass that speed.)
Yet British historian Paul Johnson, in his unorthodox history of the twentieth century, Modern Times (1983; revised 1992), maintained that a world disillusioned by World War I saw a moral dimension to relativity. Describing a set of tests regarding the behavior of the Sun’s rays around the planet Mercury during an eclipse, the book begins with the sentence: “The modern world began on 29 May 1919, when photographs of a solar eclipse, taken on the Island of Principe off West Africa and at Sobral in Brazil, confirmed the truth of a new theory of the universe.”
Imagine traveling on a spaceship at nearly the speed of light while a friend remains station-
As Johnson went on to note, “...for most people, to whom Newtonian physics... were perfectly
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P LAY I N G T R I C K S W I T H T I M E .
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ary on Earth. Both on the spaceship and at the friend’s house on Earth, there is a TV camera trained on a clock, and a signal relays the image from space to a TV monitor on Earth, and vice versa. What the TV monitor reveals is surprising: from your frame of reference on the spaceship, it seems that time is moving more slowly for your friend on Earth than for you. Your friend thinks exactly the same thing—only, from the friend’s perspective, time on the spaceship is moving more slowly than time on Earth. How can this happen?
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Frame of Reference
KEY TERMS ABSOLUTE:
Fixed; not dependent on
anything else. The value of 10 is absolute, relating to unchanging numerical principles; on the other hand, the value of 10 dol-
FRAME OF REFERENCE:
spective of a subject in observing an object. Something that is perceived
OBJECT:
or observed by a subject.
lars is relative, reflecting the economy, inflation, buying power, exchange rates with other currencies, etc. CALIBRATION:
The process of check-
ing and correcting the performance of a measuring instrument or device against a commonly accepted standard.
RELATIVE:
tion to an x-axis, y-axis, and z-axis. The system is named after the French mathe-
Dependent on something
else for its value or for other identifying qualities. The fact that the United States has a constitution is an absolute, but the fact that it was ratified in 1787 is relative: that date has meaning only within the Western calendar.
CARTESIAN COORDINATE SYSTEM:
A method of specifying coordinates in rela-
The per-
SUBJECT:
Something (usually a per-
son) that perceives or observes an object and/or its behavior. The horizontal line of refer-
matician and philosopher René Descartes
X-AXIS:
(1596-1650), who first described its princi-
ence for points in the Cartesian coordinate
ples, but it was developed greatly by French
system.
mathematician and philosopher Pierre de
Y-AXIS:
Fermat (1601-1665).
for points in the Cartesian coordinate sys-
COEFFICIENT:
A number that serves
The vertical line of reference
tem.
as a measure for some characteristic or
Z-AXIS:
property. A coefficient may also be a factor
of the Cartesian coordinate system, the z-
against which other values are multiplied
axis is the line of reference for points in the
to provide a desired result.
third dimension. Typically the x-axis
In a three-dimensional version
A number or set of
equates to “width,” the y-axis to “height,”
numbers used to specify the location of a
and the z-axis to “depth”—though in fact
point on a line, on a surface such as a
length, width, and height are all relative to
plane, or in space.
the observer’s frame of reference.
COORDINATE:
comprehensible, relativity never became more than a vague source of unease. It was grasped that absolute time and absolute length had been dethroned.... All at once, nothing seemed certain in the spheres....At the beginning of the 1920s the belief began to circulate, for the first time at a popular level, that there were no longer any absolutes: of time and space, of good and evil, of knowledge, above all of value. Mistakenly but perhaps inevitably, relativity became confused with relativism.”
Certainly many people agree that the twentieth century—an age that saw unprecedented mass murder under the dictatorships of Adolf Hitler and Josef Stalin, among others—was characterized by moral relativism, or the belief that there is no right or wrong. And just as Newton’s discoveries helped usher in the Age of Reason, when thinkers believed it was possible to solve any problem through intellectual effort, it is quite plausible that Einstein’s theory may have had this negative moral effect.
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If so, this was certainly not Einstein’s intention. Aside from the fact that, as stated, he did not set out to describe anything other than the physical behavior of objects, he continued to believe that there was no conflict between his ideas and a belief in an ordered universe: “Relativity,” he once said, “teaches us the connection between the different descriptions of one and the same reality.” WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Fleisher, Paul. Relativity and Quantum Mechanics: Principles of Modern Physics. Minneapolis, MN: Lerner Publications, 2002. “Frame of Reference” (Web site). (March 21, 2001).
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“Inertial Frame of Reference” (Web site). (March 21, 2001). Johnson, Paul. Modern Times: The World from the Twenties to the Nineties. Revised edition. New York: HarperPerennial, 1992. King, Andrew. Plotting Points and Position. Illustrated by Tony Kenyon. Brookfield, CT: Copper Beech Books, 1998. Parker, Steve. Albert Einstein and Relativity. New York: Chelsea House, 1995. Robson, Pam. Clocks, Scales, and Measurements. New York: Gloucester Press, 1993. Rutherford, F. James; Gerald Holton; and Fletcher G. Watson. Project Physics. New York: Holt, Rinehart, and Winston, 1981. Swisher, Clarice. Relativity: Opposing Viewpoints. San Diego, CA: Greenhaven Press, 1990.
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K I N E M AT I C S A N D DYNAMICS
CONCEPT Webster’s defines physics as “a science that deals with matter and energy and their interactions.” Alternatively, physics can be described as the study of matter and motion, or of matter inmotion. Whatever the particulars of the definition, physics is among the most fundamental of disciplines, and hence, the rudiments of physics are among the most basic building blocks for thinking about the world. Foundational to an understanding of physics are kinematics, the explanation of how objects move, and dynamics, the study of why they move. Both are part of a larger branch of physics called mechanics, the study of bodies in motion. These are subjects that may sound abstract, but in fact, are limitless in their applications to real life.
HOW IT WORKS The Place of Physics in the Sciences Physics may be regarded as the queen of the sciences, not because it is “better” than chemistry or astronomy, but because it is the foundation on which all others are built. The internal and interpersonal behaviors that are the subject of the social sciences (psychology, anthropology, sociology, and so forth) could not exist without the biological framework that houses the human consciousness. Yet the human body and other elements studied by the biological and medical sciences exist within a larger environment, the framework for earth sciences, such as geology.
one corner of the realm studied by astronomy; and before a universe can even exist, there must be interactions of elements, the subject of chemistry. Yet even before chemicals can react, they have to do so within a physical framework—the realm of the most basic science—physics.
The Birth of Physics in Greece T H E F I R S T H Y P O T H E S I S . Indeed, physics stands in relation to the sciences as philosophy does to thought itself: without philosophy to provide the concept of concepts, it would be impossible to develop a consistent worldview in which to test ideas. It is no accident, then, that the founder of the physical sciences was also the world’s first philosopher, Thales (c. 625?-547? B.C.) of Miletus in Greek Asia Minor (now part of Turkey.) Prior to Thales’s time, religious figures and mystics had made statements regarding ethics or the nature of deity, but none had attempted statements concerning the fundamental nature of reality.
For instance, the Bible offers a story of Earth’s creation in the Book of Genesis which was well-suited to the understanding of people in the first millennium before Christ. But the writer of the biblical creation story made no attempt to explain how things came into being. He was concerned, rather, with showing that God had willed the existence of all physical reality by calling things into being—for example, by saying, “Let there be light.”
Earth sciences belong to a larger grouping of physical sciences, each more fundamental in concerns and broader in scope. Earth, after all, is but
Thales, on the other hand, made a genuine philosophical and scientific statement when he said that “Everything is water.” This was the first hypothesis, a statement capable of being scientif-
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ically tested for accuracy. Thales’s pronouncement did not mean he believed all things were necessarily made of water, literally. Rather, he appears to have been referring to a general tendency of movement: that the whole world is in a fluid state. AT T E M P T I N G TO UNDERS TA N D P H Y S I CA L R E A L I T Y. While
we can respect Thales’s statement for its truly earth-shattering implications, we may be tempted to read too much into it. Nonetheless, it is striking that he compared physical reality to water. On the one hand, there is the fact that water is essential to all life, and pervades Earth—but that is a subject more properly addressed by the realms of chemistry and the biological sciences. Perhaps of more interest to the physicist is the allusion to a fluid nature underlying all physical reality. The physical realm is made of matter, which appears in four states: solid, liquid, gas, and plasma. The last of these is not the same as blood plasma: containing many ionized atoms or molecules which exhibit collective behavior, plasma is the substance from which stars, for instance, are composed. Though not plentiful on Earth, within the universe it may be the most common of all four states. Plasma is akin to gas, but different in molecular structure; the other three states differ at the molecular level as well. Nonetheless, it is possible for a substance such as water—genuine H2O, not the figurative water of Thales—to exist in liquid, gas, or solid form, and the dividing line between these is not always fixed. In fact, physicists have identified a phenomenon known as the triple point: at a certain temperature and pressure, a substance can be solid, liquid, and gas all at once! The above statement shows just how challenging the study of physical reality can be, and indeed, these concepts would be far beyond the scope of Thales’s imagination, had he been presented with them. Though he almost certainly deserves to be called a “genius,” he lived in a world that viewed physical processes as a product of the gods’ sometimes capricious will. The behavior of the tides, for instance, was attributed to Poseidon. Though Thales’s statement began the process of digging humanity out from under the burden of superstition that had impeded scientific progress for centuries, the road forward would be a long one.
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M AT H E M AT I C S , MEASUREM E N T, A N D M AT T E R. In the two cen-
turies after Thales’s death, several other thinkers advanced understanding of physical reality in one way or another. Pythagoras (c. 580-c. 500 B.C.) taught that everything could be quantified, or related to numbers. Though he entangled this idea with mysticism and numerology, the concept itself influenced the idea that physical processes could be measured. Likewise, there were flaws at the heart of the paradoxes put forth by Zeno of Elea (c. 495-c. 430 B.C.), who set out to prove that motion was impossible—yet he was also the first thinker to analyze motion seriously. In one of Zeno’s paradoxes, he referred to an arrow being shot from a bow. At every moment of its flight, it could be said that the arrow was at rest within a space equal to its length. Though it would be some 2,500 years before slow-motion photography, in effect he was asking his listeners to imagine a snapshot of the arrow in flight. If it was at rest in that “snapshot,” he asked, so to speak, and in every other possible “snapshot,” when did the arrow actually move? These paradoxes were among the most perplexing questions of premodern times, and remain a subject of inquiry even today. In fact, it seems that Zeno unwittingly (for there is no reason to believe that he deliberately deceived his listeners) inserted an error in his paradoxes by treating physical space as though it were composed of an infinite number of points. In the ideal world of geometric theory, a point takes up no space, and therefore it is correct to say that a line contains an infinite number of points; but this is not the case in the real world, where a “point” has some actual length. Hence, if the number of points on Earth were limitless, so too would be Earth itself. Zeno’s contemporary Leucippus (c. 480-c. 420 B.C.) and his student Democritus (c. 460-370 B.C.) proposed a new and highly advanced model for the tiniest point of physical space: the atom. It would be some 2,300 years, however, before physicists returned to the atomic model.
Aristotle’s Flawed Physics The study of matter and motion began to take shape with Aristotle (384-322 B.C.); yet, though his Physics helped establish a framework for the discipline, his errors are so profound that any praise must be qualified. Certainly, Aristotle was
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one of the world’s greatest thinkers, who originated a set of formalized realms of study. However, in Physics he put forth an erroneous explanation of matter and motion that still prevailed in Europe twenty centuries later.
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Actually, Aristotle’s ideas disappeared in the late ancient period, as learning in general came to a virtual halt in Europe. That his writings— which on the whole did much more to advance the progress of science than to impede it—survived at all is a tribute to the brilliance of Arab, rather than European, civilization. Indeed, it was in the Arab world that the most important scientific work of the medieval period took place. Only after about 1200 did Aristotelian thinking once again enter Europe, where it replaced a crude jumble of superstitions that had been substituted for learning. T H E F O U R E L E M E N T S . According to Aristotelian physics, all objects consisted, in varying degrees, of one or more elements: air, fire, water, and earth. In a tradition that went back to Thales, these elements were not necessarily pure: water in the everyday world was composed primarily of the element water, but also contained smaller amounts of the other elements. The planets beyond Earth were said to be made up of a “fifth element,” or quintessence, of which little could be known.
The differing weights and behaviors of the elements governed the behavior of physical objects. Thus, water was lighter than earth, for instance, but heavier than air or fire. It was due to this difference in weight, Aristotle reasoned, that certain objects fall faster than others: a stone, for instance, because it is composed primarily of earth, will fall much faster than a leaf, which has much less earth in it. Aristotle further defined “natural” motion as that which moved an object toward the center of the Earth, and “violent” motion as anything that propelled an object toward anything other than its “natural” destination. Hence, all horizontal or upward motion was “violent,” and must be the direct result of a force. When the force was removed, the movement would end.
ARISTOTLE. (The Bettmann Archive. Reproduced by permission.)
revolving around it. Though in constant movement, these heavenly bodies were always in their “natural” place, because they could only move on the firmly established—almost groove-like— paths of their orbits around Earth. This in turn meant that the physical properties of matter and motion on other planets were completely different from the laws that prevailed on Earth. Of course, virtually every precept within the Aristotelian system is incorrect, and Aristotle compounded the influence of his errors by promoting a disdain for quantification. Specifically, he believed that mathematics had little value for describing physical processes in the real world, and relied instead on pure observation without attempts at measurement.
Moving Beyond Aristotle
ter is the destination of all “natural” motion, it is easy to comprehend the Aristotelian cosmology, or model of the universe. Earth itself was in the center, with all other bodies (including the Sun)
Faulty as Aristotle’s system was, however, it possessed great appeal because much of it seemed to fit with the evidence of the senses. It is not at all immediately apparent that Earth and the other planets revolve around the Sun, nor is it obvious that a stone and a leaf experience the same acceleration as they fall toward the ground. In fact, quite the opposite appears to be the case: as everyone knows, a stone falls faster than a leaf. Therefore, it would seem reasonable—on the
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Kinematics and Dynamics
Kinematics: How Objects Move By the sixteenth century, the Aristotelian worldview had become so deeply ingrained that few European thinkers would have considered the possibility that it could be challenged. Professors all over Europe taught Aristotle’s precepts to their students, and in this regard the University of Pisa in Italy was no different. Yet from its classrooms would emerge a young man who not only questioned, but ultimately overturned the Aristotelian model: Galileo Galilei (1564-1642.)
GALILEO. (Archive Photos, Inc. Reproduced by permission.)
surface of it, at least—to accept Aristotle’s conclusion that this difference results purely from a difference in weight. Today, of course, scientists—and indeed, even people without any specialized scientific knowledge—recognize the lack of merit in the Aristotelian system. The stone does fall faster than the leaf, but only because of air resistance, not weight. Hence, if they fell in a vacuum (a space otherwise entirely devoid of matter, including air), the two objects would fall at exactly the same rate.
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Challenges to Aristotle had been slowly growing within the scientific communities of the Arab and later the European worlds during the preceding millennium. Yet the ideas that most influenced Galileo in his break with Aristotle came not from a physicist but from an astronomer, Nicolaus Copernicus (1473-1543.) It was Copernicus who made a case, based purely on astronomical observation, that the Sun and not Earth was at the center of the universe. Galileo embraced this model of the cosmos, but was later forced to renounce it on orders from the pope in Rome. At that time, of course, the Catholic Church remained the single most powerful political entity in Europe, and its endorsement of Aristotelian views—which philosophers had long since reconciled with Christian ideas—is a measure of Aristotle’s impact on thinking. GALILEO’S REVOLUTION IN P H Y S I CS . After his censure by the Church,
As with a number of truths about matter and motion, this is not one that appears obvious, yet it has been demonstrated. To prove this highly nonintuitive hypothesis, however, required an approach quite different from Aristotle’s—an approach that involved quantification and the separation of matter and motion into various components. This was the beginning of real progress in physics, and in a sense may be regarded as the true birth of the discipline. In the years that followed, understanding of physics would grow rapidly, thanks to advancements of many individuals; but their studies could not have been possible without the work of one extraordinary thinker who dared to question the Aristotelian model.
Galileo was placed under house arrest and was forbidden to study astronomy. Instead he turned to physics—where, ironically, he struck the blow that would destroy the bankrupt scientific system endorsed by Rome. In 1638, he published Discourses and Mathematical Demonstrations Concerning Two New Sciences Pertaining to Mathematics and Local Motion, a work usually referred to as Two New Sciences. In it, he laid the groundwork for physics by emphasizing a new method that included experimentation, demonstration, and quantification of results.
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In this book—highly readable for a work of physics written in the seventeenth century— Galileo used a dialogue, an established format among philosophers and scientists of the past.
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The character of Salviati argued for Galileo’s ideas and Simplicio for those of Aristotle, while the genial Sagredo sat by and made occasional comments. Through Salviati, Galileo chose to challenge Aristotle on an issue that to most people at the time seemed relatively settled: the claim that objects fall at differing speeds according to their weight. In order to proceed with his aim, Galileo had to introduce a number of innovations, and indeed, he established the subdiscipline of kinematics, or how objects move. Aristotle had indicated that when objects fall, they fall at the same rate from the moment they begin to fall until they reach their “natural” position. Galileo, on the other hand, suggested an aspect of motion, unknown at the time, that became an integral part of studies in physics: acceleration.
Scalars and Vectors Even today, many people remain confused as to what acceleration is. Most assume that acceleration means only an increase in speed, but in fact this represents only one of several examples of acceleration. Acceleration is directly related to velocity, often mistakenly identified with speed. In fact, speed is what scientists today would call a scalar quantity, or one that possesses magnitude but no specific direction. Speed is the rate at which the position of an object changes over a given period of time; thus people say “miles (or kilometers) per hour.” A story problem concerning speed might state that “A train leaves New York City at a rate of 60 miles (96.6 km/h). How far will it have traveled in 73 minutes?” Note that there is no reference to direction, whereas if the story problem concerned velocity—a vector, that is, a quantity involving both magnitude and direction—it would include some crucial qualifying phrase after “New York City”: “for Boston,” perhaps, or “northward.” In practice, the difference between speed and velocity is nearly as large as that between a math problem and real life: few people think in terms of driving 60 miles, for instance, without also considering the direction they are traveling.
at the head of the previous one. Then it is possible to draw a vector from the tail of the first to the head of the last. This is the sum of the vectors, known as a resultant, which measures the net change. Suppose, for instance, that a car travels east 4 mi (6.44 km), then due north 3 mi (4.83 km). This may be drawn on a graph with four units along the x axis, then 3 units along the y axis, making two sides of a triangle. The number of sides to the resulting shape is always one more than the number of vectors being added; the final side is the resultant. From the tail of the first segment, a diagonal line drawn to the head of the last will yield a measurement of 5 units—the resultant, which in this case would be equal to 5 mi (8 km) in a northeasterly direction. V E LO C I T Y A N D AC C E L E RA T I O N . The directional component of velocity
makes it possible to consider forms of motion other than linear, or straight-line, movement. Principal among these is circular, or rotational motion, in which an object continually changes direction and thus, velocity. Also significant is projectile motion, in which an object is thrown, shot, or hurled, describing a path that is a combination of horizontal and vertical components. Furthermore, velocity is a key component in acceleration, which is defined as a change in velocity. Hence, acceleration can mean one of five things: an increase in speed with no change in direction (the popular, but incorrect, definition of the overall concept); a decrease in speed with no change in direction; a decrease or increase of speed with a change in direction; or a change in direction with no change in speed. If a car speeds up or slows down while traveling in a straight line, it experiences acceleration. So too does an object moving in rotational motion, even if its speed does not change, because its direction will change continuously.
Dynamics: Why Objects Move
One can apply the same formula with velocity, though the process is more complicated. To obtain change in distance, one must add vectors, and this is best done by means of a diagram. You can draw each vector as an arrow on a graph, with the tail of each vector
G A L I L E O ’ S T E S T. To return to Galileo, he was concerned primarily with a specific form of acceleration, that which occurs due to the force of gravity. Aristotle had provided an explanation of gravity—if a highly flawed one— with his claim that objects fall to their “natural” position; Galileo set out to develop the first truly scientific explanation concerning how objects fall to the ground.
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According to Galileo’s predictions, two metal balls of differing sizes would fall with the same rate of acceleration. To test his hypotheses, however, he could not simply drop two balls from a rooftop—or have someone else do so while he stood on the ground—and measure their rate of fall. Objects fall too fast, and lacking sophisticated equipment available to scientists today, he had to find another means of showing the rate at which they fell. This he did by resorting to a method Aristotle had shunned: the use of mathematics as a means of modeling the behavior of objects. This is such a deeply ingrained aspect of science today that it is hard to imagine a time when anyone would have questioned it, and that very fact is a tribute to Galileo’s achievement. Since he could not measure speed, he set out to find an equation relating total distance to total time. Through a detailed series of steps, Galileo discovered that in uniform or constant acceleration from rest—that is, the acceleration he believed an object experiences due to gravity—there is a proportional relationship between distance and time. With this mathematical model, Galileo could demonstrate uniform acceleration. He did this by using an experimental model for which observation was easier than in the case of two falling bodies: an inclined plane, down which he rolled a perfectly round ball. This allowed him to extrapolate that in free fall, though velocity was greater, the same proportions still applied and therefore, acceleration was constant. P O I N T I N G T H E WAY T O WA R D N E W T O N . The effects of Galileo’s system were
enormous: he demonstrated mathematically that acceleration is constant, and established a method of hypothesis and experiment that became the basis of subsequent scientific investigation. He did not, however, attempt to calculate a figure for the acceleration of bodies in free fall; nor did he attempt to explain the overall principle of gravity, or indeed why objects move as they do—the focus of a subdiscipline known as dynamics.
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he lived in England, where the pope had no power—was free to explore the implications of his physical studies without fear of Rome’s intervention. Born in the very year Galileo died, his name was Sir Isaac Newton (1642-1727.) N E W T O N ’ S T H R E E LAW S O F M O T I O N . In discussing the movement of the
planets, Galileo had coined the term inertia to describe the tendency of an object in motion to remain in motion, and an object at rest to remain at rest. This idea would be the starting point of Newton’s three laws of motion, and Newton would greatly expand on the concept of inertia. The three laws themselves are so significant to the understanding of physics that they are treated separately elsewhere in this volume; here they are considered primarily in terms of their implications regarding the larger topic of matter and motion. Introduced by Newton in his Principia (1687), the three laws are: • First law of motion: An object at rest will remain at rest, and an object in motion will remain in motion, at a constant velocity unless or until outside forces act upon it. • Second law of motion: The net force acting upon an object is a product of its mass multiplied by its acceleration. • Third law of motion: When one object exerts a force on another, the second object exerts on the first a force equal in magnitude but opposite in direction. These laws made final the break with Aristotle’s system. In place of “natural” motion, Newton presented the concept of motion at a uniform velocity—whether that velocity be a state of rest or of uniform motion. Indeed, the closest thing to “natural” motion (that is, true “natural” motion) is the behavior of objects in outer space. There, free from friction and away from the gravitational pull of Earth or other bodies, an object set in motion will remain in motion forever due to its own inertia. It follows from this observation, incidentally, that Newton’s laws were and are universal, thus debunking the old myth that the physical properties of realms outside Earth are fundamentally different from those of Earth itself.
At the end of Two New Sciences, Sagredo offered a hopeful prediction: “I really believe that... the principles which are set forth in this little treatise will, when taken up by speculative minds, lead to another more remarkable result....” This prediction would come true with the work of a man who, because he lived in a somewhat more enlightened time—and because
the principle of inertia, and the second law makes reference to the means by which inertia is measured: mass, or the resistance of an object to a
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M A S S A N D G R A V I TAT I O N A L AC C E L E RAT I O N . The first law establishes
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Kinematics and Dynamics
KEY TERMS A change in velocity.
ACCELERATION:
A quantity that possesses
SCALAR:
The study of why objects
only magnitude, with no specific direction.
move as they do; compare with kinematics.
Mass, time, and speed are all scalars. The
DYNAMICS:
FORCE:
The product of mass multi-
plied by acceleration. HYPOTHESIS:
A statement capable of
being scientifically tested for accuracy. INERTIA:
The tendency of an object in
opposite of a scalar is a vector. The rate at which the position
SPEED:
of an object changes over a given period of time. Space entirely devoid of
VACUUM:
motion to remain in motion, and of an
matter, including air.
object at rest to remain at rest.
VECTOR:
KINEMATICS:
The study of how
objects move; compare with dynamics.
A quantity that possesses
both magnitude and direction. Velocity, acceleration, and weight (which involves
A measure of inertia, indicating
the downward acceleration due to gravity)
the resistance of an object to a change in its
are examples of vectors. Its opposite is a
motion—including a change in velocity.
scalar.
MASS:
MATTER:
The material of physical real-
ity. There are four basic states of matter: solid, liquid, gas, and plasma. MECHANICS:
The study of bodies in
motion.
The speed of an object in a
VELOCITY:
particular direction. WEIGHT:
A measure of the gravitation-
al force on an object; the product of mass multiplied by the acceleration due to grav-
The sum of two or more
ity. (The latter is equal to 32 ft or 9.8 m per
vectors, which measures the net change in
second per second, or 32 ft/9.8 m per sec-
distance and direction.
ond squared.)
RESULTANT:
change in its motion—including a change in velocity. Mass is one of the most fundamental notions in the world of physics, and it too is the subject of a popular misconception—one which confuses it with weight. In fact, weight is a force, equal to mass multiplied by the acceleration due to gravity.
velocity is also increasing at a rate of 32 ft per second per second. Hence, after 2 seconds, its velocity will be 64 ft (per second; after 3 seconds 96 ft per second, and so on.
It was Newton, through a complicated series of steps he explained in his Principia, who made possible the calculation of that acceleration—an act of quantification that had eluded Galileo. The figure most often used for gravitational acceleration at sea level is 32 ft (9.8 m) per second squared. This means that in the first second, an object falls at a velocity of 32 ft per second, but its
Mass does not vary anywhere in the universe, whereas weight changes with any change in the gravitational field. When United States astronaut Neil Armstrong planted the American flag on the Moon in 1969, the flagpole (and indeed Armstrong himself) weighed much less than on Earth. Yet it would have required exactly the same amount of force to move the pole (or, again, Armstrong) from side to side as it would have on Earth, because their mass and therefore their inertia had not changed.
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Beyond Mechanics Kinematics and Dynamics
The implications of Newton’s three laws go far beyond what has been described here; but again, these laws, as well as gravity itself, receive a much more thorough treatment elsewhere in this volume. What is important in this context is the gradually unfolding understanding of matter and motion that formed the basis for the study of physics today. After Newton came the Swiss mathematician and physicist Daniel Bernoulli (1700-1782), who pioneered another subdiscipline, fluid dynamics, which encompasses the behavior of liquids and gases in contact with solid objects. Air itself is an example of a fluid, in the scientific sense of the term. Through studies in fluid dynamics, it became possible to explain the principles of air resistance that cause a leaf to fall more slowly than a stone—even though the two are subject to exactly the same gravitational acceleration, and would fall at the same speed in a vacuum. EXTENDING THE REALM OF P H Y S I CA L S T U DY. The work of Galileo,
Newton, and Bernoulli fit within one of five major divisions of classical physics: mechanics, or the study of matter, motion, and forces. The other principal divisions are acoustics, or studies in sound; optics, the study of light; thermodynamics, or investigations regarding the relationships between heat and other varieties of energy; and electricity and magnetism. (These subjects, and subdivisions within them, also receive extensive treatment elsewhere in this book.) Newton identified one type of force, gravitation, but in the period leading up to the time of Scottish physicist James Clerk Maxwell (18311879), scientists gradually became aware of a new fundamental interaction in the universe. Building on studies of numerous scientists, Maxwell hypothesized that electricity and magnetism are in fact differing manifestations of a second variety of force, electromagnetism. M O D E R N P H Y S I CS . The term classical physics, used above, refers to the subjects of study from Galileo’s time through the end of the nineteenth century. Classical physics deals primarily with subjects that can be discerned by the senses, and addressed processes that could be observed on a large scale. By contrast, modern
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physics, which had its beginnings with the work of Max Planck (1858-1947), Albert Einstein (1879-1955), Niels Bohr (1885-1962), and others at the beginning of the twentieth century, addresses quite a different set of topics. Modern physics is concerned primarily with the behavior of matter at the molecular, atomic, or subatomic level, and thus its truths cannot be grasped with the aid of the senses. Nor is classical physics much help in understanding modern physics. The latter, in fact, recognizes two forces unknown to classical physicists: weak nuclear force, which causes the decay of some subatomic particles, and strong nuclear force, which binds the nuclei of atoms with a force 1 trillion (1012) times as great as that of the weak nuclear force. Things happen in the realm of modern physics that would have been inconceivable to classical physicists. For instance, according to quantum mechanics—first developed by Planck—it is not possible to make a measurement without affecting the object (e.g., an electron) being measured. Yet even atomic, nuclear, and particle physics can be understood in terms of their effects on the world of experience: challenging as these subjects are, they still concern—though within a much more complex framework—the physical fundamentals of matter and motion. WHERE TO LEARN MORE Ballard, Carol. How Do We Move? Austin, TX: Raintree Steck-Vaughn, 1998. Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Fleisher, Paul. Objects in Motion: Principles of Classical Mechanics. Minneapolis, MN: Lerner Publications, 2002. Hewitt, Sally. Forces Around Us. New York: Children’s Press, 1998. Measure for Measure: Sites That Do the Work for You (Web site). (March 7, 2001). Motion, Energy, and Simple Machines (Web site). (March 7, 2001). Physlink.com (Web site). (March 7, 2001). Rutherford, F. James; Gerald Holton; and Fletcher G. Watson. Project Physics. New York: Holt, Rinehart, and Winston, 1981. Wilson, Jerry D. Physics: Concepts and Applications, second edition. Lexington, MA: D. C. Heath, 1981.
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D E N S I T Y A N D VO LU M E
CONCEPT Density and volume are simple topics, yet in order to work within any of the hard sciences, it is essential to understand these two types of measurement, as well as the fundamental quantity involved in conversions between them—mass. Measuring density makes it possible to distinguish between real gold and fake gold, and may also give an astronomer an important clue regarding the internal composition of a planet.
mental quality, mass, in determining this significantly less fundamental property of weight. According to the second law of motion, weight is a force equal to mass multiplied by acceleration. Acceleration, in turn, is equal to change in velocity divided by change in time. Velocity, in turn, is equal to distance (a form of length) divided by time. If one were to express weight in terms of l, t, and m, with these representing, respectively, the fundamental properties of length, time, and mass, it would be expressed as
M
HOW IT WORKS There are four fundamental standards by which most qualities in the physical world can be measured: length, mass, time, and electric current. The volume of a cube, for instance, is a unit of length cubed: the length is multiplied by the width and multiplied by the height. Width and height, however, are not distinct standards of measurement: they are simply versions of length, distinguished by their orientation. Whereas length is typically understood as a distance along an x-axis in one-dimensional space, width adds a second dimension, and height a third. Of particular concern within this essay are length and mass, since volume is measured in terms of length, and density in terms of the ratio between mass and volume. Elsewhere in this book, the distinction between mass and weight has been presented numerous times from the standpoint of a person whose mass and weight are measured on Earth, and again on the Moon. Mass, of course, does not change, whereas weight does, due to the difference in gravitational force exerted by Earth as compared with that of its satellite, the Moon. But consider instead the role of the funda-
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•
t
D
2
—clearly, a much more complicated formula than that of mass!
Mass So what is mass? Again, the second law of motion, derived by Sir Isaac Newton (16421727), is the key: mass is the ratio of force to acceleration. This topic, too, is discussed in numerous places throughout this book; what is actually of interest here is a less precise identification of mass, also made by Newton. Before formulating his laws of motion, Newton had used a working definition of mass as the quantity of matter an object possesses. This is not of much value for making calculations or measurements, unlike the definition in the second law. Nonetheless, it serves as a useful reminder of matter’s role in the formula for density. Matter can be defined as a physical substance not only having mass, but occupying space. It is composed of atoms (or in the case of subatomic particles, it is part of an atom), and is
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Density and Volume
HOW
DOES A GIGANTIC STEEL SHIP, SUCH AS THE SUPERTANKER PICTURED HERE, STAY AFLOAT, EVEN THOUGH IT
HAS A WEIGHT DENSITY FAR GREATER THAN THE WATER BELOW IT?
THE
ANSWER LIES IN ITS CURVED HULL, WHICH
CONTAINS A LARGE AMOUNT OF OPEN SPACE AND ALLOWS THE SHIP TO SPREAD ITS AVERAGE DENSITY TO A LOWER LEVEL THAN THE WATER. (Photograph by Vince Streano/Corbis. Reproduced by permission.)
convertible with energy. The form or state of matter itself is not important: on Earth it is primarily observed as a solid, liquid, or gas, but it can also be found (particularly in other parts of the universe) in a fourth state, plasma.
ed by volume. It so happens that the three items represent the three states of matter on Earth: liquid (water), solid (iron), and gas (helium). For the most part, solids tend to be denser than liquids, and liquids denser than gasses.
Yet there are considerable differences among types of matter—among various elements and states of matter. This is apparent if one imagines three gallon jugs, one containing water, the second containing helium, and the third containing iron filings. The volume of each is the same, but obviously, the mass is quite different.
One of the interesting things about density, as distinguished from mass and volume, is that it has nothing to do with the amount of material. A kilogram of iron differs from 10 kilograms of iron both in mass and volume, but the density of both samples is the same. Indeed, as discussed below, the known densities of various materials make it possible to determine whether a sample of that material is genuine.
The reason, of course, is that at a molecular level, there is a difference in mass between the compound H2O and the elements helium and iron. In the case of helium, the second-lightest of all elements after hydrogen, it would take a great deal of helium for its mass to equal that of iron. In fact, it would take more than 43,000 gallons of helium to equal the mass of the iron in one gallon jug!
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Volume Mass, because of its fundamental nature, is sometimes hard to comprehend, and density requires an explanation in terms of mass and volume. Volume, on the other hand, appears to be quite straightforward—and it is, when one is describing a solid of regular shape. In other situations, however, volume is more complicated.
Rather than comparing differences in molecular mass among the three substances, it is easier to analyze them in terms of density, or mass divid-
As noted earlier, the volume of a cube can be obtained simply by multiplying length by width by height. There are other means for measuring
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SINCE SCIENTISTS KNOW EARTH’S MASS AS WELL AS ITS VOLUME, TY—APPROXIMATELY 5 G/CM3. (Corbis. Reproduced by permission.)
the volume of other straight-sided objects, such as a pyramid. That formula applies, indeed, for any polyhedron (a three-dimensional closed solid bounded by a set number of plane figures) that constitutes a modified cube in which the lengths of the three dimensions are unequal— that is, an oblong shape.
THEY ARE EASILY ABLE TO COMPUTE ITS DENSI-
REAL-LIFE A P P L I C AT I O N S Measuring Volume
For a cylinder or sphere, volume measurements can be obtained by applying formulae involving radius (r) and the constant π, roughly equal to 3.14. The formula for volume of a cylinder is V = πr2h, where h is the height. A sphere’s volume can be obtained by the formula (4/3)πr3. Even the volume of a cone can be easily calculated: it is onethird that of a cylinder of equal base and height.
What about the volume of a solid that is irregular in shape? Some irregularly shaped objects, such as a scooter, which consists primarily of one round wheel and a number of oblong shapes, can be measured by separating them into regular shapes. Calculus may be employed with more complex problems to obtain the volume of an irregular shape—but the most basic method is simply to immerse the object in water. This procedure involves measuring the volume of the water before and after immersion, and calculating the difference. Of course, the object being
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measured cannot be water-soluble; if it is, its volume must be measured in a non-water-based liquid such as alcohol. Measuring liquid volumes is easy, given the fact that liquids have no definite shape, and will simply take the shape of the container in which they are placed. Gases are similar to liquids in the sense that they expand to fit their container; however, measurement of gas volume is a more involved process than that used to measure either liquids or solids, because gases are highly responsive to changes in temperature and pressure. If the temperature of water is raised from its freezing point to its boiling point (32° to 212°F or 0 to 100°C), its volume will increase by only 2%. If its pressure is doubled from 1 atm (defined as normal air pressure at sea level—14.7 poundsper-square-inch or 1.013 x 105 Pa) to 2 atm, volume will decrease by only 0.01%. Yet, if air were heated from 32° to 212°F, its volume would increase by 37%; and if its pressure were doubled from 1 atm to 2, its volume would decrease by 50%. Not only do gases respond dramatically to changes in temperature and pressure, but also, gas molecules tend to be non-attractive toward one another—that is, they do not tend to stick together. Hence, the concept of “volume” involving gas is essentially meaningless, unless its temperature and pressure are known.
Buoyancy: Volume and Density Consider again the description above, of an object with irregular shape whose volume is measured by immersion in water. This is not the only interesting use of water and solids when dealing with volume and density. Particularly intriguing is the concept of buoyancy expressed in Archimedes’s principle.
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and ran naked through the streets of Syracuse shouting “Eureka!” (I have found it). What Archimedes had discovered was, in short, the reason why ships float: because the buoyant, or lifting, force of an object immersed in fluid is equal to the weight of the fluid displaced by the object. H O W A S T E E L S H I P F LOAT S O N WAT E R. Today most ships are made of
steel, and therefore, it is even harder to understand why an aircraft carrier weighing many thousands of tons can float. After all, steel has a weight density (the preferred method for measuring density according to the British system of measures) of 480 pounds per cubic foot, and a density of 7,800 kilograms-per-cubic-meter. By contrast, sea water has a weight density of 64 pounds per cubic foot, and a density of 1,030 kilograms-per-cubic-meter. This difference in density should mean that the carrier would sink like a stone—and indeed it would, if all the steel in it were hammered flat. As it is, the hull of the carrier (or indeed of any seaworthy ship) is designed to displace or move a quantity of water whose weight is greater than that of the vessel itself. The weight of the displaced water—that is, its mass multiplied by the downward acceleration due to gravity—is equal to the buoyant force that the ocean exerts on the ship. If the ship weighs less than the water it displaces, it will float; but if it weighs more, it will sink. Put another way, when the ship is placed in the water, it displaces a certain quantity of water whose weight can be expressed in terms of Vdg— volume multiplied by density multiplied by the downward acceleration due to gravity. The density of sea water is a known figure, as is g (32 ft or 9.8 m/sec2); thus the only variable for the water displaced is its volume.
More than twenty-two centuries ago, the Greek mathematician, physicist, and inventor Archimedes (c. 287-212 B.C.) received orders from the king of his hometown—Syracuse, a Greek colony in Sicily—to weigh the gold in the royal crown. According to legend, it was while bathing that Archimedes discovered the principle that is today named after him. He was so excited, legend maintains, that he jumped out of his bath
For the buoyant force on the ship, g will of course be the same, and the value of V will be the same as for the water. In order for the ship to float, then, its density must be much less than that of the water it has displaced. This can be achieved by designing the ship in order to maximize displacement. The steel is spread over as large an area as possible, and the curved hull, when seen in cross section, contains a relatively large area of open space. Obviously, the density of this space is much less than that of water; thus, the average density of the ship is greatly reduced, which enables it to float.
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Density and Volume
KEY TERMS ARCHIMEDES’S PRINCIPLE:
A rule
of physics which holds that the buoyant force of an object immersed in fluid is
part of an atom), and is convertible into energy. SPECIFIC GRAVITY:
an object or substance relative to the densi-
by the object. It is named after the Greek
ty of water; or more generally, the ratio
mathematician, physicist, and inventor
between the densities of two objects or
Archimedes (c. 287-212 B.C.), who first
substances.
identified it. BUOYANCY:
The tendency of an object
immersed in a fluid to float. This can be explained by Archimedes’s principle. DENSITY:
VOLUME:
The
amount
ter within a given area.
of
three-
dimensional space an object occupies. Volume is usually expressed in cubic units of length.
The ratio of mass to vol-
ume—in other words, the amount of mat-
WEIGHT DENSITY:
The proper term
for density within the British system of weights and measures. The pound is a unit
According to the second law of
of weight rather than of mass, and thus
motion, mass is the ratio of force to acceler-
British units of density are usually ren-
ation. Mass may likewise be defined, though
dered in terms of weight density—that is,
much less precisely, as the amount of mat-
pounds-per-cubic-foot. By contrast, the
ter an object contains. Mass is also the
metric or international units measure mass
product of volume multiplied by density.
density (referred to simply as “density”),
MASS:
Physical substance that occu-
which is rendered in terms of kilograms-
pies space, has mass, is composed of atoms
per-cubic-meter, or grams-per-cubic-
(or in the case of subatomic particles, is
centimeter.
MATTER:
Comparing Densities As noted several times, the densities of numerous materials are known quantities, and can be easily compared. Some examples of density, all expressed in terms of kilograms per cubic meter, are: • • • • • • • • • •
The density of
equal to the weight of the fluid displaced
Hydrogen: 0.09 kg/m3 Air: 1.3 kg/m3 Oak: 720 kg/m3 Ethyl alcohol: 790 kg/m3 Ice: 920 kg/m3 Pure water: 1,000 kg/m3 Concrete: 2,300 kg/m3 Iron and steel: 7,800 kg/m3 Lead: 11,000 kg/m3 Gold: 19,000 kg/m3
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Note that pure water (as opposed to sea water, which is 3% denser) has a density of 1,000 kilograms per cubic meter, or 1 gram per cubic centimeter. This value is approximate; however, at a temperature of 39.2°F (4°C) and under normal atmospheric pressure, it is exact, and so, water is a useful standard for measuring the specific gravity of other substances. S P E C I F I C G RAV I T Y A N D T H E D E N S I T I E S O F P LA N E T S . Specific
gravity is the ratio between the densities of two objects or substances, and it is expressed as a number without units of measure. Due to the value of 1 g/cm3 for water, it is easy to determine the specific gravity of a given substance, which will have the same number value as its density. For example, the specific gravity of concrete, which has a density of 2.3 g/cm3, is 2.3. The speVOLUME 2: REAL-LIFE PHYSICS
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cific gravities of gases are usually determined in comparison to the specific gravity of dry air. Most rocks near the surface of Earth have a specific gravity of somewhere between 2 and 3, while the specific gravity of the planet itself is about 5. How do scientists know that the density of Earth is around 5 g/cm3? The computation is fairly simple, given the fact that the mass and volume of the planet are known. And given the fact that most of what lies close to Earth’s surface— sea water, soil, rocks—has a specific gravity well below 5, it is clear that Earth’s interior must contain high-density materials, such as nickel or iron. In the same way, calculations regarding the density of other objects in the Solar System provide a clue as to their interior composition. Closer to home, a comparison of density makes it possible to determine whether a piece of jewelry alleged to be solid gold is really genuine. To determine the answer, one must drop it in a beaker of water with graduated units of measure clearly marked. (Here, figures are given in cubic centimeters, since these are easiest to use in this context.) ALL
T H AT
GLITTERS.
Suppose the item has a mass of 10 grams. The density of gold is 19 g/cm3, and since V = m/d = 10/19, the volume of water displaced by the gold should be 0.53 cm3. Suppose that instead, the item displaced 0.91 cm3 of water. Clearly, it is not gold, but what is it?
26
pure gold and pure lead, one could calculate what portion of the item was gold and which lead. It is possible, of course, that it could contain some other metal, but given the high specific gravity of lead, and the fact that its density is relatively close to that of gold, lead is a favorite gold substitute among jewelry counterfeiters. WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Chahrour, Janet. Flash! Bang! Pop! Fizz!: Exciting Science for Curious Minds. Illustrated by Ann Humphrey Williams. Hauppauge, N.Y.: Barron’s, 2000. “Density and Specific Gravity” (Web site). (March 27, 2001). “Density, Volume, and Cola” (Web site). (March 27, 2001). “The Mass Volume Density Challenge” (Web site). (March 27, 2001). “Metric Density and Specific Gravity” (Web site). (March 27, 2001). “Mineral Properties: Specific Gravity” The Mineral and Gemstone Kingdom (Web site). (March 27, 2001). Robson, Pam. Clocks, Scales and Measurements. New York: Gloucester Press, 1993.
Given the figures for mass and volume, its density would be equal to m/V = 10/0.91 = 11 g/cm3—which happens to be the density of lead. If on the other hand the amount of water displaced were somewhere between the values for
Willis, Shirley. Tell Me How Ships Float. Illustrated by the author. New York: Franklin Watts, 1999.
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“Volume, Mass, and Density” (Web site). (March 27, 2001).
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C O N S E R VAT I O N L A W S
CONCEPT The term “conservation laws” might sound at first like a body of legal statutes geared toward protecting the environment. In physics, however, the term refers to a set of principles describing certain aspects of the physical universe that are preserved throughout any number of reactions and interactions. Among the properties conserved are energy, linear momentum, angular momentum, and electrical charge. (Mass, too, is conserved, though only in situations well below the speed of light.) The conservation of these properties can be illustrated by examples as diverse as dropping a ball (energy); the motion of a skater spinning on ice (angular momentum); and the recoil of a rifle (linear momentum).
HOW IT WORKS The conservation laws describe physical properties that remain constant throughout the various processes that occur in the physical world. In physics, “to conserve” something means “to result in no net loss of ” that particular component. For each such component, the input is the same as the output: if one puts a certain amount of energy into a physical system, the energy that results from that system will be the same as the energy put into it. The energy may, however, change forms. In addition, the operations of the conservation laws are—on Earth, at least—usually affected by a number of other forces, such as gravity, friction, and air resistance. The effects of these forces, combined with the changes in form that take place within a given conserved property, sometimes make it difficult to perceive the working of the conservation laws. It was stated above that
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the resulting energy of a physical system will be the same as the energy that was introduced to it. Note, however, that the usable energy output of a system will not be equal to the energy input. This is simply impossible, due to the factors mentioned above—particularly friction. When one puts gasoline into a motor, for instance, the energy that the motor puts out will never be as great as the energy contained in the gasoline, because part of the input energy is expended in the operation of the motor itself. Similarly, the angular momentum of a skater on ice will ultimately be dissipated by the resistant force of friction, just as that of a Frisbee thrown through the air is opposed both by gravity and air resistance—itself a specific form of friction. In each of these cases, however, the property is still conserved, even if it does not seem so to the unaided senses of the observer. Because the motor has a usable energy output less than the input, it seems as though energy has been lost. In fact, however, the energy has only changed forms, and some of it has been diverted to areas other than the desired output. (Both the noise and the heat of the motor, for instance, represent uses of energy that are typically considered undesirable.) Thus, upon closer study of the motor—itself an example of a system—it becomes clear that the resulting energy, if not the desired usable output, is the same as the energy input. As for the angular momentum examples in which friction, or air resistance, plays a part, here too (despite all apparent evidence to the contrary) the property is conserved. This is easier to understand if one imagines an object spinning in outer space, free from the opposing force of friction. Thanks to the conservation of angular
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Conservation Laws
AS
THIS HUNTER FIRES HIS RIFLE, THE RIFLE PRODUCES A BACKWARD
“KICK”
AGAINST HIS SHOULDER.
THIS
KICK,
WITH A VELOCITY IN THE OPPOSITE DIRECTION OF THE BULLET ’S TRAJECTORY, HAS A MOMENTUM EXACTLY THE SAME AS THAT OF THE BULLET ITSELF: HENCE MOMENTUM IS CONSERVED. (Photograph by Tony Arruza/Corbis. Reproduced by
permission.)
momentum, an object set into rotation in space will continue to spin indefinitely. Thus, if an astronaut in the 1960s, on a spacewalk from his capsule, had set a screwdriver spinning in the emptiness of the exosphere, the screwdriver would still be spinning today!
and kinetic energy. Every system possesses a certain quantity of both, and the sum of its potential and kinetic energy is known as mechanical energy. The mechanical energy within a system does not change, but the relative values of potential and kinetic energy may be altered.
Energy and Mass
A S I M P L E E XA M P L E O F M E C H A N I CA L E N E R GY. If one held a base-
Among the most fundamental statements in all of science is the conservation of energy: a system isolated from all outside factors will maintain the same total amount of energy, even though energy transformations from one form or another take place. Energy is manifested in many varieties, including thermal, electromagnetic, sound, chemical, and nuclear energy, but all these are merely reflections of three basic types of energy. There is potential energy, which an object possesses by virtue of its position; kinetic energy, which it possesses by virtue of its motion; and rest energy, which it possesses by virtue of its mass.
28
ball at the top of a tall building, it would have a certain amount of potential energy. Once it was dropped, it would immediately begin losing potential energy and gaining kinetic energy proportional to the potential energy it lost. The relationship between the two forms, in fact, is inverse: as the value of one variable decreases, that of the other increases in exact proportion.
The last of these three will be discussed in the context of the relationship between energy and mass; at present the concern is with potential
The ball cannot keep falling forever, losing potential energy and gaining kinetic energy. In fact, it can never gain an amount of kinetic energy greater than the potential energy it possessed in the first place. At the moment before it hits the ground, the ball’s kinetic energy is equal to the potential energy it possessed at the top of the building. Correspondingly, its potential energy is zero—the same amount of kinetic energy it possessed before it was dropped.
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Then, as the ball hits the ground, the energy is dispersed. Most of it goes into the ground, and depending on the rigidity of the ball and the ground, this energy may cause the ball to bounce. Some of the energy may appear in the form of sound, produced as the ball hits bottom, and some will manifest as heat. The total energy, however, will not be lost: it will simply have changed form.
Conservation Laws
R E S T E N E R G Y. The values for mechanical energy in the above illustration would most likely be very small; on the other hand, the rest or mass energy of the baseball would be staggering. Given the weight of 0.333 pounds for a regulation baseball, which on Earth converts to 0.15 kg in mass, it would possess enough energy by virtue of its mass to provide a year’s worth of electrical power to more than 150,000 American homes. This leads to two obvious questions: how can a mere baseball possess all that energy? And if it does, how can the energy be extracted and put to use?
The answer to the second question is, “By accelerating it to something close to the speed of light”—which is more than 27,000 times faster than the fastest speed ever achieved by humans. (The astronauts on Apollo 10 in May 1969 reached nearly 25,000 MPH (40,000 km/h), which is more than 33 times the speed of sound but still insignificant when compared to the speed of light.) The answer to the first question lies in the most well-known physics formula of all time: E = mc2 In 1905, Albert Einstein (1879-1955) published his Special Theory of Relativity, which he followed a decade later with his General Theory of Relativity. These works introduced the world to the above-mentioned formula, which holds that energy is equal to mass multiplied by the squared speed of light. This formula gained its widespread prominence due to the many implications of Einstein’s Relativity, which quite literally changed humanity’s perspective on the universe. Most concrete among those implications was the atom bomb, made possible by the understanding of mass and energy achieved by Einstein.
AS SURYA BONALY
GOES INTO A SPIN ON THE ICE, SHE
DRAWS IN HER ARMS AND LEG, REDUCING THE MOMENT OF INERTIA. LAR
BECAUSE
MOMENTUM ,
OF THE CONSERVATION OF ANGU-
HER
ANGULAR
VELOCITY
WILL
INCREASE, MEANING THAT SHE WILL SPIN MUCH FASTER.
(Bolemian Nomad Picturemakers/Corbis. Reproduced by permission.)
mechanical energy, its relation to the other forms can be easily shown. All three are defined in terms of mass. Potential energy is equal to mgh, where m is mass, g is gravity, and h is height. Kinetic energy is equal to 1⁄2 mv2, where v is velocity. In fact—using a series of steps that will not be demonstrated here—it is possible to directly relate the kinetic and rest energy formulae.
In fact, E = mc2 is the formula for rest energy, sometimes called mass energy. Though rest energy is “outside” of kinetic and potential energy in the sense that it is not defined by the abovedescribed interactions within the larger system of
The kinetic energy formula describes the behavior of objects at speeds well below the speed of light, which is 186,000 mi (297,600 km) per second. But at speeds close to that of the speed of light, 1⁄2 mv2 does not accurately reflect the energy possessed by the object. For instance, if v were equal to 0.999c (where c represents the speed of light), then the application of the formula 1⁄2 mv2 would yield a value equal to less than 3% of the object’s real energy. In order to calculate the true energy of an object at 0.999c, it would be necessary to apply a different formula for total energy, one that takes into account the fact that, at such a speed, mass itself becomes energy.
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C O N S E R V AT I O N
OF
MASS.
Mass itself is relative at speeds approaching c, and, in fact, becomes greater and greater the closer an object comes to the speed of light. This may seem strange in light of the fact that there is, after all, a law stating that mass is conserved. But mass is only conserved at speeds well below c: as an object approaches 186,000 mi (297,600 km) per second, the rules are altered. The conservation of mass states that total mass is constant, and is unaffected by factors such as position, velocity, or temperature, in any system that does not exchange any matter with its environment. Yet, at speeds close to c, the mass of an object increases dramatically. In such a situation, the mass would be equal to the rest, or starting mass, of the object divided by 8(1 – (v2/c2), where v is the object’s speed of relative motion. The denominator of this equation will always be less than one, and the greater the value of v, the smaller the value of the denominator. This means that at a speed of c, the denominator is zero—in other words, the object’s mass is infinite! Obviously, this is not possible, and indeed, what the formula actually shows is that no object can travel faster than the speed of light. Of particular interest to the present discussion, however, is the fact, established by relativity theory, that mass can be converted into energy. Hence, as noted earlier, a baseball or indeed any object can be converted into energy—and since the formula for rest energy requires that the mass be multiplied by c2, clearly, even an object of virtually negligible mass can generate a staggering amount of energy. This conversion of mass to energy happens well below the speed of light, in a very small way, when a stick of dynamite explodes. A portion of that stick becomes energy, and the fact that this portion is equal to just 6 parts out of 100 billion indicates the vast proportions of energy available from converted mass.
Other Conservation Laws In addition to the conservation of energy, as well as the limited conservation of mass, there are laws governing the conservation of momentum, both for an object in linear (straight-line) motion, and for one in angular (rotational) motion. Momentum is a property that a moving body possesses by virtue of its mass and velocity, which determines the amount of force and time
30
VOLUME 2: REAL-LIFE PHYSICS
required to stop it. Linear momentum is equal to mass multiplied by velocity, and the conservation of linear momentum law states that when the sum of the external force vectors acting on a physical system is equal to zero, the total linear momentum of the system remains unchanged, or conserved. Angular momentum, or the momentum of an object in rotational motion, is equal to mr2ω, where m is mass, r is the radius of rotation, and ω (the Greek letter omega) stands for angular velocity. According to the conservation of angular momentum law, when the sum of the external torques acting on a physical system is equal to zero, the total angular momentum of the system remains unchanged. Torque is a force applied around an axis of rotation. When playing the old game of “spin the bottle,” for instance, one is applying torque to the bottle and causing it to rotate. E L E C T R I C C H A R G E . The conservation of both linear and angular momentum are best explained in the context of real-life examples, provided below. Before going on to those examples, however, it is appropriate here to discuss a conservation law that is outside the realm of everyday experience: the conservation of electric charge, which holds that for an isolated system, the net electric charge is constant.
This law is “outside the realm of everyday experience” such that one cannot experience it through the senses, but at every moment, it is happening everywhere. Every atom has positively charged protons, negatively charged electrons, and uncharged neutrons. Most atoms are neutral, possessing equal numbers of protons and electrons; but, as a result of some disruption, an atom may have more protons than electrons, and thus, become positively charged. Conversely, it may end up with a net negative charge due to a greater number of electrons. But the protons or electrons it released or gained did not simply appear or disappear: they moved from one part of the system to another—that is, from one atom to another atom, or to several other atoms. Throughout these changes, the charge of each proton and electron remains the same, and the net charge of the system is always the sum of its positive and negative charges. Thus, it is impossible for any electrical charge in the universe to be smaller than that of a proton or electron. Likewise, throughout the universe, there is
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always the same number of negative and positive electrical charges: just as energy changes form, the charges simply change position. There are also conservation laws describing the behavior of subatomic particles, such as the positron and the neutrino. However, the most significant of the conservation laws are those involving energy (and mass, though with the limitations discussed above), linear momentum, angular momentum, and electrical charge.
REAL-LIFE A P P L I C AT I O N S Conservation of Linear Momentum: Rifles and Rockets F I R I N G A R I F L E . The conservation of linear momentum is reflected in operations as simple as the recoil of a rifle when it is fired, and in those as complex as the propulsion of a rocket through space. In accordance with the conservation of momentum, the momentum of a system must be the same after it undergoes an operation as it was before the process began. Before firing, the momentum of a rifle and bullet is zero, and therefore, the rifle-bullet system must return to that same zero-level of momentum after it is fired. Thus, the momentum of the bullet must be matched—and “cancelled” within the system under study—by a corresponding backward momentum.
When a person shooting a gun pulls the trigger, it releases the bullet, which flies out of the barrel toward the target. The bullet has mass and velocity, and it clearly has momentum; but this is only half of the story. At the same time it is fired, the rifle produces a “kick,” or sharp jolt, against the shoulder of the person who fired it. This backward kick, with a velocity in the opposite direction of the bullet’s trajectory, has a momentum exactly the same as that of the bullet itself: hence, momentum is conserved. But how can the rearward kick have the same momentum as that of the bullet? After all, the bullet can kill a person, whereas, if one holds the rifle correctly, the kick will not even cause any injury. The answer lies in several properties of linear momentum. First of all, as noted earlier, momentum is equal to mass multiplied by velocity; the actual proportions of mass and velocity,
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however, are not important as long as the backward momentum is the same as the forward momentum. The bullet is an object of relatively small mass and high velocity, whereas the rifle is much larger in mass, and hence, its rearward velocity is correspondingly small.
Conservation Laws
In addition, there is the element of impulse, or change in momentum. Impulse is the product of force multiplied by change or interval in time. Again, the proportions of force and time interval do not matter, as long as they are equal to the momentum change—that is, the difference in momentum that occurs when the rifle is fired. To avoid injury to one’s shoulder, clearly force must be minimized, and for this to happen, time interval must be extended. If one were to fire the rifle with the stock (the rear end of the rifle) held at some distance from one’s shoulder, it would kick back and could very well produce a serious injury. This is because the force was delivered over a very short time interval—in other words, force was maximized and time interval minimized. However, if one holds the rifle stock firmly against one’s shoulder, this slows down the delivery of the kick, thus maximizing time interval and minimizing force. R O C K E T I N G T H R O U G H S PAC E .
Contrary to popular belief, rockets do not move by pushing against a surface such as a launchpad. If that were the case, then a rocket would have nothing to propel it once it had been launched, and certainly there would be no way for a rocket to move through the vacuum of outer space. Instead, what propels a rocket is the conservation of momentum. Upon ignition, the rocket sends exhaust gases shooting downward at a high rate of velocity. The gases themselves have mass, and thus, they have momentum. To balance this downward momentum, the rocket moves upward—though, because its mass is greater than that of the gases it expels, it will not move at a velocity as high as that of the gases. Once again, the upward or forward momentum is exactly the same as the downward or backward momentum, and linear momentum is conserved. Rather than needing something to push against, a rocket in fact performs best in outer space, where there is nothing—neither launchpad nor even air—against which to push. Not only is “pushing” irrelevant to the operation of
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Conservation Laws
KEY TERMS A set of principles describing physical properties that remain constant—that is, are conserved—throughout the various processes that occur in the physical world. The most significant of these laws concerns the conservation of energy (as well as, with qualifications, the conservation of mass); conservation of linear momentum; conservation of angular momentum; and conservation of electrical charge.
CONSERVATION OF MASS:
CONSERVATION OF ANGULAR MO-
mass begins converting to energy.
CONSERVATION
LAWS:
A physical law stating that when the sum of the external torques acting on a physical system is equal to zero, the total angular momentum of the system remains unchanged. Angular momentum is the momentum of an object in rotational motion, and torque is a force applied around an axis of rotation.
A phys-
ical principle stating that total mass is constant, and is unaffected by factors such as position, velocity, or temperature, in any system that does not exchange any matter with its environment. Unlike the other conservation laws, however, conservation of mass is not universally applicable, but applies only at speeds significant lower than that of light—186,000 mi (297,600 km) per second. Close to the speed of light,
MENTUM:
In physics, “to conserve”
something means “to result in no net loss of ” that particular component. It is possible that within a given system, the component may change form or position, but as long as the net value of the component remains the same, it has been conserved. The force that resists
CONSERVATION OF ELECTRICAL
FRICTION:
A physical law which holds that for an isolated system, the net electrical charge is constant.
motion when the surface of one object
CHARGE:
A law of physics stating that within a system isolated from all other outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place.
CONSERVATION OF ENERGY:
CONSERVATION OF LINEAR MO-
A physical law stating that when the sum of the external force vectors acting on a physical system is equal to zero, the total linear momentum of the system remains unchanged—or is conserved.
MENTUM:
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CONSERVE:
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comes into contact with the surface of another. MOMENTUM:
A property that a mov-
ing body possesses by virtue of its mass and velocity, which determines the amount of force and time required to stop it. SYSTEM:
In physics, the term “system”
usually refers to any set of physical interactions isolated from the rest of the universe. Anything outside of the system, including all factors and forces irrelevant to a discussion of that system, is known as the environment.
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the rocket, but the rocket moves much more efficiently without the presence of air resistance. In the same way, on the relatively frictionless surface of an ice-skating rink, conservation of linear momentum (and hence, the process that makes possible the flight of a rocket through space) is easy to demonstrate. If, while standing on the ice, one throws an object in one direction, one will be pushed in the opposite direction with a corresponding level of momentum. However, since a person’s mass is presumably greater than that of the object thrown, the rearward velocity (and, therefore, distance) will be smaller. Friction, as noted earlier, is not the only force that counters conservation of linear momentum on Earth: so too does gravity, and thus, once again, a rocket operates much better in space than it does when under the influence of Earth’s gravitational field. If a bullet is fired at a bottle thrown into the air, the linear momentum of the spent bullet and the shattered pieces of glass in the infinitesimal moment just after the collision will be the same as that of the bullet and the bottle a moment before impact. An instant later, however, gravity will accelerate the bullet and the pieces downward, thus leading to a change in total momentum.
Conservation of Angular Momentum: Skaters and Other Spinners As noted earlier, angular momentum is equal to mr2ω, where m is mass, r is the radius of rotation, and ω stands for angular velocity. In fact, the first two quantities, mr2, are together known as moment of inertia. For an object in rotation, moment of inertia is the property whereby objects further from the axis of rotation move faster, and thus, contribute a greater share to the overall kinetic energy of the body. One of the most oft-cited examples of angular momentum—and of its conservation— involves a skater or ballet dancer executing a spin. As the skater begins the spin, she has one leg planted on the ice, with the other stretched behind her. Likewise, her arms are outstretched, thus creating a large moment of inertia. But when she goes into the spin, she draws in her
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arms and leg, reducing the moment of inertia. In accordance with conservation of angular momentum, mr2ω will remain constant, and therefore, her angular velocity will increase, meaning that she will spin much faster.
Conservation Laws
C O N S TA N T O R I E N TAT I O N . The motion of a spinning top and a Frisbee in flight also illustrate the conservation of angular momentum. Particularly interesting is the tendency of such an object to maintain a constant orientation. Thus, a top remains perfectly vertical while it spins, and only loses its orientation once friction from the floor dissipates its velocity and brings it to a stop. On a frictionless surface, however, it would remain spinning—and therefore upright—forever.
A Frisbee thrown without spin does not provide much entertainment; it will simply fall to the ground like any other object. But if it is tossed with the proper spin, delivered from the wrist, conservation of angular momentum will keep it in a horizontal position as it flies through the air. Once again, the Frisbee will eventually be brought to ground by the forces of air resistance and gravity, but a Frisbee hurled through empty space would keep spinning for eternity. WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. “Conservation Laws: An Online Physics Textbook” (Web site). (March 12, 2001). “Conservation Laws: The Most Powerful Laws of Physics” (Web site). (March 12, 2001). “Conservation of Energy.” NASA (Web site). (March 12, 2001). Elkana, Yehuda. The Discovery of the Conservation of Energy. With a foreword by I. Bernard Cohen. Cambridge, MA: Harvard University Press, 1974. “Momentum and Its Conservation” (Web site). (March 12, 2001). Rutherford, F. James; Gerald Holton; and Fletcher G. Watson. Project Physics. New York: Holt, Rinehart, and Winston, 1981. Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.
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S C I E N C E O F E V E RY DAY T H I N G S real-life Physics
K I N E M AT I C S A N D PA R T I C L E D Y N A M I C S MOMENTUM C E N T R I P E TA L F O R C E FRICTION LAWS OF MOTION GRAVITY PROJECTILE MOTION TORQUE
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Momentum
MOMENTUM
CONCEPT
Momentum and Inertia
The faster an object is moving—whether it be a baseball, an automobile, or a particle of matter— the harder it is to stop. This is a reflection of momentum, or specifically, linear momentum, which is equal to mass multiplied by velocity. Like other aspects of matter and motion, momentum is conserved, meaning that when the vector sum of outside forces equals zero, no net linear momentum within a system is ever lost or gained. A third important concept is impulse, the product of force multiplied by length in time. Impulse, also defined as a change in momentum, is reflected in the proper methods for hitting a baseball with force or surviving a car crash.
It might be tempting to confuse momentum with another physical concept, inertia. Inertia, as defined by the second law of motion, is the tendency of an object in motion to remain in motion, and of an object at rest to remain at rest. Momentum, by definition, involves a body in motion, and can be defined as the tendency of a body in motion to continue moving at a constant velocity.
HOW IT WORKS Like many other aspects of physics, the word “momentum” is a part of everyday life. The common meaning of momentum, however, unlike many other physics terms, is relatively consistent with its scientific meaning. In terms of formula, momentum is equal to the product of mass and velocity, and the greater the value of that product, the greater the momentum. Consider the term “momentum” outside the world of physics, as applied, for example, in the realm of politics. If a presidential candidate sees a gain in public-opinion polls, then wins a debate and embarks on a whirlwind speaking tour, the media comments that he has “gained momentum.” As with momentum in the framework of physics, what these commentators mean is that the candidate will be hard to stop—or to carry the analogy further, that he is doing enough of the right things (thus gaining “mass”), and doing them quickly enough, thereby gaining velocity. S C I E N C E O F E V E RY DAY T H I N G S
Not only does momentum differ from inertia in that it relates exclusively to objects in motion, but (as will be discussed below) the component of velocity in the formula for momentum makes it a vector—that is, a quantity that possesses both magnitude and direction. There is at least one factor that momentum very clearly has in common with inertia: mass, a measure of inertia indicating the resistance of an object to a change in its motion.
Mass and Weight Unlike velocity, mass is a scalar, a quantity that possesses magnitude without direction. Mass is often confused with weight, a vector quantity equal to its mass multiplied by the downward acceleration due to gravity. The weight of an object changes according to the gravitational force of the planet or other celestial body on which it is measured. Hence, the mass of a person on the Moon would be the same as it is on Earth, whereas the person’s weight would be considerably less, due to the smaller gravitational pull of the Moon. Given the unchanging quality of mass as opposed to weight, as well as the fact that scientists themselves prefer the much simpler metric VOLUME 2: REAL-LIFE PHYSICS
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Momentum
WHEN
BILLIARD BALLS COLLIDE, THEIR HARDNESS RESULTS IN AN ELASTIC COLLISION—ONE IN WHICH KINETIC ENER-
GY IS CONSERVED. (Photograph by John-Marshall Mantel/Corbis. Reproduced by permission.)
system, metric units will generally be used in the following discussion. Where warranted, of course, conversion to English or British units (for example, the pound, a unit of weight) will be provided. However, since the English unit of mass, the slug, is even more unfamiliar to most Americans than its metric equivalent, the kilogram, there is little point in converting kilos into slugs.
Velocity and Speed Not only is momentum often confused with inertia, and mass with weight, but in the everyday world the concepts of velocity and speed tend to be blurred. Speed is the rate at which the position of an object changes over a given period of time, expressed in terms such as “50 MPH.” It is a scalar quantity.
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Linear Momentum and Its Conservation Momentum itself is sometimes designated as p. It should be stressed that the form of momentum discussed here is strictly linear, or straight-line, momentum, in contrast to angular momentum, more properly discussed within the framework of rotational motion. Both angular and linear momentum abide by what are known as conservation laws. These are statements concerning quantities that, under certain conditions, remain constant or unchanging. The conservation of linear momentum law states that when the sum of the external force vectors acting on a physical system is equal to zero, the total linear momentum of the system remains unchanged—or conserved.
Velocity, by contrast, is a vector. If one were to say “50 miles per hour toward the northeast,” this would be an expression of velocity. Vectors are typically designated in bold, without italics; thus velocity is typically abbreviated v. Scalars, on the other hand, are rendered in italics. Hence, the formula for momentum is usually shown as mv.
The conservation of linear momentum is reflected both in the recoil of a rifle and in the propulsion of a rocket through space. When a rifle is fired, it produces a “kick”—that is, a sharp jolt to the shoulder of the person who has fired it—corresponding to the momentum of the bullet. Why, then, does the “kick” not knock a person’s shoulder off the way a bullet would? Because the rifle’s mass is much greater than that of the bullet, meaning that its velocity is much smaller.
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As for rockets, they do not—contrary to popular belief—move by pushing against a surface, such as a launch pad. If that were the case, then a rocket would have nothing to propel it once it is launched, and certainly there would be no way for a rocket to move through the vacuum of outer space. Instead, as it burns fuel, the rocket expels exhaust gases that exert a backward momentum, and the rocket itself travels forward with a corresponding degree of momentum.
Momentum
Systems Here, “system” refers to any set of physical interactions isolated from the rest of the universe. Anything outside of the system, including all factors and forces irrelevant to a discussion of that system, is known as the environment. In the pool-table illustration shown earlier, the interaction of the billiard balls in terms of momentum is the system under discussion. It is possible to reduce a system even further for purposes of clarity: hence, one might specify that the system consists only of the pool balls, the force applied to them, and the resulting momentum interactions. Thus, we will ignore the friction of the pool table’s surface, and the assumption will be that the balls are rolling across a frictionless plane.
WHEN
PARACHUTISTS LAND, THEY KEEP THEIR KNEES
BENT AND OFTEN ROLL OVER—ALL IN AN EFFORT TO LENGTHEN THE PERIOD OF THE FORCE OF IMPACT, THUS REDUCING ITS EFFECTS. (Photograph by James A. Sugar/Corbis.
Reproduced by permission.)
in velocity over a change or interval in time. Expressed as a formula, this is a
Impulse For an object to have momentum, some force must have set it in motion, and that force must have been applied over a period of time. Likewise, when the object experiences a collision or any other event that changes its momentum, that change may be described in terms of a certain amount of force applied over a certain period of time. Force multiplied by time interval is impulse, expressed in the formula F • δt, where F is force, δ (the Greek letter delta) means “a change” or “change in...”; and t is time.
= ∆v
∆t .
Thus, force is equal to
) )
m ∆v ∆t , an equation that can be rewritten as Fδt = mδv. In other words, impulse is equal to change in momentum.
As with momentum itself, impulse is a vector quantity. Whereas the vector component of momentum is velocity, the vector quantity in impulse is force. The force component of impulse can be used to derive the relationship between impulse and change in momentum. According to the second law of motion, F = m a; that is, force is equal to mass multiplied by acceleration. Acceleration can be defined as a change
This relationship between impulse and momentum change, derived here in mathematical terms, will be discussed below in light of several well-known examples from the real world. Note that the metric units of impulse and momentum are actually interchangeable, though they are typically expressed in different forms, for the purpose of convenience. Hence, momentum is usually rendered in terms of kilogram-meters-per-second (kg • m/s), whereas impulse is typically shown as newton-seconds (N • s). In the English system, momentum is shown in units of slug-feet per-
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another so that they collide head-on. Due to the properties of clay as a substance, the two lumps will tend to stick. Assuming the lumps are not of equal mass, they will continue traveling in the same direction as the lump with greater momentum.
Momentum
As they meet, the two lumps form a larger mass MV that is equal to the sum of their two individual masses. Once again, MV = m1v1 + m2v2. The M in MV is the sum of the smaller values m, and the V is the vector sum of velocity. Whereas M is larger than m1 or m2—the reason being that scalars are simply added like ordinary numbers—V is smaller than v1 or v2. This lower number for net velocity as compared to particle velocity will always occur when two objects are moving in opposite directions. (If the objects are moving in the same direction, V will have a value between that of v1 and v2.)
AS SAMMY SOSA’S
BAT HITS THIS BALL, IT APPLIES A
TREMENDOUS MOMENTUM CHANGE TO THE BALL. CONTACT WITH THE BALL,
SOSA
AFTER
WILL CONTINUE HIS
SWING, THEREBY CONTRIBUTING TO THE MOMENTUM CHANGE AND ALLOWING THE BALL TO TRAVEL FARTHER.
(AFP/Corbis. Reproduced by permission.)
second, and impulse in terms of the poundsecond.
REAL-LIFE A P P L I C AT I O N S When Two Objects Collide Two moving objects, both possessing momentum by virtue of their mass and velocity, collide with one another. Within the system created by their collision, there is a total momentum MV that is equal to their combined mass and the vector sum of their velocity. This is the case with any system: the total momentum is the sum of the various individual momentum products. In terms of a formula, this is expressed as MV = m1v1 + m2v2 + m3v3 +... and so on. As noted earlier, the total momentum will be conserved; however, the actual distribution of momentum within the system may change.
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To add the vector sum of the two lumps in collision, it is best to make a diagram showing the bodies moving toward one another, with arrows illustrating the direction of velocity. By convention, in such diagrams the velocity of an object moving to the right is rendered as a positive number, and that of an object moving to the left is shown with a negative number. It is therefore easier to interpret the results if the object with the larger momentum is shown moving to the right. The value of V will move in the same direction as the lump with greater momentum. But since the two lumps are moving in opposite directions, the momentum of the smaller lump will cancel out a portion of the greater lump’s momentum—much as a negative number, when added to a positive number of greater magnitude, cancels out part of the positive number’s value. They will continue traveling in the direction of the lump with greater momentum, now with a combined mass equal to the arithmetic sum of their masses, but with a velocity much smaller than either had before impact.
T W O LU M P S O F C LAY. Consider the behavior of two lumps of clay, thrown at one
B I L L I A R D B A L L S . The game of pool provides an example of a collision in which one object, the cue ball, is moving, while the other— known as the object ball—is stationary. Due to the hardness of pool balls, and their tendency not to stick to one another, this is also an example of an almost perfectly elastic collision—one in which kinetic energy is conserved.
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The colliding lumps of clay, on the other hand, are an excellent example of an inelastic collision, or one in which kinetic energy is not conserved. The total energy in a given system, such as that created by the two lumps of clay in collision, is conserved; however, kinetic energy may be transformed, for instance, into heat energy and/or sound energy as a result of collision. Whereas inelastic collisions involve soft, sticky objects, elastic collisions involve rigid, non-sticky objects. Kinetic energy and momentum both involve components of velocity and mass: p (momentum) is equal to mv, and KE (kinetic energy) equals 1⁄2 mv2. Due to the elastic nature of poolball collisions, when the cue ball strikes the object ball, it transfers its velocity to the latter. Their masses are the same, and therefore the resulting momentum and kinetic energy of the object ball will be the same as that possessed by the cue ball prior to impact. If the cue ball has transferred all of its velocity to the object ball, does that mean it has stopped moving? It does. Assuming that the interaction between the cue ball and the object ball constitutes a closed system, there is no other source from which the cue ball can acquire velocity, so its velocity must be zero. It should be noted that this illustration treats pool-ball collisions as though they were 100% elastic, though in fact, a portion of kinetic energy in these collisions is transformed into heat and sound. Also, for a cue ball to transfer all of its velocity to the object ball, it must hit it straighton. If the balls hit off-center, not only will the object ball move after impact, but the cue ball will continue to move—roughly at 90° to a line drawn through the centers of the two balls at the moment of impact.
Impulse: Breaking or Building the Impact
Impulse, again, is equal to momentum change—and also equal to force multiplied by time interval (or change in time). This means that the greater the force and the greater the amount of time over which it is applied, the greater the momentum change. Even more interesting is the fact that one can achieve the same momentum change with differing levels of force and time interval. In other words, a relatively low degree of force applied over a relatively long period of time would produce the same momentum change as a relatively high amount of force over a relatively short period of time.
Momentum
The conservation of kinetic energy in a collision is, as noted earlier, a function of the relative elasticity of that collision. The question of whether KE is transferred has nothing to do with impulse. On the other hand, the question of how KE is transferred—or, even more specifically, the interval over which the transfer takes place—is very much related to impulse. Kinetic energy, again, is equal to 1⁄2 mv2. If a moving car were to hit a stationary car head-on, it would transfer a quantity of kinetic energy to the stationary car equal to one-half its own mass multiplied by the square of its velocity. (This, of course, assumes that the collision is perfectly elastic, and that the mass of the cars is exactly equal.) A transfer of KE would also occur if two moving cars hit one another headon, especially in a highly elastic collision. Assuming one car had considerably greater mass and velocity than the other, a high degree of kinetic energy would be transferred—which could have deadly consequences for the people in the car with less mass and velocity. Even with cars of equal mass, however, a high rate of acceleration can bring about a potentially lethal degree of force. C R U M P L E Z O N E S I N CA R S . In a highly elastic car crash, two automobiles would bounce or rebound off one another. This would mean a dramatic change in direction—a reversal, in fact—hence, a sudden change in velocity and therefore momentum. In other words, the figure for mδv would be high, and so would that for impulse, Fδt.
When a cue ball hits an object ball in pool, it is safe to assume that a powerful impact is desired. The same is true of a bat hitting a baseball. But what about situations in which a powerful impact is not desired—as for instance when cars are crashing? There is, in fact, a relationship between impulse, momentum change, transfer of kinetic energy, and the impact—desirable or undesirable—experienced as a result.
On the other hand, it is possible to have a highly inelastic car crash, accompanied by a small change in momentum. It may seem logical to think that, in a crash situation, it would be better for two cars to bounce off one another than
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Momentum
KEY TERMS ACCELERATION:
A change velocity.
IMPULSE:
Acceleration can be expressed as a formula
time required to cause a change in
δv/δt—that is, change in velocity divided
momentum. Impulse is the product of
by change, or interval, in time.
force multiplied by a change, or interval, in
CONSERVATION
OF
LINEAR
time (Fδt):
the greater the momentum,
A physical law, which
the greater the force needed to change it,
states that when the sum of the external
and the longer the period of time over
force vectors acting on a physical system is
which it must be applied.
MOMENTUM:
equal to zero, the total linear momentum
INELASTIC COLLISION:
A collision
of the system remains unchanged—or is
in which kinetic energy is not conserved.
conserved.
(The total energy is conserved: kinetic In physics, “to conserve”
energy itself, however, may be transformed
something (for example, momentum or
into heat energy or sound energy.) Typical-
kinetic energy) means “to result in no net
ly, inelastic collisions involve non-rigid,
loss of ” that particular component. It is
sticky objects—for instance, lumps of clay.
possible that within a given system, one
At the other extreme is an elastic collision.
CONSERVE:
type of energy may be transformed into another type, but the net energy in the system will remain the same. ELASTIC COLLISION:
INERTIA:
The tendency of an object in
motion to remain in motion, and of an object at rest to remain at rest.
A collision in
which kinetic energy is conserved. Typically elastic collisions involve rigid, non-sticky
KINETIC ENERGY:
The energy an
object possesses by virtue of its motion. A measure of inertia, indicating
objects such as pool balls. At the other
MASS:
extreme is an inelastic collision.
the resistance of an object to a change in its
for them to crumple together. In fact, however, the latter option is preferable. When the cars crumple rather than rebounding, they do not experience a reversal in direction. They do experience a change in speed, of course, but the momentum change is far less than it would be if they rebounded. Furthermore, crumpling lengthens the amount of time during which the change in velocity occurs, and thus reduces impulse. But even with the reduced impulse of this momentum change, it is possible to further reduce the effect of force, another aspect of impact. Remember that mδv = Fδt: the value of force and time interval do not matter, as long as their product is equal to the momentum change. Because F and
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The amount of force and
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δt are inversely proportional, an increase in impact time will reduce the effects of force. For this reason, car manufacturers actually design and build into their cars a feature known as a crumple zone. A crumple zone—and there are usually several in a single automobile—is a section in which the materials are put together in such a way as to ensure that they will crumple when the car experiences a collision. Of course, the entire car cannot be one big crumple zone— this would be fatal for the driver and riders; however, the incorporation of crumple zones at key points can greatly reduce the effect of the force a car and its occupants must endure in a crash. Another major reason for crumple zones is to keep the passenger compartment of the car
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Momentum
KEY TERMS
CONTINUED
motion—including a change in velocity. A
all factors and forces irrelevant to a discus-
kilogram is a unit of mass, whereas a
sion of that system, is known as the envi-
pound is a unit of weight.
ronment.
MOMENTUM:
A property that a mov-
A quantity that possesses
VECTOR:
ing body possesses by virtue of its mass and
both magnitude and direction—as con-
velocity, which determines the amount of
trasted with a scalar, which possesses mag-
force and time (impulse) required to stop
nitude without direction. Vector quantities
it. Momentum—actually linear momen-
are usually expressed in bold, non-itali-
tum, as opposed to the angular momen-
cized letters, thus: F (force). They may also
tum of an object in rotational motion—is
be shown by placing an arrow over the let-
equal to mass multiplied by velocity.
ter designating the specific property, as for
SCALAR:
A quantity that possesses
instance v for velocity.
only magnitude, with no specific direc-
VECTOR
tion—as contrasted with a vector, which
yields the net result of all the vectors
possesses both magnitude and direction.
applied in a particular situation. In the case
Scalar quantities are usually expressed in
of momentum, the vector component is
italicized letters, thus: m (mass).
velocity. The best method is to make a dia-
SUM:
A calculation that
The rate at which the position
gram showing bodies in collision, with
of an object changes over a given period of
arrows illustrating the direction of velocity.
time.
On such a diagram, motion to the right is
SPEED:
SYSTEM:
In physics, the term “system”
usually refers to any set of physical interac-
assigned a positive value, and to the left a negative value.
tions isolated from the rest of the universe.
VELOCITY:
Anything outside of the system, including
particular direction.
intact. Many injuries are caused when the body of the car intrudes on the space of the occupants—as, for instance, when the floor buckles, or when the dashboard is pushed deep into the passenger compartment. Obviously, it is preferable to avoid this by allowing the fender to collapse.
The speed of an object in a
collision with part of the car. As it deflates, it is receding toward the dashboard even as the driver’s or passenger’s body is being hurled toward the dashboard. It slows down impact, extending the amount of time during which the force is distributed.
mizing force in a car accident, in this case by reducing the time over which the occupants move forward toward the dashboard or windshield. The airbag rapidly inflates, and just as rapidly begins to deflate, within the split-second that separates the car’s collision and a person’s
By the same token, a skydiver or paratrooper does not hit the ground with legs outstretched: he or she would be likely to suffer a broken bone or worse from such a foolish stunt. Rather, as a parachutist prepares to land, he or she keeps knees bent, and upon impact immediately rolls over to the side. Thus, instead of experiencing the force of impact over a short period of time, the parachutist lengthens the amount of time that force is experienced, which reduces its effects.
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The same principle applies if one were catching a water balloon. In order to keep it from bursting, one needs to catch the balloon in midair, then bring it to a stop slowly by “traveling” with it for a few feet before reducing its momentum down to zero. Once again, there is no way around the fact that one is attempting to bring about a substantial momentum change—a change equal in value to the momentum of the object in movement. Nonetheless, by increasing the time component of impulse, one reduces the effects of force. In old Superman comics, the “Man of Steel” often caught unfortunate people who had fallen, or been pushed, out of tall buildings. The cartoons usually showed him, at a stationary position in midair, catching the person before he or she could hit the ground. In fact, this would not save their lives: the force component of the sudden momentum change involved in being caught would be enough to kill the person. Of course, it is a bit absurd to quibble over scientific accuracy in Superman, but in order to make the situation more plausible, the “Man of Steel” should have been shown catching the person, then slowly following through on the trajectory of the fall toward earth. T H E C R A C K O F T H E B AT : I N C R E AS I N G I M PU L S E . But what if—
to once again turn the tables—a strong force is desired? This time, rather than two pool balls striking one another, consider what happens when a batter hits a baseball. Once more, the correlation between momentum change and impulse can create an advantage, if used properly. As the pitcher hurls the ball toward home plate, it has a certain momentum; indeed, a pitch thrown by a major-league player can send the ball toward the batter at speeds around 100 MPH (160 km/h)—a ball having considerable momentum). In order to hit a line drive or “knock the ball out of the park,” the batter must therefore cause a significant change in momentum.
44
sports—and it applies as much in tennis or golf as in baseball—as “following through.” By increasing the time of impact, the batter has increased impulse and thus, momentum change. Obviously, the mass of the ball has not been altered; the difference, then, is a change in velocity. How is it possible that in earlier examples, the effects of force were decreased by increasing the time interval, whereas in the baseball illustration, an increase in time interval resulted in a more powerful impact? The answer relates to differences in direction and elasticity. The baseball and the bat are colliding head-on in a relatively elastic situation; by contrast, crumpling cars are inelastic. In the example of a person catching a water balloon, the catcher is moving in the same direction as the balloon, thus reducing momentum change. Even in the case of the paratrooper, the ground is stationary; it does not move toward the parachutist in the way that the baseball moves toward the bat. WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Bonnet, Robert L. and Dan Keen. Science Fair Projects: Physics. Illustrated by Frances Zweifel. New York: Sterling, 1999. Fleisher, Paul. Objects in Motion: Principles of Classical Mechanics. Minneapolis, MN: Lerner Publications, 2002. Gardner, Robert. Experimenting with Science in Sports. New York: F. Watts, 1993. “Lesson 1: The Impulse Momentum Change Theorem” (Web site) (March 19, 2001). “Momentum” (Web site). (March 19, 2001). Physlink.com (Web site). (March 7, 2001). Rutherford, F. James; Gerald Holton; and Fletcher G. Watson. Project Physics. New York: Holt, Rinehart, and Winston, 1981. Schrier, Eric and William F. Allman. Newton at the Bat: The Science in Sports. New York: Charles Scribner’s Sons, 1984.
Consider the momentum change in terms of the impulse components. The batter can only apply so much force, but it is possible to magnify impulse greatly by increasing the amount of time over which the force is delivered. This is known in
Zubrowski, Bernie. Raceways: Having Fun with Balls and Tracks. Illustrated by Roy Doty. New York: William Morrow, 1985.
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C E N T R I P E TA L F O R C E
CONCEPT Most people have heard of centripetal and centrifugal force. Though it may be somewhat difficult to keep track of which is which, chances are anyone who has heard of the two concepts remembers that one is the tendency of objects in rotation to move inward, and the other is the tendency of rotating objects to move outward. It may come as a surprise, then, to learn that there is no such thing, strictly speaking, as centrifugal (outward) force. There is only centripetal (inward) force and the inertia that makes objects in rotation under certain situations move outward, for example, a car making a turn, the movement of a roller coaster— even the spinning of a centrifuge.
HOW IT WORKS Like many other principles in physics, centripetal force ultimately goes back to a few simple precepts relating to the basics of motion. Consider an object in uniform circular motion: an object moves around the center of a circle so that its speed is constant or unchanging. The formula for speed—or rather, average speed—is distance divided by time; hence, people say, for instance, “miles (or kilometers) per hour.” In the case of an object making a circle, distance is equal to the circumference, or distance around, the circle. From geometry, we know that the formula for calculating the circumference of a circle is 2πr, where r is the radius, or the distance from the circumference to the center. The figure π may be rendered as 3.141592..., though in fact, it is an irrational number: the decimal figures continue forever without repetition or pattern. S C I E N C E O F E V E RY DAY T H I N G S
From the above, it can be discerned that the formula for the average speed of an object moving around a circle is 2πr divided by time. Furthermore, we can see that there is a proportional relationship between radius and average speed. If the radius of a circle is doubled, but an object at the circle’s periphery makes one complete revolution in the same amount of time as before, this means that the average speed has doubled as well. This can be shown by setting up two circles, one with a radius of 2, the other with a radius of 4, and using some arbitrary period of time—say, 2 seconds. The above conclusion carries with it an interesting implication with regard to speeds at different points along the radius of a circle. Rather than comparing two points moving around the circumferences of two different circles—one twice as big as the other—in the same period of time, these two points could be on the same circle: one at the periphery, and one exactly halfway along the radius. Assuming they both traveled a complete circle in the same period of time, the proportional relationship described earlier would apply. This means, then, that the further out on the circle one goes, the greater the average speed.
Velocity = Speed + Direction Speed is a scalar, meaning that it has magnitude but no specific direction; by contrast, velocity is a vector—a quantity with both a magnitude (that is, speed) and a direction. For an object in circular motion, the direction of velocity is the same as that in which the object is moving at any given point. Consider the example of the city of Atlanta, Georgia, and Interstate-285, one of several instances in which a city is surrounded by a “loop” highway. Local traffic reporters avoid givVOLUME 2: REAL-LIFE PHYSICS
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means that it is experiencing acceleration. As with the subject of centripetal force and “centrifugal force,” most people have a mistaken view of acceleration, believing that it refers only to an increase in speed. In fact, acceleration is a change in velocity, and can thus refer either to a change in speed or direction. Nor must that change be a positive one; in other words, an object undergoing a reduction in speed is also experiencing acceleration.
Centripetal Force
The acceleration of an object in rotational motion is always toward the center of the circle. This may appear to go against common sense, which should indicate that acceleration moves in the same direction as velocity, but it can, in fact, be proven in a number of ways. One method would be by the addition of vectors, but a “hands-on” demonstration may be more enlightening than an abstract geometrical proof.
TYPICALLY,
A CENTRIFUGE CONSISTS OF A BASE; A
ROTATING TUBE PERPENDICULAR TO THE BASE; AND VIALS ATTACHED BY MOVABLE CENTRIFUGE ARMS TO THE ROTATING TUBE.
THE
MOVABLE ARMS ARE HINGED AT
THE TOP OF THE ROTATING TUBE, AND THUS CAN MOVE UPWARD AT AN ANGLE APPROACHING
WHEN
90°
TO THE TUBE.
THE TUBE BEGINS TO SPIN, CENTRIPETAL FORCE
PULLS THE MATERIAL IN THE VIALS TOWARD THE CENTER. (Photograph by Charles D. Winters. National Audubon Society
Collection/Photo Researchers, Inc. Reproduced by permission.)
ing mere directional coordinates for spots on that highway (for instance, “southbound on 285”), because the area where traffic moves south depends on whether one is moving clockwise or counterclockwise. Hence, reporters usually say “southbound on the outer loop.” As with cars on I-285, the direction of the velocity vector for an object moving around a circle is a function entirely of its position and the direction of movement—clockwise or counterclockwise—for the circle itself. The direction of the individual velocity vector at any given point may be described as tangential; that is, describing a tangent, or a line that touches the circle at just one point. (By definition, a tangent line cannot intersect the circle.)
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It is possible to make a simple accelerometer, a device for measuring acceleration, with a lit candle inside a glass. The candle should be standing at a 90°-angle to the bottom of the glass, attached to it by hot wax as you would affix a burning candle to a plate. When you hold the candle level, the flame points upward; but if you spin the glass in a circle, the flame will point toward the center of that circle—in the direction of acceleration.
Mass ⫻ Acceleration = Force Since we have shown that acceleration exists for an object spinning around a circle, it is then possible for us to prove that the object experiences some type of force. The proof for this assertion lies in the second law of motion, which defines force as the product of mass and acceleration: hence, where there is acceleration and mass, there must be force. Force is always in the direction of acceleration, and therefore the force is directed toward the center of the circle.
It follows, then, that the direction of an object in movement around a circle is changing; hence, its velocity is also changing—and this in turn
In the above paragraph, we assumed the existence of mass, since all along the discussion has concerned an object spinning around a circle. By definition, an object—that is, an item of matter, rather than an imaginary point—possesses mass. Mass is a measure of inertia, which can be explained by the first law of motion: an object in motion tends to remain in motion, at the same speed and in the same direction (that is, at the same velocity) unless or until some outside force acts on it. This tendency to maintain velocity is inertia. Put another way, it is inertia that causes an object standing still to remain motionless, and
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Centripetal Force
A
CLOTHOID LOOP IN A ROLLER COASTER IN
HAINES CITY, FLORIDA. AT
THE TOP OF A LOOP, YOU FEEL LIGHTER
THAN NORMAL; AT THE BOTTOM, YOU FEEL HEAVIER. (The Purcell Team/Corbis. Reproduced by permission.)
likewise, it is inertia which dictates that a moving object will “try” to keep moving.
Centripetal Force Now that we have established the existence of a force in rotational motion, it is possible to give it a name: centripetal force, or the force that causes an object in uniform circular motion to move toward the center of the circular path. This is not a “new” kind of force; it is merely force as applied in circular or rotational motion, and it is absolutely essential. Hence, physicists speak of a “centripetal force requirement”: in the absence of centripetal force, an object simply cannot turn. Instead, it will move in a straight line.
“seeking the center.” What, then, of centrifugal, a word that means “fleeing the center”? It would be correct to say that there is such a thing as centrifugal motion; but centrifugal force is quite a different matter. The difference between centripetal force and a mere centrifugal tendency— a result of inertia rather than of force—can be explained by referring to a familiar example.
REAL-LIFE A P P L I C AT I O N S Riding in a Car
The Latin roots of centripetal together mean
When you are riding in a car and the car accelerates, your body tends to move backward against
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the seat. Likewise, if the car stops suddenly, your body tends to move forward, in the direction of the dashboard. Note the language here: “tends to move” rather than “is pushed.” To say that something is pushed would imply that a force has been applied, yet what is at work here is not a force, but inertia—the tendency of an object in motion to remain in motion, and an object at rest to remain at rest. A car that is not moving is, by definition, at rest, and so is the rider. Once the car begins moving, thus experiencing a change in velocity, the rider’s body still tends to remain in the fixed position. Hence, it is not a force that has pushed the rider backward against the seat; rather, force has pushed the car forward, and the seat moves up to meet the rider’s back. When stopping, once again, there is a sudden change in velocity from a certain value down to zero. The rider, meanwhile, is continuing to move forward due to inertia, and thus, his or her body has a tendency to keep moving in the direction of the now-stationary dashboard. This may seem a bit too simple to anyone who has studied inertia, but because the human mind has such a strong inclination to perceive inertia as a force in itself, it needs to be clarified in the most basic terms. This habit is similar to the experience you have when sitting in a vehicle that is standing still, while another vehicle alongside moves backward. In the first split-second of awareness, your mind tends to interpret the backward motion of the other car as forward motion on the part of the car in which you are sitting—even though your own car is standing still. Now we will consider the effects of centripetal force, as well as the illusion of centrifugal force. When a car turns to the left, it is undergoing a form of rotation, describing a 90°-angle or one-quarter of a circle. Once again, your body experiences inertia, since it was in motion along with the car at the beginning of the turn, and thus you tend to move forward. The car, at the same time, has largely overcome its own inertia and moved into the leftward turn. Thus the car door itself is moving to the left. As the door meets the right side of your body, you have the sensation of being pushed outward against the door, but in fact what has happened is that the door has moved inward.
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rants further discussion below. But while on the subject of riding in an automobile, we need to examine another illustration of centripetal force. It should be noted in this context that for a car to make a turn at all, there must be friction between the tires and the road. Friction is the force that resists motion when the surface of one object comes into contact with the surface of another; yet ironically, while opposing motion, friction also makes relative motion possible. Suppose, then, that a driver applies the brakes while making a turn. This now adds a force tangential, or at a right angle, to the centripetal force. If this force is greater than the centripetal force—that is, if the car is moving too fast—the vehicle will slide forward rather than making the turn. The results, as anyone who has ever been in this situation will attest, can be disastrous. The above highlights the significance of the centripetal force requirement: without a sufficient degree of centripetal force, an object simply cannot turn. Curves are usually banked to maximize centripetal force, meaning that the roadway tilts inward in the direction of the curve. This banking causes a change in velocity, and hence, in acceleration, resulting in an additional quantity known as reaction force, which provides the vehicle with the centripetal force necessary for making the turn. The formula for calculating the angle at which a curve should be banked takes into account the car’s speed and the angle of the curve, but does not include the mass of the vehicle itself. As a result, highway departments post signs stating the speed at which vehicles should make the turn, but these signs do not need to include specific statements regarding the weight of given models.
The Centrifuge To return to the subject of “centrifugal force”— which, as noted earlier, is really just centrifugal motion—you might ask, “If there is no such thing as centrifugal force, how does a centrifuge work?” Used widely in medicine and a variety of sciences, a centrifuge is a device that separates particles within a liquid. One application, for instance, is to separate red blood cells from plasma.
The illusion of centrifugal force is so deeply ingrained in the popular imagination that it war-
Typically a centrifuge consists of a base; a rotating tube perpendicular to the base; and two vials attached by movable centrifuge arms to the
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rotating tube. The movable arms are hinged at the top of the rotating tube, and thus can move upward at an angle approaching 90° to the tube. When the tube begins to spin, centripetal force pulls the material in the vials toward the center. Materials that are denser have greater inertia, and thus are less responsive to centripetal force. Hence, they seem to be pushed outward, but in fact what has happened is that the less dense material has been pulled inward. This leads to the separation of components, for instance, with plasma on the top and red blood cells on the bottom. Again, the plasma is not as dense, and thus is more easily pulled toward the center of rotation, whereas the red blood cells respond less, and consequently remain on the bottom. The centrifuge was invented in 1883 by Carl de Laval (1845-1913), a Swedish engineer, who used it to separate cream from milk. During the 1920s, the chemist Theodor Svedberg (18841971), who was also Swedish, improved on Laval’s work to create the ultracentrifuge, used for separating very small particles of similar weight. In a typical ultracentrifuge, the vials are no larger than 0.2 in (0.6 cm) in diameter, and these may rotate at speeds of up to 230,000 revolutions per minute. Most centrifuges in use by industry rotate in a range between 1,000 and 15,000 revolutions per minute, but others with scientific applications rotate at a much higher rate, and can produce a force more than 25,000 times as great as that of gravity. In 1994, researchers at the University of Colorado created a sort of super-centrifuge for simulating stresses applied to dams and other large structures. The instrument has just one centrifuge arm, measuring 19.69 ft (6 m), attached to which is a swinging basket containing a scale model of the structure to be tested. If the model is 1/50 the size of the actual structure, then the centrifuge is set to create a centripetal force 50 times that of gravity.
Industrial uses of the centrifuge include that for which Laval invented it—separation of cream from milk—as well as the separation of impurities from other substances. Water can be removed from oil or jet fuel with a centrifuge, and likewise, waste-management agencies use it to separate solid materials from waste water prior to purifying the water itself.
Centripetal Force
Closer to home, a washing machine on spin cycle is a type of centrifuge. As the wet clothes spin, the water in them tends to move outward, separating from the clothes themselves. An even simpler, more down-to-earth centrifuge can be created by tying a fairly heavy weight to a rope and swinging it above one’s head: once again, the weight behaves as though it were pushed outward, though in fact, it is only responding to inertia.
Roller Coasters and Centripetal Force People ride roller coasters, of course, for the thrill they experience, but that thrill has more to do with centripetal force than with speed. By the late twentieth century, roller coasters capable of speeds above 90 MPH (144 km/h) began to appear in amusement parks around America; but prior to that time, the actual speeds of a roller coaster were not particularly impressive. Seldom, if ever, did they exceed that of a car moving down the highway. On the other hand, the acceleration and centripetal force generated on a roller coaster are high, conveying a sense of weightlessness (and sometimes the opposite of weightlessness) that is memorable indeed. Few parts of a roller coaster ride are straight and flat—usually just those segments that mark the end of one ride and the beginning of another. The rest of the track is generally composed of dips and hills, banked turns, and in some cases, clothoid loops. The latter refers to a geometric shape known as a clothoid, rather like a teardrop upside-down.
The Colorado centrifuge has also been used to test the effects of explosions on buildings. Because the combination of forces—centripetal, gravity, and that of the explosion itself—is so great, it takes a very small quantity of explosive to measure the effects of a blast on a model of the building.
Because of its shape, the clothoid has a much smaller radius at the top than at the bottom—a key factor in the operation of the roller coaster ride through these loops. In days past, rollercoaster designers used perfectly circular loops, which allowed cars to enter them at speeds that were too high, built too much force and resulted in injuries for riders. Eventually, engineers recognized the clothoid as a means of providing a safe, fun ride.
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Centripetal Force
KEY TERMS ACCELERATION: CENTRIFUGAL:
A change in velocity. A term describing the
scalar is contrasted with a vector.
tendency of objects in uniform circular
SPEED:
motion to move away from the center of
of an object changes over a given period of
the circular path. Though the term “cen-
time.
trifugal force” is often used, it is inertia,
The rate at which the position
TANGENTIAL:
Movement along a tan-
rather than force, that causes the object to
gent, or a line that touches a circle at just
move outward.
one point and does not intersect the circle.
CENTRIPETAL
FORCE:
The force
UNIFORM
CIRCULAR
MOTION:
that causes an object in uniform circular
The motion of an object around the center
motion to move toward the center of the
of a circle in such a manner that speed is
circular path. INERTIA:
constant or unchanging. The tendency of an object in
motion to remain in motion, and of an object at rest to remain at rest.
VECTOR:
A quantity that possesses
both magnitude and direction. Velocity, acceleration, and weight (which involves
A measure of inertia, indicating
the downward acceleration due to gravity)
the resistance of an object to a change in its
are examples of vectors. It is contrasted
motion—including a change in velocity.
with a scalar.
MASS:
SCALAR:
A quantity that possesses
only magnitude, with no specific direction.
As you move into the clothoid loop, then up, then over, and down, you are constantly changing position. Speed, too, is changing. On the way up the loop, the roller coaster slows due to a decrease in kinetic energy, or the energy that an object possesses by virtue of its movement. At the top of the loop, the roller coaster has gained a great deal of potential energy, or the energy an object possesses by virtue of its position, and its kinetic energy is at zero. But once it starts going down the other side, kinetic energy—and with it speed—increases rapidly once again. Throughout the ride, you experience two forces, gravity, or weight, and the force (due to motion) of the roller coaster itself, known as normal force. Like kinetic and potential energy— which rise and fall correspondingly with dips and hills—normal force and gravitational force are locked in a sort of “competition” throughout the roller-coaster rider. For the coaster to have its
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Mass, time, and speed are all scalars. A
VOLUME 2: REAL-LIFE PHYSICS
VELOCITY:
The speed of an object in a
particular direction.
proper effect, normal force must exceed that of gravity in most places. The increase in normal force on a rollercoaster ride can be attributed to acceleration and centripetal motion, which cause you to experience something other than gravity. Hence, at the top of a loop, you feel lighter than normal, and at the bottom, heavier. In fact, there has been no real change in your weight: it is, like the idea of “centrifugal force” discussed earlier, a matter of perception. WHERE TO LEARN MORE Aylesworth, Thomas G. Science at the Ball Game. New York: Walker, 1977. Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Buller, Laura and Ron Taylor. Forces of Nature. Illustrations by John Hutchinson and Stan North. New York: Marshall Cavendish, 1990.
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“Centrifugal Force—Rotational Motion.” National Aeronautics and Space Administration (Web site). (March 5, 2001). “Circular and Satellite Motion” (Web site). (March 5, 2001). Cobb, Vicki. Why Doesn’t the Earth Fall Up? And Other Not Such Dumb Questions About Motion. Illustrated by Ted Enik. New York: Lodestar Books, 1988. Lefkowitz, R. J. Push! Pull! Stop! Go! A Book About Forces
S C I E N C E O F E V E RY DAY T H I N G S
and Motion. Illustrated by June Goldsborough. New York: Parents’ Magazine Press, 1975. “Rotational Motion.” Physics Department, University of Guelph (Web site). (March 4, 2001). Schaefer, Lola M. Circular Movement. Mankato, MN: Pebble Books, 2000. Snedden, Robert. Forces. Des Plaines, IL: Heinemann Library, 1999. Whyman, Kathryn. Forces in Action. New York: Gloucester Press, 1986.
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FRICTION Friction
CONCEPT Friction is the force that resists motion when the surface of one object comes into contact with the surface of another. In a machine, friction reduces the mechanical advantage, or the ratio of output to input: an automobile, for instance, uses onequarter of its energy on reducing friction. Yet, it is also friction in the tires that allows the car to stay on the road, and friction in the clutch that makes it possible to drive at all. From matches to machines to molecular structures, friction is one of the most significant phenomena in the physical world.
HOW IT WORKS The definition of friction as “the force that resists motion when the surface of one object comes into contact with the surface of another” does not exactly identify what it is. Rather, the statement describes the manifestation of friction in terms of how other objects respond. A less sophisticated version of such a definition would explain electricity, for instance, as “the force that runs electrical appliances.” The reason why friction cannot be more firmly identified is simple: physicists do not fully understand what it is. Much the same could be said of force, defined by Sir Isaac Newton’s (1642-1727) second law of motion as the product of mass multiplied acceleration. The fact is that force is so fundamental that it defies full explanation, except in terms of the elements that compose it, and compared to force, friction is relatively easy to identify. In fact, friction plays a part in the total force that must be opposed in order for movement to take place in many situations. So, too, does grav-
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ity—and gravity, unlike force itself, is much easier to explain. Since gravity plays a role in friction, it is worthwhile to review its essentials. Newton’s first law of motion identifies inertia, a tendency of objects in the physical universe that is sometimes mistaken for friction. When an object is in motion or at rest, the first law states, it will remain in that state at a constant velocity (which is zero for an object at rest) unless or until an outside force acts on it. This tendency to remain in a given state of motion is inertia. Inertia is not a force: on the contrary, a very small quantity of force may accelerate an object, thus overcoming its inertia. Inertia is, however, a component of force, since mass is a measure of inertia. In the case of gravitational force, mass is multiplied by the acceleration due to gravity, which is equal to 32 ft (9.8 m)/sec2. People in everyday life are familiar with another term for gravitational force: weight. Weight, in turn, is an all-important factor in friction, as revealed in the three laws governing the friction between an object at rest and the surface on which it sits. According to the first of these, friction is proportional to the weight of the object. The second law states that friction is not determined by the surface area of the object— that is, the area that touches the surface on which the object rests. In fact, the contact area between object and surface is a dependant variable, a function of weight. The second law might seem obvious if one were thinking of a relatively elastic object—say, a garbage bag filled with newspapers sitting on the finished concrete floor of a garage. Clearly as more newspapers are added, thus increasing the
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weight, its surface area would increase as well. But what if one were to compare a large cardboard box (the kind, for instance, in which televisions or computers are shipped) with an ordinary concrete block of the type used in foundations for residential construction? Obviously, the block has more friction against the concrete floor; but at the same time, it is clear that despite its greater weight, the block has less surface area than the box. How can this be?
Friction
The answer is that “surface area” is quite literally more than meets the eye. Friction itself occurs at a level invisible to the naked eye, and involves the adhesive forces between molecules on surfaces pushed together by the force of weight. This is similar to the manner in which, when viewed through a high-powered lens, two complementary patches of Velcro™ are revealed as a forest of hooks on the one hand, and a sea of loops on the other. On a much more intensified level, that of molecular structure, the surfaces of objects appear as mountains and valleys. Nothing, in fact, is smooth when viewed on this scale, and hence, from a molecular perspective, it becomes clear that two objects in contact actually touch one another only in places. An increase of weight, however, begins pushing objects together, causing an increase in the actual—that is, the molecular—area of contact. Hence area of contact is proportional to weight. Just as the second law regarding friction states that surface area does not determine friction (but rather, weight determines surface area), the third law holds that friction is independent of the speed at which an object is moving along a surface— provided that speed is not zero. The reason for this provision is that an object with no speed (that is, one standing perfectly still) is subject to the most powerful form of friction, static friction. The latter is the friction that an object at rest must overcome to be set in motion; however, this should not be confused with inertia, which is relatively easy to overcome through the use of force. Inertia, in fact, is far less complicated than static friction, involving only mass rather than weight. Nor is inertia affected by the composition of the materials touching one another. As stated earlier, friction is proportional to weight, which suggests that another factor is involved. And indeed there is another factor, known as coefficient of friction. The latter, desig-
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THE
RAISED TREAD ON AN AUTOMOBILE’S TIRES, COU-
PLED WITH THE ROUGHENED ROAD SURFACE, PROVIDES SUFFICIENT FRICTION FOR THE DRIVER TO BE ABLE TO TURN THE CAR AND TO STOP. (Photograph by Martyn God-
dard/Corbis. Reproduced by permission.)
nated by the Greek letter mu (µ), is constant for any two types of surface in contact with one another, and provides a means of comparing the friction between them to that between other surfaces. For instance, the coefficient of static friction for wood on wood is 0.5; but for metal on metal with lubrication in between, it is only 0.03. A rubber tire on dry concrete yields the highest coefficient of static friction, 1.0, which is desirable in that particular situation. Coefficients are much lower for the second type of friction, sliding friction, the frictional resistance experienced by a body in motion. Whereas the earlier figures measured the relative resistance to putting certain objects into motion, the sliding-friction coefficient indicates the relative resistance against those objects once they are moving. To use the same materials mentioned above, the coefficient of sliding friction for wood on wood is 0.3; for two lubricated metals 0.03 (no change); and for a rubber tire on dry concrete 0.7. Finally, there is a third variety of friction, one in which coefficients are so low as to be neg-
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REAL-LIFE A P P L I C AT I O N S
Friction
Self-Motivation Through Friction Friction, in fact, always opposes movement; why, then, is friction necessary—as indeed it is—for walking, and for keeping a car on the road? The answer relates to the differences between friction and inertia alluded to earlier. In situations of static friction, it is easy to see how a person might confuse friction with inertia, since both serve to keep an object from moving. In situations of sliding or rolling friction, however, it is easier to see the difference between friction and inertia.
ACTOR JACK BUCHANAN PLE
DISPLAY
OF
LIT THIS MATCH USING A SIM-
FRICTION:
DRAGGING
THE
MATCH
AGAINST THE BACK OF THE MATCHBOX. (Photograph by Hul-
ton-Deutsch Collection/Corbis. Reproduced by permission.)
ligible: rolling friction, or the frictional resistance that a wheeled object experiences when it rolls over a relatively smooth, flat surface. In ideal circumstances, in fact, there would be absolutely no resistance between a wheel and a road. However, there exists no ideal—that is, perfectly rigid— wheel or road; both objects “give” in response to the other, the wheel by flattening somewhat and the road by experiencing indentation. Up to this point, coefficients of friction have been discussed purely in comparative terms, but in fact, they serve a function in computing frictional force—that is, the force that must be overcome to set an object in motion, or to keep it in motion. Frictional force is equal to the coefficient of friction multiplied by normal force—that is, the perpendicular force that one object or surface exerts on another. On a horizontal plane, normal force is equal to gravity and hence weight. In this equation, the coefficient of friction establishes a limit to frictional force: in order to move an object in a given situation, one must exert a force in excess of the frictional force that keeps it from moving.
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Whereas friction is always opposed to movement, inertia is not. When an object is not moving, its inertia does oppose movement—but when the object is in motion, then inertia resists stopping. In the absence of friction or other forces, inertia allows an object to remain in motion forever. Imagine a hockey player hitting a puck across a very, very large rink. Because ice has a much smaller coefficient of friction with regard to the puck than does dirt or asphalt, the puck will travel much further. Still, however, the ice has some friction, and, therefore, the puck will come to a stop at some point. Now suppose that instead of ice, the surface and objects in contact with it were friction-free, possessing a coefficient of zero. Then what would happen if the player hit the puck? Assuming for the purposes of this thought experiment, that the rink covered the entire surface of Earth, it would travel and travel and travel, ultimately going around the planet. It would never stop, because there would be no friction to stop it, and therefore inertia would have free rein. The same would be true if one were to firmly push the hockey player with enough force (small in the absence of friction) to set him in motion: he would continue riding around the planet indefinitely, borne by his skates. But what if instead of being set in motion, the hockey player tried to set himself in motion by the action of his skates against the rink’s surface? He would be unable to move even a hair’s breadth. The fact is that while static friction opposes the movement of an object from a position of rest to a state of motion, it may—assuming it can be overcome to begin motion at all—be indispensable to that movement. As with the skater in per-
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petual motion across the rink, the absence of friction means that inertia is “in control;” with friction, however, it is possible to overcome inertia.
Friction in Driving a Car The same principle applies to a car’s tires: if they were perfectly smooth—and, to make matters worse, the road were perfectly smooth as well— the vehicle would keep moving forward when the driver attempted to stop. For this reason, tires are designed with raised tread to maintain a high degree of friction, gripping the road tightly and dispersing water when the roadway is wet. The force of friction, in fact, pervades the entire operation of a car, and makes it possible for the tires themselves to turn. The turning force, or torque, that the driver exerts on the steering wheel is converted into forces that drive the tires, and these in turn use friction to provide traction. Between steering wheel and tires, of course, are a number of steps, with the engine rotating the crankshaft and transmitting power to the clutch, which applies friction to translate the motion of the crankshaft to the gearbox. When the driver of a car with a manual transmission presses down on the clutch pedal, this disengages the clutch itself. A clutch is a circular mechanism containing (among other things) a pressure plate, which lifts off the clutch plate. As a result, the flywheel—the instrument that actually transmits force from the crankshaft—is disengaged from the transmission shaft. With the clutch thus disengaged, the driver changes gears, and after the driver releases the clutch pedal, springs return the pressure plate and the clutch plate to their place against the flywheel. The flywheel then turns the transmission shaft. Controlled friction in the clutch makes this operation possible; likewise the synchromesh within the gearbox uses friction to bring the gearwheels into alignment. This is a complicated process, but at the heart of it is an engagement of gear teeth in which friction forces them to come to the same speed. Friction is also essential to stopping a car— not just with regard to the tires, but also with respect to the brakes. Whether they are disk brakes or drum brakes, two elements must come together with a force more powerful than the engine’s, and friction provides that needed force. In disk brakes, brake pads apply friction to both
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sides of the spinning disks, and in drum brakes, brake shoes transmit friction to the inside of a spinning drum. This braking force is then transmitted to the tires, which apply friction to the road and thus stop the car.
Friction
Efficiency and Friction The automobile is just one among many examples of a machine that could not operate without friction. The same is true of simple machines such as screws, as well as nails, pliers, bolts, and forceps. At the heart of this relationship is a paradox, however, because friction inevitably reduces the efficiency of machines: a car, as noted earlier, exerts fully one-quarter of its power simply on overcoming the force of friction both within its engine and from air resistance as it travels down the road. In scientific terms, efficiency or mechanical advantage is measured by the ratio of force output to force input. Clearly, in most situations it is ideal to maximize output and minimize input, and over the years inventors have dreamed of creating a mechanism—a perpetual motion machine—to do just that. In this idealized machine, one would apply a certain amount of energy to set it into operation, and then it would never stop; hence the ratio of output to input would be nearly infinite. Unfortunately, the perpetual motion machine is a dream every bit as elusive as the mythical Fountain of Youth. At least this is true on Earth, where friction will always cause a system to lose kinetic energy, or the energy of movement. No matter what the design, the machine will eventually lose energy and stop; however, this is not true in outer space, where friction is very small—though it still exists. In space it might truly be possible to set a machine in motion and let inertia do the rest; thus perhaps perpetual motion actually is more than a dream. It should also be noted that mechanical advantage is not always desirable. A screw is a highly inefficient machine: one puts much more force into screwing it in than the screw will exert once it is in place. Yet this is exactly the purpose of a screw: an “efficient” one, or one that worked its way back out of the place into which it had been screwed, would in fact be of little use. Once again, it is friction that provides a screw with its strangely efficient form of inefficiency. Nonetheless, friction, in spite of the
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advantages discussed above, is as undesirable as it is desirable. With friction, there is always something lost; however, there is a physical law that energy does not simply disappear; it just changes form. In the case of friction, the energy that could go to moving the machine is instead translated into sound—or even worse, heat.
When Sparks Fly In movement involving friction, molecules vibrate, bringing about a rise in temperature. This can be easily demonstrated by simply rubbing one’s hands together quickly, as a person is apt to do when cold: heat increases. For a machine composed of metal parts, this increase in temperature can be disastrous, leading to serious wear and damage. This is why various forms of lubricant are applied to systems subject to friction. An automobile uses grease and oil, as well as ball bearings, which are tiny uniform balls of metal that imitate the behavior of oil-based substances on a large scale. In a molecule of oil— whether it is a petroleum-related oil or the type of oil that comes from living things—positive and negative electrical charges are distributed throughout the molecule. By contrast, in water the positive charges are at one end of the molecule and the negative at the other. This creates a tight bond as the positive end of one water molecule adheres to the negative end of another. With oil, the relative absence of attraction between molecules means that each is in effect a tiny ball separate from the others. The ball-like molecules “roll” between metal elements, providing the buffer necessary to reduce friction. Yet for every statement one can make concerning friction, there is always another statement with which to counter it. Earlier it was noted that the wheel, because it reduced friction greatly, provided an enormous technological boost to societies. Yet long before the wheel— hundreds of thousands of years ago—an even more important technological breakthrough occurred when humans made a discovery that depended on maximizing friction: fire, or rather the means of making fire. Unlike the wheel, fire occurs in nature, and can spring from a number of causes, but when human beings harnessed the means of making fire on their own, they had to rely on the heat that comes from friction.
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using a little stick with a phosphorus tip. This stick, of course, is known as a match. In a strikeanywhere match, the head contains all the chemicals needed to create a spark. To ignite this type of match, one need only create frictional heat by rubbing it against a surface, such as sandpaper, with a high coefficient of friction. The chemicals necessary for ignition in safety matches, on the other hand, are dispersed between the match head and a treated strip, usually found on the side of the matchbox or matchbook. The chemicals on the tip and those on the striking surface must come into contact for ignition to occur, but once again, there must be friction between the match head and the striking pad. Water reduces friction with its heavy bond, as it does with a car’s tires on a rainy day, which explains why matches are useless when wet.
The Outer Limits of Friction Clearly friction is a complex subject, and the discoveries of modern physics only promise to add to that complexity. In a February 1999 online article for Physical Review Focus, Dana Mackenzie reported that “Engineers hope to make microscopic engines and gears as ordinary in our lives as microscopic circuits are today. But before this dream becomes a reality, they will have to deal with laws of friction that are very different from those that apply to ordinary-sized machines.” The earlier statement that friction is proportional to weight, in fact, applies only in the realm of classical physics. The latter term refers to the studies of physicists up to the end of the nineteenth century, when the concerns were chiefly the workings of large objects whose operations could be discerned by the senses. Modern physics, on the other hand, focuses on atomic and molecular structures, and addresses physical behaviors that could not have been imagined prior to the twentieth century.
By the early nineteenth century, inventors had developed an easy method of creating fire by
According to studies conducted by Alan Burns and others at Sandia National Laboratories in Albuquerque, New Mexico, molecular interactions between objects in very close proximity create a type of friction involving repulsion rather than attraction. This completely upsets the model of friction understood for more than a century, and indicates new frontiers of discovery concerning the workings of friction at a molecular level.
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Friction
KEY TERMS A change in velocity.
one another. On a plane without any
A figure, constant for a particular pair of surfaces in contact, that can be multiplied by the normal force between them to calculate the frictional force they experience.
incline (which would add acceleration in
The product of mass multiplied by acceleration.
when it rolls over a relatively smooth, flat
ACCELERATION:
COEFFICIENT OF FRICTION:
FORCE:
The force that resists motion when the surface of one object comes into contact with the surface of another. Varieties including sliding friction, static friction, and rolling friction. The degree of friction between two specific surfaces is proportional to coefficient of friction. FRICTION:
The force necessary to set an object in motion, or to keep it in motion; equal to normal force multiplied by coefficient of friction. FRICTIONAL FORCE:
The tendency of an object in motion to remain in motion, and of an object at rest to remain at rest. INERTIA:
addition to that of gravity) normal force is the same as weight. ROLLING FRICTION:
The frictional
resistance that a circular object experiences surface. With a coefficient of friction much smaller than that of sliding friction, rolling friction involves by far the least amount of resistance among the three varieties of friction. SLIDING FRICTION:
The frictional
resistance experienced by a body in motion. Here the coefficient of friction is greater than that for rolling friction, but less than for static friction. The rate at which the position
SPEED:
of an object changes over a given period of time. STATIC
FRICTION:
The frictional
resistance that a stationary object must overcome before it can go into motion. Its
A measure of inertia, indicating the resistance of an object to a change in its motion—including a change in velocity.
coefficient of friction is greater than that of
The ratio of force output to force input in a machine.
VELOCITY:
The perpendicular force with which two objects press against
force on an object; the product of mass mul-
MASS:
MECHANICAL
ADVANTAGE:
NORMAL FORCE:
WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Buller, Laura and Ron Taylor. Forces of Nature. Illustrations by John Hutchinson and Stan North. New York: Marshall Cavendish, 1990.
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sliding friction, and thus largest among the three varieties of friction. The speed of an object in a
particular direction. WEIGHT:
A measure of the gravitational
tiplied by the acceleration due to gravity.
Dixon, Malcolm and Karen Smith. Forces and Movement. Mankato, MN: Smart Apple Media, 1998. “Friction.” How Stuff Works (Web site). (March 8, 2001). “Friction and Interactions” (Web site). (March 8, 2001).
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Levy, Matthys and Richard Panchyk. Engineering the City: How Infrastructure Works. Chicago: Chicago Review Press, 2000. Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998.
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Rutherford, F. James; Gerald Holton; and Fletcher G. Watson. Project Physics. New York: Holt, Rinehart, and Winston, 1981. Skateboard Science (Web site).
Mackenzie, Dana. “Friction of Molecules.” Physical Review Focus (Web site).
Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.
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L AWS OF MOTION
Laws of Motion
CONCEPT In all the universe, there are few ideas more fundamental than those expressed in the three laws of motion. Together these explain why it is relatively difficult to start moving, and then to stop moving; how much force is needed to start or stop in a given situation; and how one force relates to another. In their beauty and simplicity, these precepts are as compelling as a poem, and like the best of poetry, they identify something that resonates through all of life. The applications of these three laws are literally endless: from the planets moving through the cosmos to the first seconds of a car crash to the action that takes place when a person walks. Indeed, the laws of motion are such a part of daily life that terms such as inertia, force, and reaction extend into the realm of metaphor, describing emotional processes as much as physical ones.
HOW IT WORKS The three laws of motion are fundamental to mechanics, or the study of bodies in motion. These laws may be stated in a number of ways, assuming they contain all the components identified by Sir Isaac Newton (1642-1727). It is on his formulation that the following are based:
exerts a force on another, the second object exerts on the first a force equal in magnitude but opposite in direction.
Laws of Man vs. Laws of Nature These, of course, are not “laws” in the sense that people normally understand that term. Human laws, such as injunctions against stealing or parking in a fire lane, are prescriptive: they state how the world should be. Behind the prescriptive statements of civic law, backing them up and giving them impact, is a mechanism—police, courts, and penalties—for ensuring that citizens obey. A scientific law operates in exactly the opposite fashion. Here the mechanism for ensuring that nature “obeys” the law comes first, and the “law” itself is merely a descriptive statement concerning evident behavior. With human or civic law, it is clearly possible to disobey: hence, the justice system exists to discourage disobedience. In the case of scientific law, disobedience is clearly impossible—and if it were not, the law would have to be amended.
• First law of motion: An object at rest will remain at rest, and an object in motion will remain in motion, at a constant velocity unless or until outside forces act upon it. • Second law of motion: The net force acting upon an object is a product of its mass multiplied by its acceleration. • Third law of motion: When one object
This is not to say, however, that scientific laws extend beyond their own narrowly defined limits. On Earth, the intrusion of outside forces—most notably friction—prevents objects from behaving perfectly according to the first law of motion. The common-sense definition of friction calls to mind, for instance, the action that a match makes as it is being struck; in its broader scientific meaning, however, friction can be defined as any force that resists relative motion between two bodies in contact.
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THE CARGO BAY OF THE SPACE SHUTTLE DISCOVERY, shown just after releasing a satellite. Once released into the frictionless vacuum around Earth, the satellite will move indefinitely around Earth without need for the motive power of an engine. The planet’s gravity keeps it at a fixed height, and at that height, it could theoretically circle Earth forever. (Corbis. Reproduced by permission.)
The operations of physical forces on Earth are continually subject to friction, and this includes not only dry bodies, but liquids, for instance, which are subject to viscosity, or internal friction. Air itself is subject to viscosity, which prevents objects from behaving perfectly in accordance with the first law of motion. Other forces, most notably that of gravity, also come into play to stop objects from moving endlessly once they have been set in motion.
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radius, it would continue travelling indefinitely. But even this craft would likely run into another object, such as a planet, and would then be drawn into its orbit. In such a case, however, it can be said that outside forces have acted upon it, and thus the first law of motion stands.
The vacuum of outer space presents scientists with the most perfect natural laboratory for testing the first law of motion: in theory, if they were to send a spacecraft beyond Earth’s orbital
The orbit of a satellite around Earth illustrates both the truth of the first law, as well as the forces that limit it. To break the force of gravity, a powered spacecraft has to propel the satellite into the exosphere. Yet once it has reached the frictionless vacuum, the satellite will move indefinitely around Earth without need for the motive power of an engine—it will get a “free ride,”
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thanks to the first law of motion. Unlike the hypothetical spacecraft described above, however, it will not go spinning into space, because it is still too close to Earth. The planet’s gravity keeps it at a fixed height, and at that height, it could theoretically circle Earth forever. The first law of motion deserves such particular notice, not simply because it is the first law. Nonetheless, it is first for a reason, because it establishes a framework for describing the behavior of an object in motion. The second law identifies a means of determining the force necessary to move an object, or to stop it from moving, and the third law provides a picture of what happens when two objects exert force on one another. The first law warrants special attention because of misunderstandings concerning it, which spawned a debate that lasted nearly twenty centuries. Aristotle (384-322 B.C.) was the first scientist to address seriously what is now known as the first law of motion, though in fact, that term would not be coined until about two thousand years after his death. As its title suggests, his Physics was a seminal work, a book in which Aristotle attempted to give form to, and thus define the territory of, studies regarding the operation of physical processes. Despite the great philosopher’s many achievements, however, Physics is a highly flawed work, particularly with regard to what became known as his theory of impetus— that is, the phenomena addressed in the first law of motion.
Aristotle’s Mistake According to Aristotle, a moving object requires a continual application of force to keep it moving: once that force is no longer applied, it ceases to move. You might object that, when a ball is in flight, the force necessary to move it has already been applied: a person has thrown the ball, and it is now on a path that will eventually be stopped by the force of gravity. Aristotle, however, would have maintained that the air itself acts as a force to keep the ball in flight, and that when the ball drops—of course he had no concept of “gravity” as such—it is because the force of the air on the ball is no longer in effect. These notions might seem patently absurd to the modern mind, but they went virtually unchallenged for a thousand years. Then in the sixth century A.D., the Byzantine philosopher Johannes Philoponus (c. 490-570) wrote a criS C I E N C E O F E V E RY DAY T H I N G S
tique of Physics. In what sounds very much like a precursor to the first law of motion, Philoponus held that a body will keep moving in the absence of friction or opposition.
Laws of Motion
He further maintained that velocity is proportional to the positive difference between force and resistance—in other words, that the force propelling an object must be greater than the resistance. As long as force exceeds resistance, Philoponus held, a body will remain in motion. This in fact is true: if you want to push a refrigerator across a carpeted floor, you have to exert enough force not only to push the refrigerator, but also to overcome the friction from the floor itself. The Arab philosophers Ibn Sina (Avicenna; 980-1037) and Ibn Bâjja (Avempace; fl. c. 1100) defended Philoponus’s position, and the French scholar Peter John Olivi (1248-1298) became the first Western thinker to critique Aristotle’s statements on impetus. Real progress on the subject, however, did not resume until the time of Jean Buridan (1300-1358), a French physicist who went much further than Philoponus had eight centuries earlier. In his writing, Buridan offered an amazingly accurate analysis of impetus that prefigured all three laws of motion. It was Buridan’s position that one object imparts to another a certain amount of power, in proportion to its velocity and mass, that causes the second object to move a certain distance. This, as will be shown below, was amazingly close to actual fact. He was also correct in stating that the weight of an object may increase or decrease its speed, depending on other circumstances, and that air resistance slows an object in motion. The true breakthrough in understanding the laws of motion, however, came as the result of work done by three extraordinary men whose lives stretched across nearly 250 years. First came Nicolaus Copernicus (1473-1543), who advanced what was then a heretical notion: that Earth, rather than being the center of the universe, revolved around the Sun along with the other planets. Copernicus made his case purely in terms of astronomy, however, with no direct reference to physics.
Galileo’s Challenge: The Copernican Model Galileo Galilei (1564-1642) likewise embraced a heliocentric (Sun-centered) model of the uniVOLUME 2: REAL-LIFE PHYSICS
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verse—a position the Church forced him to renounce publicly on pain of death. As a result of his censure, Galileo realized that in order to prove the Copernican model, it would be necessary to show why the planets remain in motion as they do. In explaining this, he coined the term inertia to describe the tendency of an object in motion to remain in motion, and an object at rest to remain at rest. Galileo’s observations, in fact, formed the foundation for the laws of motion. In the years that followed Galileo’s death, some of the world’s greatest scientific minds became involved in the effort to understand the forces that kept the planets in motion around the Sun. Among them were Johannes Kepler (15711630), Robert Hooke (1635-1703), and Edmund Halley (1656-1742). As a result of a dispute between Hooke and Sir Christopher Wren (16321723) over the subject, Halley brought the question to his esteemed friend Isaac Newton. As it turned out, Newton had long been considering the possibility that certain laws of motion existed, and these he presented in definitive form in his Principia (1687). The impact of the Newton’s book, which included his observations on gravity, was nothing short of breathtaking. For the next three centuries, human imagination would be ruled by the Newtonian framework, and only in the twentieth century would the onset of new ideas reveal its limitations. Yet even today, outside the realm of quantum mechanics and relativity theory—in other words, in the world of everyday experience— Newton’s laws of motion remain firmly in place.
REAL-LIFE A P P L I C AT I O N S The First Law of Motion in a Car Crash It is now appropriate to return to the first law of motion, as formulated by Newton: an object at rest will remain at rest, and an object in motion will remain in motion, at a constant velocity unless or until outside forces act upon it. Examples of this first law in action are literally unlimited.
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velocity. The latter term, though it is commonly understood to be the same as speed, is in fact more specific: velocity can be defined as the speed of an object in a particular direction. In a car moving forward at a fixed rate of 60 MPH (96 km/h), everything in the car—driver, passengers, objects on the seats or in the trunk— is also moving forward at the same rate. If that car then runs into a brick wall, its motion will be stopped, and quite abruptly. But though its motion has stopped, in the split seconds after the crash it is still responding to inertia: rather than bouncing off the brick wall, it will continue plowing into it. What, then, of the people and objects in the car? They too will continue to move forward in response to inertia. Though the car has been stopped by an outside force, those inside experience that force indirectly, and in the fragment of time after the car itself has stopped, they continue to move forward—unfortunately, straight into the dashboard or windshield. It should also be clear from this example exactly why seatbelts, headrests, and airbags in automobiles are vitally important. Attorneys may file lawsuits regarding a client’s injuries from airbags, and homespun opponents of the seatbelt may furnish a wealth of anecdotal evidence concerning people who allegedly died in an accident because they were wearing seatbelts; nonetheless, the first law of motion is on the side of these protective devices. The admittedly gruesome illustration of a car hitting a brick wall assumes that the driver has not applied the brakes—an example of an outside force changing velocity—or has done so too late. In any case, the brakes themselves, if applied too abruptly, can present a hazard, and again, the significant factor here is inertia. Like the brick wall, brakes stop the car, but there is nothing to stop the driver and/or passengers. Nothing, that is, except protective devices: the seat belt to keep the person’s body in place, the airbag to cushion its blow, and the headrest to prevent whiplash in rear-end collisions.
One of the best illustrations, in fact, involves something completely outside the experience of Newton himself: an automobile. As a car moves down the highway, it has a tendency to remain in motion unless some outside force changes its
Inertia also explains what happens to a car when the driver makes a sharp, sudden turn. Suppose you are is riding in the passenger seat of a car moving straight ahead, when suddenly the driver makes a quick left turn. Though the car’s tires turn instantly, everything in the vehicle—its frame, its tires, and its contents—is still respond-
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Laws of Motion
WHEN A VEHICLE HITS A WALL, AS SHOWN HERE IN A CRASH TEST, ITS MOTION WILL BE STOPPED, AND QUITE ABRUPTLY. BUT THOUGH ITS MOTION HAS STOPPED, IN THE SPLIT SECONDS AFTER THE CRASH IT IS STILL RESPONDING TO INERTIA: RATHER THAN BOUNCING OFF THE BRICK WALL, IT WILL CONTINUE PLOWING INTO IT. (Photograph by Tim Wright/Corbis. Reproduced by permission.)
ing to inertia, and therefore “wants” to move forward even as it is turning to the left.
From Parlor Tricks to Space Ships
As the car turns, the tires may respond to this shift in direction by squealing: their rubber surfaces were moving forward, and with the sudden turn, the rubber skids across the pavement like a hard eraser on fine paper. The higher the original speed, of course, the greater the likelihood the tires will squeal. At very high speeds, it is possible the car may seem to make the turn “on two wheels”— that is, its two outer tires. It is even possible that the original speed was so high, and the turn so sharp, that the driver loses control of the car.
It would be wrong to conclude from the carrelated illustrations above that inertia is always harmful. In fact it can help every bit as much as it can potentially harm, a fact shown by two quite different scenarios.
Here inertia is to blame: the car simply cannot make the change in velocity (which, again, refers both to speed and direction) in time. Even in less severe situations, you are likely to feel that you have been thrown outward against the rider’s side door. But as in the car-and-brick-wall illustration used earlier, it is the car itself that first experiences the change in velocity, and thus it responds first. You, the passenger, then, are moving forward even as the car has turned; therefore, rather than being thrown outward, you are simply meeting the leftward-moving door even as you push forward.
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The beneficial quality to the first scenario may be dubious: it is, after all, a mere parlor trick, albeit an entertaining one. In this famous stunt, with which most people are familiar even if they have never seen it, a full table setting is placed on a table with a tablecloth, and a skillful practitioner manages to whisk the cloth out from under the dishes without upsetting so much as a glass. To some this trick seems like true magic, or at least sleight of hand; but under the right conditions, it can be done. (This information, however, carries with it the warning, “Do not try this at home!”) To make the trick work, several things must align. Most importantly, the person doing it has to be skilled and practiced at performing the feat. On a physical level, it is best to minimize the friction between the cloth and settings on the one hand, and the cloth and table on the other. It is also important to maximize the mass (a property
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that will be discussed below) of the table settings, thus making them resistant to movement. Hence, inertia—which is measured by mass—plays a key role in making the tablecloth trick work. You might question the value of the tablecloth stunt, but it is not hard to recognize the importance of the inertial navigation system (INS) that guides planes across the sky. Prior to the 1970s, when INS made its appearance, navigation techniques for boats and planes relied on reference to external points: the Sun, the stars, the magnetic North Pole, or even nearby areas of land. This created all sorts of possibilities for error: for instance, navigation by magnet (that is, a compass) became virtually useless in the polar regions of the Arctic and Antarctic. By contrast, the INS uses no outside points of reference: it navigates purely by sensing the inertial force that results from changes in velocity. Not only does it function as well near the poles as it does at the equator, it is difficult to tamper with an INS, which uses accelerometers in a sealed, shielded container. By contrast, radio signals or radar can be “confused” by signals from the ground—as, for instance, from an enemy unit during wartime. As the plane moves along, its INS measures movement along all three geometrical axes, and provides a continuous stream of data regarding acceleration, velocity, and displacement. Thanks to this system, it is possible for a pilot leaving California for Japan to enter the coordinates of a halfdozen points along the plane’s flight path, and let the INS guide the autopilot the rest of the way.
Soviet airspace over the Kamchatka Peninsula and later Sakhalin Island. There a Soviet Su-15 shot it down, killing all the plane’s passengers. In the aftermath of the Flight 007 shootdown, the Soviets accused the United States and South Korea of sending a spy plane into their airspace. (Among the passengers was Larry McDonald, a staunchly anti-Communist Congressman from Georgia.) It is more likely, however, that the tragedy of 007 resulted from errors in navigation which probably had something to do with the INS. The fact is that the R-20 flight plan had been designed to keep aircraft well out of Soviet airspace, and at the time KAL 007 passed over Kamchatka, it should have been 200 mi (320 km) to the east—over the Sea of Japan. Among the problems in navigating a transpacific flight is the curvature of the Earth, combined with the fact that the planet continues to rotate as the aircraft moves. On such long flights, it is impossible to “pretend,” as on a short flight, that Earth is flat: coordinates have to be adjusted for the rounded surface of the planet. In addition, the flight plan must take into account that (in the case of a flight from California to Japan), Earth is moving eastward even as the plane moves westward. The INS aboard KAL 007 may simply have failed to correct for these factors, and thus the error compounded as the plane moved further. In any case, INS will eventually be rendered obsolete by another form of navigation technology: the global positioning satellite (GPS) system.
Understanding Inertia Yet INS has its limitations, as illustrated by the tragedy that occurred aboard Korean Air Lines (KAL) Flight 007 on September 1, 1983. The plane, which contained 269 people and crew members, departed Anchorage, Alaska, on course for Seoul, South Korea. The route they would fly was an established one called “R-20,” and it appears that all the information regarding their flight plan had been entered correctly in the plane’s INS.
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From examples used above, it should be clear that inertia is a more complex topic than you might immediately guess. In fact, inertia as a process is rather straightforward, but confusion regarding its meaning has turned it into a complicated subject.
This information included coordinates for internationally recognized points of reference, actually just spots on the northern Pacific with names such as NABIE, NUKKS, NEEVA, and so on, to NOKKA, thirty minutes east of Japan. Yet, just after passing the fishing village of Bethel, Alaska, on the Bering Sea, the plane started to veer off course, and ultimately wandered into
In everyday terminology, people typically use the word inertia to describe the tendency of a stationary object to remain in place. This is particularly so when the word is used metaphorically: as suggested earlier, the concept of inertia, like numerous other aspects of the laws of motion, is often applied to personal or emotional processes as much as the physical. Hence, you could say, for instance, “He might have changed professions and made more money, but inertia kept him at his old job.” Yet you could just as easily say, for
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example, “He might have taken a vacation, but inertia kept him busy.” Because of the misguided way that most people use the term, it is easy to forget that “inertia” equally describes a tendency toward movement or nonmovement: in terms of Newtonian mechanics, it simply does not matter. The significance of the clause “unless or until outside forces act upon it” in the first law indicates that the object itself must be in equilibrium—that is, the forces acting upon it must be balanced. In order for an object to be in equilibrium, its rate of movement in a given direction must be constant. Since a rate of movement equal to 0 is certainly constant, an object at rest is in equilibrium, and therefore qualifies; but also, any object moving in a constant direction at a constant speed is also in equilibrium.
The Second Law: Force, Mass, Acceleration As noted earlier, the first law of motion deserves special attention because it is the key to unlocking the other two. Having established in the first law the conditions under which an object in motion will change velocity, the second law provides a measure of the force necessary to cause that change. Understanding the second law requires defining terms that, on the surface at least, seem like a matter of mere common sense. Even inertia requires additional explanation in light of terms related to the second law, because it would be easy to confuse it with momentum. The measure of inertia is mass, which reflects the resistance of an object to a change in its motion. Weight, on the other hand, measures the gravitational force on an object. (The concept of force itself will require further definition shortly.) Hence a person’s mass is the same everywhere in the universe, but their weight would differ from planet to planet. This can get somewhat confusing when you attempt to convert between English and metric units, because the pound is a unit of weight or force, whereas the kilogram is a unit of mass. In fact it would be more appropriate to set up kilograms against the English unit called the slug (equal to 14.59 kg), or to compare pounds to the metric unit of force, the newton (N), which is equal to the acceleration of one meter per second per second on an object of 1 kg in mass.
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Hence, though many tables of weights and measures show that 1 kg is equal to 2.21 lb, this is only true at sea level on Earth. A person with a mass of 100 kg on Earth would have the same mass on the Moon; but whereas he might weigh 221 lb on Earth, he would be considerably lighter on the Moon. In other words, it would be much easier to lift a 221-lb man on the Moon than on Earth, but it would be no easier to push him aside.
Laws of Motion
To return to the subject of momentum, whereas inertia is measured by mass, momentum is equal to mass multiplied by velocity. Hence momentum, which Newton called “quantity of motion,” is in effect inertia multiplied by velocity. Momentum is a subject unto itself; what matters here is the role that mass (and thus inertia) plays in the second law of motion. According to the second law, the net force acting upon an object is a product of its mass multiplied by its acceleration. The latter is defined as a change in velocity over a given time interval: hence acceleration is usually presented in terms of “feet (or meters) per second per second”—that is, feet or meters per second squared. The acceleration due to gravity is 32 ft (9.8 m) per second per second, meaning that as every second passes, the speed of a falling object is increasing by 32 ft (9.8 m) per second. The second law, as stated earlier, serves to develop the first law by defining the force necessary to change the velocity of an object. The law was integral to the confirming of the Copernican model, in which planets revolve around the Sun. Because velocity indicates movement in a single (straight) direction, when an object moves in a curve—as the planets do around the Sun—it is by definition changing velocity, or accelerating. The fact that the planets, which clearly possessed mass, underwent acceleration meant that some force must be acting on them: a gravitational pull exerted by the Sun, most massive object in the solar system. Gravity is in fact one of four types of force at work in the universe. The others are electromagnetic interactions, and “strong” and “weak” nuclear interactions. The other three were unknown to Newton—yet his definition of force is still applicable. Newton’s calculation of gravitational force (which, like momentum, is a subject unto itself) made it possible for Halley to determine that the comet he had observed in
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1682—the comet that today bears his name— would reappear in 1758, as indeed it has for every 75–76 years since then. Today scientists use the understanding of gravitational force imparted by Newton to determine the exact altitude necessary for a satellite to remain stationary above the same point on Earth’s surface. The second law is so fundamental to the operation of the universe that you seldom notice its application, and it is easiest to illustrate by examples such as those above—of astronomers and physicists applying it to matters far beyond the scope of daily life. Yet the second law also makes it possible, for instance, to calculate the amount of force needed to move an object, and thus people put it into use every day without knowing that they are doing so.
The Third Law: Action and Reaction As with the second law, the third law of motion builds on the first two. Having defined the force necessary to overcome inertia, the third law predicts what will happen when one force comes into contact with another force. As the third law states, when one object exerts a force on another, the second object exerts on the first a force equal in magnitude but opposite in direction. Unlike the second law, this one is much easier to illustrate in daily life. If a book is sitting on a table, that means that the book is exerting a force on the table equal to its mass multiplied by its rate of acceleration. Though it is not moving, the book is subject to the rate of gravitational acceleration, and in fact force and weight (which is defined as mass multiplied by the rate of acceleration due to gravity) are the same. At the same time, the table pushes up on the book with an exactly equal amount of force—just enough to keep it stationary. If the table exerted more force that the book—in other words, if instead of being an ordinary table it were some sort of pneumatic press pushing upward—then the book would fly off the table.
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beams and the foundation of the building, and the building and the ground, and so on. These pairs of forces exist everywhere. When you walk, you move forward by pushing backward on the ground with a force equal to your mass multiplied by your rate of downward gravitational acceleration. (This force, in other words, is the same as weight.) At the same time, the ground actually pushes back with an equal force. You do not perceive the fact that Earth is pushing you upward, simply because its enormous mass makes this motion negligible—but it does push. If you were stepping off of a small unmoored boat and onto a dock, however, something quite different would happen. The force of your leap to the dock would exert an equal force against the boat, pushing it further out into the water, and as a result, you would likely end up in the water as well. Again, the reaction is equal and opposite; the problem is that the boat in this illustration is not fixed in place like the ground beneath your feet. Differences in mass can result in apparently different reactions, though in fact the force is the same. This can be illustrated by imagining a mother and her six-year-old daughter skating on ice, a relatively frictionless surface. Facing one another, they push against each other, and as a result each moves backward. The child, of course, will move backward faster because her mass is less than that of her mother. Because the force they exerted is equal, the daughter’s acceleration is greater, and she moves farther. Ice is not a perfectly frictionless surface, of course: otherwise, skating would be impossible. Likewise friction is absolutely necessary for walking, as you can illustrate by trying to walk on a perfectly slick surface—for instance, a skating rink covered with oil. In this situation, there is still an equally paired set of forces—your body presses down on the surface of the ice with as much force as the ice presses upward—but the lack of friction impedes the physical process of pushing off against the floor.
There is no such thing as an unpaired force in the universe. The table rests on the floor just as the book rests on it, and the floor pushes up on the table with a force equal in magnitude to that with which the table presses down on the floor. The same is true for the floor and the supporting beams that hold it up, and for the supporting
It will only be possible to overcome inertia by recourse to outside intervention, as for instance if someone who is not on the ice tossed out a rope attached to a pole in the ground. Alternatively, if the person on the ice were carrying a heavy load of rocks, it would be possible to move by throwing the rocks backward. In this situation, you are exerting force on the rock, and this
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Laws of Motion
KEY TERMS A change in velocity
ACCELERATION:
over a given time period. EQUILIBRIUM:
A situation in which
the forces acting upon an object are in
MECHANICS:
The study of bodies in
motion. MOMENTUM:
The product of mass
multiplied by velocity.
balance. FRICTION:
Any force that resists the
motion of body in relation to another with which it is in contact. INERTIA:
The tendency of an object in
motion to remain in motion, and of an object at rest to remain at rest. MASS:
A measure of inertia, indicating
The rate at which the position
SPEED:
of an object changes over a given period of time. VELOCITY:
The speed of an object in a
particular direction. VISCOSITY: The internal friction in a
fluid that makes it resistant to flow.
the resistance of an object to a change in its A measure of the gravitation-
motion—including a change in velocity. A
WEIGHT:
kilogram is a unit of mass, whereas a
al force on an object. A pound is a unit of
pound is a unit of weight. The mass of an
weight, whereas a kilogram is a unit of
object remains the same throughout the
mass. Weight thus would change from
universe, whereas its weight is a function of
planet to planet, whereas mass remains
gravity on any given planet.
constant throughout the universe.
backward force results in a force propelling the thrower forward. This final point about friction and movement is an appropriate place to close the discussion on the laws of motion. Where walking or skating are concerned—and in the absence of a bag of rocks or some other outside force—friction is necessary to the action of creating a backward force and therefore moving forward. On the other hand, the absence of friction would make it possible for an object in movement to continue moving indefinitely, in line with the first law of motion. In either case, friction opposes inertia. The fact is that friction itself is a force. Thus, if you try to slide a block of wood across a floor, friction will stop it. It is important to remember this, lest you fall into the fallacy that bedeviled Aristotle’s thinking and thus confused the world for many centuries. The block did not stop moving because the force that pushed it was no longer being applied; it stopped because an
S C I E N C E O F E V E RY DAY T H I N G S
opposing force, friction, was greater than the force that was pushing it. WHERE TO LEARN MORE Ardley, Neil. The Science Book of Motion. San Diego: Harcourt Brace Jovanovich, 1992. Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Chase, Sara B. Moving to Win: The Physics of Sports. New York: Messner, 1977. Fleisher, Paul. Secrets of the Universe: Discovering the Universal Laws of Science. Illustrated by Patricia A. Keeler. New York: Atheneum, 1987. “The Laws of Motion.” How It Flies (Web site). (February 27, 2001). Newton, Isaac (translated by Andrew Motte, 1729). The Principia (Web site). (February 27, 2001). Newton’s Laws of Motion (Web site). (February 27, 2001).
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“Newton’s Laws of Motion.” Dryden Flight Research Center, National Aeronautics and Space Administration (NASA) (Web site). (February 27, 2001).
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(Web site). (February 27, 2001). Roberts, Jeremy. How Do We Know the Laws of Motion? New York: Rosen, 2001.
“Newton’s Laws of Motion: Movin’ On.” Beyond Books
Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.
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Gravity and Gravitation
G R AV I T Y A N D G R AV I TAT I O N
CONCEPT Gravity is, quite simply, the force that holds together the universe. People are accustomed to thinking of it purely in terms of the gravitational pull Earth exerts on smaller bodies—a stone, a human being, even the Moon—or perhaps in terms of the Sun’s gravitational pull on Earth. In fact, everything exerts a gravitational attraction toward everything else, an attraction commensurate with the two body’s relative mass, and inversely related to the distance between them. The earliest awareness of gravity emerged in response to a simple question: why do objects fall when released from any restraining force? The answers, which began taking shape in the sixteenth century, were far from obvious. In modern times, understanding of gravitational force has expanded manyfold: gravity is clearly a law throughout the universe—yet some of the more complicated questions regarding gravitational force are far from settled.
philosopher exerted an incalculable influence on the development of scientific thought. Aristotle’s contributions to the advancement of the sciences were many and varied, yet his influence in physics was at least as harmful as it was beneficial. Furthermore, the fact that intellectual progress began slowing after several fruitful centuries of development in Greece only compounded the error. By the time civilization had reached the Middle Ages (c. 500 A.D.) the Aristotelian model of physical reality had been firmly established, and an entire millennium passed before it was successfully challenged. Wrong though it was in virtually all particulars, the Aristotelian system offered a comforting symmetry amid the troubled centuries of the early medieval period. It must have been reassuring indeed to believe that the physical universe was as simple as the world of human affairs was complex. According to this neat model, all materials on Earth consisted of four elements: earth, water, air, and fire.
Greek philosophers of the period from the sixth to the fourth century B.C. grappled with a variety of questions concerning the fundamental nature of physical reality, and the forces that bind that reality into a whole. Among the most advanced thinkers of that period was Democritus (c. 460370 B.C.), who put forth a hypothesis many thousands of years ahead of its time: that all of matter interacts at the atomic level.
Each element had its natural place. Hence, earth was always the lowest, and in some places, earth was covered by water. Water must then be higher, but clearly air was higher still, since it covered earth and water. Highest of all was fire, whose natural place was in the skies above the air. Reflecting these concentric circles were the orbits of the Sun, the Moon, and the five known planets. Their orbital paths, in the Aristotelian model of the universe—a model developed to a great degree by the astronomer Ptolemy (c. 100170)—were actually spheres that revolved around Earth with clockwork precision.
Aristotle (384-322 B.C.), however, rejected the explanation offered by Democritus, an unfortunate circumstance given the fact that the great
On Earth, according to the Aristotelian model, objects tended to fall toward the ground in accordance with the admixtures of differing
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Gravity and Gravitation
BECAUSE
OF
EARTH’S
GRAVITY, THE WOMAN BEING SHOT OUT OF THIS CANNON WILL EVENTUALLY FALL
TO THE GROUND RATHER THAN ASCEND INTO OUTER SPACE. (Underwood & Underwood/Corbis. Reproduced by
permission.)
elements they contained. A rock, for instance, was mostly earth, and hence it sought its own level, the lowest of all four elements. For the same reason, a burning fire rose, seeking the heights that were fire’s natural domain. It followed from this that an object falls faster or slower, depending on the relative mixtures of elements in it: or, to use more modern terms, the heavier the object, the faster it falls.
rejected his heliocentric (Sun-centered) model in favor of the geocentric or Earth-centered one. In subsequent centuries, no less a political authority than the Catholic Church gave its approval to the Ptolemaic system. This system seemed to fit well with a literal interpretation of biblical passages concerning God’s relationship with man, and man’s relationship to the cosmos; hence, the heliocentric model of Copernicus constituted an offense to morality.
Galileo Takes Up the Copernican Challenge
For this reason, Copernicus was hesitant to defend his ideas publicly, yet these concepts found their way into the consciousness of European thinkers, causing a paradigm shift so fundamental that it has been dubbed “the Copernican Revolution.” Still, Copernicus offered no explanation as to why the planets behaved as they did: hence, the true leader of the Copernican Revolution was not Copernicus himself but Galileo Galilei (1564-1642.)
Over the centuries, a small but significant body of scientists and philosophers—each working independent from the other but building on the ideas of his predecessors—slowly began chipping away at the Aristotelian framework. The pivotal challenge came in the early part of the century, and the thinker who put it forward was not a physicist but an astronomer: Nicolaus Copernicus (1473-1543.)
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Based on his study of the planets, Copernicus offered an entirely new model of the universe, one that placed the Sun and not Earth at its center. He was not the first to offer such an idea: half a century after Aristotle’s death, Aristarchus (fl. 270 B.C.) had a similar idea, but Ptolemy
Initially, Galileo set out to study and defend the ideas of Copernicus through astronomy, but soon the Church forced him to recant. It is said that after issuing a statement in which he refuted the proposition that Earth moves—a direct attack on the static harmony of the Aristotelian/Ptolemaic model—he protested in pri-
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vate: “E pur si muove!” (But it does move!) Placed under house arrest by authorities from Rome, he turned his attention to an effort that, ironically, struck the fatal blow against the old model of the cosmos: a proof of the Copernican system according to the laws of physics.
Gravity and Gravitation
G R A V I TAT I O N A L A C C E L E R A T I O N . In the process of defending Copernicus,
Galileo actually inaugurated the modern history of physics as a science (as opposed to what it had been during the Middle Ages: a nest of suppositions masquerading as knowledge). Specifically, Galileo set out to test the hypothesis that objects fall as they do, not because of their weight, but as a consequence of gravitational force. If this were so, the acceleration of falling bodies would have to be the same, regardless of weight. Of course, it was clear that a stone fell faster than a feather, but Galileo reasoned that this was a result of factors other than weight, and later investigations confirmed that air resistance and friction, not weight, are responsible for this difference. On the other hand, if one drops two objects that have similar air resistance but differing weight—say, a large stone and a smaller one— they fall at almost exactly the same rate. To test this directly, however, would have been difficult for Galileo: stones fall so fast that, even if dropped from a great height, they would hit the ground too soon for their rate of fall to be tested with the instruments then available. Instead, Galileo used the motion of a pendulum, and the behavior of objects rolling or sliding down inclined planes, as his models. On the basis of his observations, he concluded that all bodies are subject to a uniform rate of gravitational acceleration, later calibrated at 32 ft (9.8 m) per second. What this means is that for every 32 ft an object falls, it is accelerating at a rate of 32 ft per second as well; hence, after 2 seconds, it falls at the rate of 64 ft (19.6 m) per second; after 3 seconds, at 96 ft (29.4 m) per second, and so on.
THIS
PHOTO SHOWS AN APPLE AND A FEATHER BEING
DROPPED
IN
A
VACUUM
TUBE.
BECAUSE
OF
THE
ABSENCE OF AIR RESISTANCE, THE TWO OBJECTS FALL AT THE SAME RATE. (Photograph by James A. Sugar/Corbis. Repro-
duced by permission.)
twentieth century, when Albert Einstein (18791955) challenged it on certain specifics. Even so, Einstein’s relativity did not disprove the Newtonian system as Copernicus and Galileo disproved Aristotle’s and Ptolemy’s theories; rather, it showed the limitations of Newtonian mechanics for describing the behavior of certain objects and phenomena. However, in the ordinary world of day-to-day experience—the world in which stones drop and heavy objects are hard to lift—the Newtonian system still offers the key to how and why things work as they do. This is particularly the case with regard to gravity and gravitation.
Building on the work of his distinguished forebear, Sir Isaac Newton (1642-1727)—who, incidentally, was born the same year Galileo died— developed a paradigm for gravitation that, even today, explains the behavior of objects in virtually all situations throughout the universe. Indeed, the Newtonian model reigned until the early
Like Galileo, Newton began in part with the aim of testing hypotheses put forth by an astronomer—in this case Johannes Kepler (15711630). In the early years of the seventeenth century, Kepler published his three laws of planetary motion, which together identified the elliptical (oval-shaped) path of the planets around the Sun. Kepler had discovered a mathematical relationship that connected the distances of the planets from the Sun to the period of their revolution
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around it. Like Galileo with Copernicus, Newton sought to generalize these principles to explain, not only how the planets moved, but also why they did. Almost everyone has heard the story of Newton and the apple—specifically, that while he was sitting under an apple tree, a falling apple struck him on the head, spurring in him a great intuitive leap that led him to form his theory of gravitation. One contemporary biographer, William Stukely, wrote that he and Newton were sitting in a garden under some apple trees when Newton told him that “...he was just in the same situation, as when formerly, the notion of gravitation came into his mind. It was occasion’d by the fall of an apple, as he sat in a contemplative mood. Why should that apple always descend perpendicularly to the ground, he thought to himself. Why should it not go sideways or upwards, but constantly to the earth’s centre?” The tale of Newton and the apple has become a celebrated myth, rather like that of George Washington and the cherry tree. It is an embellishment of actual events: Newton never said that an apple hit him on the head, just that he was thinking about the way that apples fell. Yet the story has become symbolic of the creative intellectual process that occurs when a thinker makes a vast intuitive leap in a matter of moments. Of course, Newton had spent many years contemplating these ideas, and their development required great effort. What is important is that he brought together the best work of his predecessors, yet transcended all that had gone before—and in the process, forged a model that explained a great deal about how the universe functions. The result was his Philosophiae Naturalis Principia Mathematica, or “Mathematical Principles of Natural Philosophy.” Published in 1687, the book—usually referred to simply as the Principia—was one of the most influential works ever written. In it, Newton presented his three laws of motion, as well as his law of universal gravitation. The latter stated that every object in the universe attracts every other one with a force proportional to the masses of each, and inversely proportional to the square of the distance between them. This statement requires some clarification with regard to its particulars, after
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which it will be reintroduced as a mathematical formula. M ASS A N D F O R C E . The three laws
of motion are a subject unto themselves, covered elsewhere in this volume. However, in order to understand gravitation, it is necessary to understand at least a few rudimentary concepts relating to them. The first law identifies inertia as the tendency of an object in motion to remain in motion, and of an object at rest to remain at rest. Inertia is measured by mass, which—as the second law states—is a component of force. Specifically, the second law of motion states that force is equal to mass multiplied by acceleration. This means that there is an inverse relationship between mass and acceleration: if force remains constant and one of these factors increases, the other must decrease—a situation that will be discussed in some depth below. Also, as a result of Newton’s second law, it is possible to define weight scientifically. People typically assume that mass and weight are the same, and indeed they are on Earth—or at least, they are close enough to be treated as comparable factors. Thus, tables of weights and measures show that a kilogram, the metric unit of mass, is equal to 2.2 pounds, the latter being the principal unit of weight in the British system. In fact, this is—if not a case of comparing to apples to oranges—certainly an instance of comparing apples to apple pies. In this instance, the kilogram is the “apple” (a fitting Newtonian metaphor!) and the pound the “apple pie.” Just as an apple pie contains apples, but other things as well, the pound as a unit of force contains an additional factor, acceleration, not included in the kilo. B R I T I S H V S . S I U N I T S . Physicists universally prefer the metric system, which is known in the scientific community as SI (an abbreviation of the French Système International d’Unités—that is, “International System of Units”). Not only is SI much more convenient to use, due to the fact that it is based on units of 10; but in discussing gravitation, the unequal relationship between kilograms and pounds makes conversion to British units a tedious and ultimately useless task.
Though Americans prefer the British system to SI, and are much more familiar with pounds than with kilos, the British unit of mass—called the slug—is hardly a household word. By conS C I E N C E O F E V E RY DAY T H I N G S
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trast, scientists make regular use of the SI unit of force—named, appropriately enough, the newton. In the metric system, a newton (N) is the amount of force required to accelerate 1 kilogram of mass by 1 meter per second squared (m/s2) Due to the simplicity of using SI over the British system, certain aspects of the discussion below will be presented purely in terms of SI. Where appropriate, however, conversion to British units will be offered. C A L C U L AT I N G G RAV I TAT I O N A L F O R C E . The law of universal gravitation
can be stated as a formula for calculating the gravitational attraction between two objects of a certain mass, m1 AND M2: Fgrav = G • (m1M2)/ R2. Fgrav is gravitational force, and r2 the square of the distance between m1 and m2. As for G, in Newton’s time the value of this number was unknown. Newton was aware simply that it represented a very small quantity: without it, (m1m2)/r2 could be quite sizeable for objects of relatively great mass separated by a relatively small distance. When multiplied by this very small number, however, the gravitational attraction would be revealed to be very small as well. Only in 1798, more than a century after Newton’s writing, did English physicist Henry Cavendish (1731-1810) calculate the value of G. As to how Cavendish derived the figure, that is an exceedingly complex subject far beyond the scope of the present discussion. Even to identify G as a number is a challenging task. First of all, it is a unit of force multiplied by squared area, then divided by squared mass: in other words, it is expressed in terms of (N • m2)/kg2, where N stands for newtons, m for meters, and kg for kilograms. Nor is the coefficient, or numerical value, of G a whole number such as 1. A figure as large as 1, in fact, is astronomically huge compared to G, whose coefficient is 6.67 • 10-11—in other words, 0.0000000000667.
REAL-LIFE A P P L I C AT I O N S Weight vs. Mass
framework of physics requires setting aside everyday notions.
Gravity and Gravitation
First of all, why the distinction between weight and mass? People are so accustomed to converting pounds to kilos on Earth that the difference is difficult to comprehend, but if one considers the relation of mass and weight in outer space, the distinction becomes much clearer. Mass is the same throughout the universe, making it a much more fundamental characteristic—and hence, physicists typically speak in terms of mass rather than weight. Weight, on the other hand, differs according to the gravitational pull of the nearest large body. On Earth, a person weighs a certain amount, but on the Moon, this weight is much less, because the Moon possesses less mass than Earth. Therefore, in accordance with Newton’s formula for universal gravitation, it exerts less gravitational pull. By contrast, if one were on Jupiter, it would be almost impossible even to stand up, because the pull of gravity on that planet—with its greater mass—would be vastly greater than on Earth. It should be noted that mass is not at all a function of size: Jupiter does have a greater mass than Earth, but not because it is bigger. Mass, as noted earlier, is purely a measure of inertia: the more resistant an object is to a change in its velocity, the greater its mass. This in itself yields some results that seem difficult to understand as long as one remains wedded to the concept— true enough on Earth—that weight and mass are identical. A person might weigh less on the Moon, but it would be just as difficult to move that person from a resting position as it would be to do so on Earth. This is because the person’s mass, and hence his or her resistance to inertia, has not changed. Again, this is a mentally challenging concept: is not lifting a person, which implies upward acceleration, not an attempt to counteract their inertia when standing still? Does it not follow that their mass has changed? Understanding the distinction requires a greater clarification of the relationship between mass, gravity, and weight.
Before discussing the significance of the gravitational constant, however, at this point it is appropriate to address a few issues that were raised earlier—issues involving mass and weight. In many ways, understanding these properties from the
F = m a . Newton’s second law of motion, stated earlier, shows that force is equal to mass multiplied by acceleration, or in shorthand form, F = ma. To reiterate a point already made, if one assumes that force is constant, then mass and
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acceleration must have an inverse relationship. This can be illustrated by performing a simple experiment. Suppose one were to apply a certain amount of force to an empty shopping cart. Assuming the floor had just enough friction to allow movement, it would be easy for almost anyone to accelerate the shopping cart. Now assume that the shopping cart were filled with heavy lead balls, so that it weighed, say, 1,102 lb (500 kg). If one applied the same force, it would not move. What has changed, clearly, is the mass of the shopping cart. Because force remained constant, the rate of acceleration would become very small—in this case, almost infinitesimal. In the first case, with an empty shopping cart, the mass was relatively small, so acceleration was relatively high. Now to return to the subject of lifting someone on the Moon. It is true that in order to lift that person, one would have to overcome inertia, and, in that sense, it would be as difficult as it is on Earth. But the other component of force, acceleration, has diminished greatly. Weight is, again, a unit of force, but in calculating weight it is useful to make a slight change to the formula F = ma. By definition, the acceleration factor in weight is the downward acceleration due to gravity, usually rendered as g. So one’s weight is equal to mg—but on the Moon, g is much smaller than it is on Earth, and hence, the same amount of force yields much greater results. These facts shed new light on a question that bedeviled physicists at least from the time of Aristotle, until Galileo began clarifying the issue some 2,000 years later: why shouldn’t an object of greater mass fall at a different rate than one of smaller mass? There are two answers to that question, one general and one specific. The general answer—that Earth exerts more gravitational pull on an object of greater mass—requires a deeper examination of Newton’s gravitational formula. But the more specific answer, relating purely to conditions on Earth, is easily addressed by considering the effect of air resistance.
Idealization of reality makes it possible to set aside the things people think they know about the real world, where events are complicated due to friction. The latter may be defined as a force that resists motion when the surface of one object comes into contact with the surface of another. If two balls are released in an environment free from friction—one of them simply dropped while the other is rolled down a curved surface or inclined plane—they will reach the bottom at the same time. This seems to go against everything that is known, but that is only because what people “know” is complicated by variables that have nothing to do with gravity. The same is true for the behavior of falling objects with regard to air resistance. If air resistance were not a factor, one could fire a cannonball over horizontal space and then, when the ball reached the highest point in its trajectory, release another ball from the same height—and again, they would hit the ground at the same time. This is the case, even though the cannonball that was fired from the cannon has to cover a great deal of horizontal space, whereas the dropped ball does not. The fact is that the rate of acceleration due to gravity will be identical for the two balls, and the fact that the ball fired from a cannon also covers a horizontal distance during that same period is irrelevant.
One of Galileo’s many achievements lay in using an idealized model of reality, one that does not take into account the many complex factors that affect the behavior of objects in the real world.
T E R M I N A L V E LO C I T Y. In the real world, air resistance creates a powerful drag force on falling objects. The faster the rate of fall, the greater the drag force, until the air resistance forces a leveling in the rate of fall. At this point, the object is said to have reached terminal velocity, meaning that its rate of fall will not increase thereafter. Galileo’s idealized model, on the other hand, treated objects as though they were falling in a vacuum—space entirely devoid of matter, including air. In such a situation, the rate of acceleration would continue to grow indefinitely.
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This permitted physicists to study processes that apparently defy common sense. For instance, in the real world, an apple does drop at a greater rate of speed than does a feather. However, in a vacuum, they will drop at the same rate. Since Galileo’s time, it has become commonplace for physicists to discuss specific processes such as gravity with the assumption that all non-pertinent factors (in this case, air resistance or friction) are nonexistent or irrelevant. This greatly simplified the means of testing hypotheses.
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By means of a graph, one can compare the behavior of an object falling through air with that of an object falling in a vacuum. If the x axis measures time and the y axis downward speed, the rate of an object falling in a vacuum describes a 60°-angle. In other words, the speed of its descent is increasing at a much faster rate than is the rate of time of its descent—as indeed should be the case, in accordance with gravitational acceleration. The behavior of an object falling through air, on the other hand, describes a curve. Up to a point, the object falls at the same rate as it would in a vacuum, but soon velocity begins to increase at a much slower rate than time. Eventually, the curve levels off at the point where the object experiences terminal velocity. Air resistance and friction have been mentioned separately as though they were two different forces, but in fact air resistance is simply a prominent form of friction. Hence air resistance exerts an upward force to counter the downward force of mass multiplied by gravity—that is, weight. Since g is a constant (32 ft or 9.8 m/sec2), the greater the weight of the falling object, the longer it takes for air resistance to bring it to terminal velocity. A feather quickly reaches terminal velocity, whereas it takes much longer for a cannonball to do the same. As a result, a heavier object does take less time to fall, even from a great height, than does a light one—but this is only because of friction, and not because of “elements” seeking their “natural level.” Incidentally, if raindrops (which of course fall from a very great height) did not reach terminal velocity, they would cause serious injury by the time they hit the ground.
Applying the Gravitational Formula Using Newton’s gravitational formula, it is relatively easy to calculate the pull of gravity between two objects. It is also easy to see why the attraction is insignificant unless at least one of the objects has enormous mass. In addition, application of the formula makes it clear why G (the gravitational constant, as opposed to g, the rate of acceleration due to gravity) is such a tiny number. If two people each have a mass of 45.5 kg (100 lb) and stand 1 m (3.28 ft) apart, m1m2 is equal to 2,070 kg (4,555 lb) and r2 is equal to 1 m2. Applied to the gravitational formula, this figure is rendered as 2,070 kg2/1 m2. This number is
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then multiplied by gravitational constant, which again is equal to 6.67 • 10-11 (N • m2)/kg2. The result is a net gravitational force of 0.000000138 N (0.00000003 lb)—about the weight of a singlecell organism!
Gravity and Gravitation
E A RT H , G RAV I T Y, A N D W E I G H T.
Though it is certainly interesting to calculate the gravitational force between any two people, computations of gravity are only significant for objects of truly great mass. For instance, there is the Earth, which has a mass of 5.98 • 1024 kg— that is, 5.98 septillion (1 followed by 24 zeroes) kilograms. And, of course, Earth’s mass is relatively minor compared to that of several planets, not to mention the Sun. Yet Earth exerts enough gravitational pull to keep everything on it—living creatures, manmade structures, mountains and other natural features—stable and in place. One can calculate Earth’s gravitational force on any one person—if one wants to take the time to do so using Newton’s formula. In fact, it is much simpler than that: gravitational force is equal to weight, or m • g. Thus if a woman weighs 100 lb (445 N), this amount is also equal to the gravitational force exerted on her. By dividing 445 N by the acceleration of gravity—9.8 m/sec2—it is easy to obtain her mass: 45.4 kg. The use of the mg formula for gravitation helps, once again, to explain why heavier objects do not fall faster than lighter ones. The figure for g is a constant, but for the sake of argument, let us assume that it actually becomes larger for objects with a greater mass. This in turn would mean that the gravitational force, or weight, would be bigger than it is—thus creating an irreconcilable logic loop. Furthermore, one can compare results of two gravitation equations, one measuring the gravitational force between Earth and a large stone, the other measuring the force between Earth and a small stone. (The distance between Earth and each stone is assumed to be the same.) The result will yield a higher quantity for the force exerted on the larger stone—but only because its mass is greater. Clearly, then, the increase of force results only from an increase in mass, not acceleration.
Gravity and Curved Space As should be clear from Newton’s gravitational formula, the force of gravity works both ways: not only does a stone fall toward Earth, but Earth
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Gravity and Gravitation
KEY TERMS FORCE:
The product of mass multi-
plied by acceleration.
comes into contact with the surface of
A measure of inertia, indicating the resistance of an object to a change in its motion.
another.
TERMINAL
FRICTION:
The force that resists
motion when the surface of one object
MASS:
the decrease in the other.
A term describing the rate of fall for an object experiencing the drag force of air resistance. In a vacuum, the object would continue to accelerate with the force of gravity, but in most real-world situations, air resistance creates a powerful drag force that causes a leveling in the object’s rate of fall.
LAW OF UNIVERSAL GRAVITATION:
VACUUM:
INERTIA:
The tendency of an object in
motion to remain in motion, and of an object at rest to remain at rest. INVERSE RELATIONSHIP:
A situa-
tion involving two variables, in which one of the two increases in direct proportion to
VELOCITY:
A principle, put forth by Sir Isaac Newton
Space entirely devoid of matter, including air.
(1642-1727), which states that every object
WEIGHT:
in the universe attracts every other one with a force proportional to the masses of
actually falls toward it. The mass of Earth is so great compared to that of the stone that the movement of Earth is imperceptible—but it does happen. Furthermore, because Earth is round, when one hurls a projectile at a great distance, Earth curves away from the projectile; but eventually gravity itself forces the projectile to the ground. However, if one were to fire a rocket at 17,700 MPH (28,500 km/h), at every instant of time the projectile is falling toward Earth with the force of gravity—but the curved Earth would be falling away from it at the same moment as well. Hence, the projectile would remain in constant motion around the planet—that is, it would be in orbit. The same is true of an artificial satellite’s orbit around Earth: even as the satellite falls toward Earth, Earth falls away from it. This same relationship exists between Earth and its great natural satellite, the Moon. Likewise, with the 76
each, and inversely proportional to the square of the distance between them.
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A measure of the gravitational force on an object; the product of mass multiplied by the acceleration due to gravity.
Sun and its many satellites, including Earth: Earth plunges toward the Sun with every instant of its movement, but at every instant, the Sun falls away. W H Y I S E A RT H R O U N D ? Note
that in the above discussion, it was assumed that Earth and the Sun are round. Everyone knows that to be the case, but why? The answer is “Because they have to be”—that is, gravity will not allow them to be otherwise. In fact, the larger the mass of an object, the greater its tendency toward roundness: specifically, the gravitational pull of its interior forces the surface to assume a relatively uniform shape. There is a relatively small vertical differential for Earth’s surface: between the lowest point and the highest point is just 12.28 mi (19.6 km)—not a great distance, considering that Earth’s radius is about 4,000 mi (6,400 km). It is true that Earth bulges near the equator, but this is only because it is spinning rapidly on S C I E N C E O F E V E RY DAY T H I N G S
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its axis, and thus responding to the centripetal force of its motion, which produces a centrifugal component. If Earth were standing still, it would be much nearer to the shape of a sphere. On the other hand, an object of less mass is more likely to retain a shape that is far less than spherical. This can be shown by reference to the Martian moons Phobos and Deimos, both of which are oblong—and both of which are tiny, in terms of size and mass, compared to Earth’s Moon. Mars itself has a radius half that of Earth, yet its mass is only about 10% of Earth’s. In light of what has been said about mass, shape, and gravity, it should not surprising to learn that Mars is also home to the tallest mountain in the solar system. Standing 15 mi (24 km) high, the volcano Olympus Mons is not only much taller than Earth’s tallest peak, Mount Everest (29,028 ft [8,848 m]); it is 22% taller than the distance from the top of Mount Everest to the lowest spot on Earth, the Mariana Trench in the Pacific Ocean (-35,797 ft [-10,911 m]) A spherical object behaves with regard to gravitation as though its mass were concentrated near its center. And indeed, 33% of Earth’s mass is at is core (as opposed to the crust or mantle), even though the core accounts for only about 20% of the planet’s volume. Geologists believe that the composition of Earth’s core must be molten iron, which creates the planet’s vast electromagnetic field. T H E F R O N T I E R S O F G RAV I T Y.
The subject of curvature with regard to gravity can be both a threshold or—as it is here—a point of closure. Investigating questions over perceived anomalies in Newton’s description of the behavior of large objects in space led Einstein to his General Theory of Relativity, which posited a curved four-dimensional space-time. This led to entirely new notions concerning gravity, mass, and light. But relativity, as well as its relation to gravity, is another subject entirely. Einstein offered a new understanding of gravity, and indeed of physics itself, that has changed the way
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thinkers both inside and outside the sciences perceive the universe. Here on Earth, however, gravity behaves much as Newton described it more than three centuries ago.
Gravity and Gravitation
Meanwhile, research in gravity continues to expand, as a visit to the Web site <www.Gravity.org> reveals. Spurred by studies in relativity, a branch of science called relativistic astrophysics has developed as a synthesis of astronomy and physics that incorporates ideas put forth by Einstein and others. The <www.Gravity.org> site presents studies—most of them too abstruse for a reader who is not a professional scientist— across a broad spectrum of disciplines. Among these is bioscience, a realm in which researchers are investigating the biological effects—such as mineral loss and motion sickness—of exposure to low gravity. The results of such studies will ultimately protect the health of the astronauts who participate in future missions to outer space. WHERE TO LEARN MORE Ardley, Neil. The Science Book of Gravity. San Diego, CA: Harcourt Brace Jovanovich, 1992. Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Bendick, Jeanne. Motion and Gravity. New York: F. Watts, 1972. Dalton, Cindy Devine. Gravity. Vero Beach, FL: Rourke, 2001. David, Leonard. “Artificial Gravity and Space Travel.” BioScience, March 1992, pp. 155-159. Exploring Gravity—Curtin University, Australia (Web site). (March 18, 2001). The Gravity Society (Web site). (March 18, 2001). Nardo, Don. Gravity: The Universal Force. San Diego, CA: Lucent Books, 1990. Rutherford, F. James; Gerald Holton; and Fletcher G. Watson. Project Physics. New York: Holt, Rinehart, and Winston, 1981. Stringer, John. The Science of Gravity. Austin, TX: Raintree Steck-Vaughn, 2000.
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PROJECTILE MOTION Projectile Motion
CONCEPT A projectile is any object that has been thrown, shot, or launched, and ballistics is the study of projectile motion. Examples of projectiles range from a golf ball in flight, to a curve ball thrown by a baseball pitcher to a rocket fired into space. The flight paths of all projectiles are affected by two factors: gravity and, on Earth at least, air resistance.
HOW IT WORKS The effects of air resistance on the behavior of projectiles can be quite complex. Because effects due to gravity are much simpler and easier to analyze, and since gravity applies in more situations, we will discuss its role in projectile motion first. In most instances on Earth, of course, a projectile will be subject to both forces, but there may be specific cases in which an artificial vacuum has been created, which means it will only be subjected to the force of gravity. Furthermore, in outer space, gravity—whether from Earth or another body—is likely to be a factor, whereas air resistance (unless or until astronomers find another planet with air) will not be.
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at sea level, but since the value of g changes little with altitude—it only decreases by 5% at a height of 10 mi (16 km)—it is safe to use this number. When a plane goes into a high-speed turn, it experiences much higher apparent g. This can be as high as 9 g, which is almost more than the human body can endure. Incidentally, people call these “g-forces,” but in fact g is not a measure of force but of a single component, acceleration. On the other hand, since force is the product of mass multiplied by acceleration, and since an aircraft subject to a high g factor clearly experiences a heavy increase in net force, in that sense, the expression “g-force” is not altogether inaccurate. In a vacuum, where air resistance plays no part, the effects of g are clearly demonstrated. Hence a cannonball and a feather, dropped into a vacuum at the same moment, would fall at exactly the same rate and hit bottom at the same time.
The Cannonball or the Feather? Air Resistance vs. Mass
The acceleration due to gravity is 32 ft (9.8 m)/sec2, usually expressed as “per second squared.” This means that as every second passes, the speed of a falling object is increasing by 32 ft/sec (9.8 m). Where there is no air resistance, a ball will drop at a velocity of 32 feet per second after one second, 64 ft (19.5 m) per second after two seconds, 96 ft (29.4 m) per second after three seconds, and so on. When an object experiences the ordinary acceleration due to gravity, this figure is rendered in shorthand as g. Actually, the figure of 32 ft (9.8 m) per second squared applies
Naturally, air resistance changes the terms of the above equation. As everyone knows, under ordinary conditions, a cannonball falls much faster than a feather, not simply because the feather is lighter than the cannonball, but because the air resists it much better. The speed of descent is a function of air resistance rather than mass, which can be proved with the following experiment. Using two identical pieces of paper—meaning that their mass is exactly the same—wad one up while keeping the other flat. Then drop them. Which one lands first? The wadded piece will fall faster and land first, precisely because it is less air-resistant than the sail-like flat piece.
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Projectile Motion
BECAUSE
OF THEIR DESIGN, THE BULLETS IN THIS
.357
MAGNUM WILL COME OUT OF THE GUN SPINNING, WHICH
GREATLY INCREASES THEIR ACCURACY. (Photograph by Tim Wright/Corbis. Reproduced by permission.)
Now to analyze the motion of a projectile in a situation without air resistance. Projectile motion follows the flight path of a parabola, a curve generated by a point moving such that its distance from a fixed point on one axis is equal to its distance from a fixed line on the other axis. In other words, there is a proportional relationship between x and y throughout the trajectory or path of a projectile in motion. Most often this parabola can be visualized as a simple up-anddown curve like the shape of a domed roof. (The Gateway Arch in St. Louis, Missouri, is a steep parabola.)
ally force the projectile downward, and once it hits the ground, it can no longer continue on its horizontal trajectory. Not, at least, at the same velocity: if you were to thrust a bowling ball forward, throwing it with both hands from the solar plexus, its horizontal velocity would be reduced greatly once gravity forced it to the floor. Nonetheless, the force on the ball would probably be enough (assuming the friction on the floor was not enormous) to keep the ball moving in a horizontal direction for at least a few more feet.
In the case of a cannonball fired at a 45° angle—the angle of maximum efficiency for height and range together—gravity will eventu-
There are several interesting things about the relationship between gravity and horizontal velocity. Assuming, once again, that air resistance is not a factor, the vertical acceleration of a projectile is g. This means that when a cannonball is at the highest point of its trajectory, you could simply drop another cannonball from exactly the same height, and they would land at the same moment. This seems counterintuitive, or opposite to common sense: after all, the cannonball that was fired from the cannon has to cover a great deal of horizontal space, whereas the dropped ball does not. Nonetheless, the rate of acceleration due to gravity will be identical for the two balls, and the fact that the ball fired from a cannon also covers a horizontal distance during that same period is purely incidental.
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Instead of referring to the more abstract values of x and y, we will separate projectile motion into horizontal and vertical components. Gravity plays a role only in vertical motion, whereas obviously, horizontal motion is not subject to gravitational force. This means that in the absence of air resistance, the horizontal velocity of a projectile does not change during flight; by contrast, the force of gravity will ultimately reduce its vertical velocity to zero, and this will in turn bring a corresponding drop in its horizontal velocity.
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Gravity, combined with the first law of motion, also makes it possible (in theory at least) for a projectile to keep moving indefinitely. This actually does take place at high altitudes, when a satellite is launched into orbit: Earth’s gravitational pull, combined with the absence of air resistance or other friction, ensures that the satellite will remain in constant circular motion around the planet. The same is theoretically possible with a cannonball at very low altitudes: if one could fire a ball at 17,700 MPH (28,500 k/mh), the horizontal velocity would be great enough to put the ball into low orbit around Earth’s surface. The addition of air resistance or airflow to the analysis of projectile motion creates a number of complications, including drag, or the force that opposes the forward motion of an object in airflow. Typically, air resistance can create a drag force proportional to the squared value of a projectile’s velocity, and this will cause it to fall far short of its theoretical range. Shape, as noted in the earlier illustration concerning two pieces of paper, also affects air resistance, as does spin. Due to a principle known as the conservation of angular momentum, an object that is spinning tends to keep spinning; moreover, the orientation of the spin axis (the imaginary “pole” around which the object is spinning) tends to remain constant. Thus spin ensures a more stable flight.
REAL-LIFE A P P L I C AT I O N S Bullets on a Straight Spinning Flight One of the first things people think of when they hear the word “ballistics” is the study of gunfire patterns for the purposes of crime-solving. Indeed, this application of ballistics is a significant part of police science, because it allows lawenforcement investigators to determine when, where, and how a firearm was used. In a larger sense, however, the term as applied to firearms refers to efforts toward creating a more effective, predictable, and longer bullet trajectory.
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ted to the barrel of the musket. When fired, they bounced erratically off the sides of the barrel, and this made their trajectories unpredictable. Compounding this was the unevenness of the lead balls themselves, and this irregularity of shape could lead to even greater irregularities in trajectory. Around 1500, however, the first true rifles appeared, and these greatly enhanced the accuracy of firearms. The term rifle comes from the “rifling” of the musket barrels: that is, the barrels themselves were engraved with grooves, a process known as rifling. Furthermore, ammunitionmakers worked to improve the production process where the musket balls were concerned, producing lead rounds that were more uniform in shape and size. Despite these improvements, soldiers over the next three centuries still faced many challenges when firing lead balls from rifled barrels. The lead balls themselves, because they were made of a soft material, tended to become misshapen during the loading process. Furthermore, the gunpowder that propelled the lead balls had a tendency to clog the rifle barrel. Most important of all was the fact that these rifles took time to load—and in a situation of battle, this could cost a man his life. The first significant change came in the 1840s, when in place of lead balls, armies began using bullets. The difference in shape greatly improved the response of rounds to aerodynamic factors. In 1847, Claude-Etienne Minié, a captain in the French army, developed a bullet made of lead, but with a base that was slightly hollow. Thus when fired, the lead in the round tended to expand, filling the barrel’s diameter and gripping the rifling. As a result, the round came out of the barrel end spinning, and continued to spin throughout its flight. Not only were soldiers able to fire their rifles with much greater accuracy, but thanks to the development of chambers and magazines, they could reload more quickly.
Curve Balls, Dimpled Golf Balls, and Other Tricks with Spin
From the advent of firearms in the West during the fourteenth century until about 1500, muskets were hopelessly unreliable. This was because the lead balls they fired had not been fit-
In the case of a bullet, spin increases accuracy, ensuring that the trajectory will follow an expected path. But sometimes spin can be used in more
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complex ways, as with a curveball thrown by a baseball pitcher.
Projectile Motion
The invention of the curveball is credited to Arthur “Candy” Cummings, who as a pitcher for the Brooklyn Excelsiors at the age of 18 in 1867— an era when baseball was still very young—introduced a new throw he had spent several years perfecting. Snapping as he released the ball, he and the spectators (not to mention the startled batter for the opposing team) watched as the pitch arced, then sailed right past the batter for a strike. The curveball bedeviled baseball players and fans alike for many years thereafter, and many dismissed it as a type of optical illusion. The debate became so heated that in 1941, both Life and Look magazines ran features using stopaction photography to show that a curveball truly did curve. Even in 1982, a team of researchers from General Motors (GM) and the Massachusetts Institute of Technology (MIT), working at the behest of Science magazine, investigated the curveball to determine if it was more than a mere trick. In fact, the curveball is a trick, but there is nothing fake about it. As the pitcher releases the ball, he snaps his wrist. This puts a spin on the projectile, and air resistance does the rest. As the ball moves toward the plate, its spin moves against the air, which creates an airstream moving against the trajectory of the ball itself. The airstream splits into two lines, one curving over the ball and one curving under, as the ball sails toward home plate. For the purposes of clarity, assume that you are viewing the throw from a position between third base and home. Thus, the ball is moving from left to right, and therefore the direction of airflow is from right to left. Meanwhile the ball, as it moves into the airflow, is spinning clockwise. This means that the air flowing over the top of the ball is moving in a direction opposite to the spin, whereas that flowing under it is moving in the same direction as the spin. This creates an interesting situation, thanks to Bernoulli’s principle. The latter, formulated by Swiss mathematician and physicist Daniel Bernoulli (1700-1782), holds that where velocity is high, pressure is low—and vice versa. Bernoulli’s principle is of the utmost importance to aerodynamics, and likewise plays a significant role in the operation of a curveball. At the top of the S C I E N C E O F E V E RY DAY T H I N G S
GOLF
BALLS ARE DIMPLED BECAUSE THEY TRAVEL MUCH
FARTHER
THAN
NONDIMPLED
ONES.
(Photograph by D.
Boone/Corbis. Reproduced by permission.)
ball, its clockwise spin is moving in a direction opposite to the airflow. This produces drag, slowing the ball, increasing pressure, and thus forcing it downward. At the bottom end of the ball, however, the clockwise motion is flowing with the air, thus resulting in higher velocity and lower pressure. As per Bernoulli’s principle, this tends to pull the ball downward. In the 60-ft, 6-in (18.4-m) distance that separates the pitcher’s mound from home plate on a regulation major-league baseball field, a curveball can move downward by a foot (0.3048 m) or more. The interesting thing here is that this downward force is almost entirely due to air resistance rather than gravity, though of course gravity eventually brings any pitch to the ground, assuming it has not already been hit, caught, or bounced off a fence. A curveball represents a case in which spin is used to deceive the batter, but it is just as possible that a pitcher may create havoc at home plate by throwing a ball with little or no spin. This is called a knuckleball, and it is based on the fact that spin in general—though certainly not the deliberate spin of a curveball—tends to ensure a VOLUME 2: REAL-LIFE PHYSICS
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more regular trajectory. Because a knuckleball has no spin, it follows an apparently random path, and thus it can be every bit as tricky for the pitcher as for the batter. Golf, by contrast, is a sport in which spin is expected: from the moment a golfer hits the ball, it spins backward—and this in turn helps to explain why golf balls are dimpled. Early golf balls, known as featheries, were merely smooth leather pouches containing goose feathers. The smooth surface seemed to produce relatively low drag, and golfers were impressed that a well-hit feathery could travel 150-175 yd (137-160 m). Then in the late nineteenth century, a professor at St. Andrews University in Scotland realized that a scored or marked ball would travel farther than a smooth one. (The part about St. Andrews may simply be golfing legend, since the course there is regarded as the birthplace of golf in the fifteenth century.) Whatever the case, it is true that a scored ball has a longer trajectory, again as a result of the effect of air resistance on projectile motion. Airflow produces two varieties of drag on a sphere such as a golf ball: drag due to friction, which is only a small aspect of the total drag, and the much more significant drag that results from the separation of airflow around the ball. As with the curveball discussed earlier, air flows above and below the ball, but the issue here is more complicated than for the curved pitch. Airflow comes in two basic varieties: laminar, meaning streamlined; or turbulent, indicating an erratic, unpredictable flow. For a jet flying through the air, it is most desirable to create a laminar flow passing over its airfoil, or the curved front surface of the wing. In the case of the golf ball, however, turbulent flow is more desirable. In laminar flow, the airflow separates quickly, part of it passing over the ball and part passing under. In turbulent flow, however, separation comes later, further back on the ball. Each form of air separation produces a separation region, an area of drag that the ball pulls behind it (so to speak) as it flies through space. But because the separation comes further back on the ball in turbulent flow, the separation region itself is narrower, thus producing less drag.
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designs that included squares, rectangles, and hexagons. In time, they settled on the dimpled design known today. Golf balls made in Britain have 330 dimples, and those in America 336; in either case, the typical drive distance is much, much further than for an unscored ball—180250 yd (165-229 m).
Powered Projectiles: Rockets and Missiles The most complex form of projectile widely known in modern life is the rocket or missile. Missiles are unmanned vehicles, most often used in warfare to direct some form of explosive toward an enemy. Rockets, on the other hand, can be manned or unmanned, and may be propulsion vehicles for missiles or for spacecraft. The term rocket can refer either to the engine or to the vehicle it propels. The first rockets appeared in China during the late medieval period, and were used unsuccessfully by the Chinese against Mongol invaders in the early part of the thirteenth century. Europeans later adopted rocketry for battle, as for instance when French forces under Joan of Arc used crude rockets in an effort to break the siege on Orleans in 1429. Within a century or so, however, rocketry as a form of military technology became obsolete, though projectile warfare itself remained as effective a method as ever. From the catapults of Roman times to the cannons that appeared in the early Renaissance to the heavy artillery of today, armies have been shooting projectiles against their enemies. The crucial difference between these projectiles and rockets or missiles is that the latter varieties are self-propelled. Only around the end of World War II did rocketry and missile warfare begin to reappear in new, terrifying forms. Most notable among these was Hitler’s V-2 “rocket” (actually a missile), deployed against Great Britain in 1944, but fortunately developed too late to make an impact. The 1950s saw the appearance of nuclear warheads such as the ICBM (intercontinental ballistic missile). These were guided missiles, as opposed to the V-2, which was essentially a huge self-propelled bullet fired toward London.
Clearly, scoring the ball produced turbulent flow, and for a few years in the early twentieth century, manufacturers experimented with
More effective than the ballistic missile, however, was the cruise missile, which appeared in later decades and which included aerodynamic structures that assisted in guidance and
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Projectile Motion
IN
THE CASE OF A ROCKET, LIKE THIS
PATRIOT
MISSILE BEING LAUNCHED DURING A TEST, PROPULSION COMES BY
EXPELLING FLUID—WHICH IN SCIENTIFIC TERMS CAN MEAN A GAS AS WELL AS A LIQUID—FROM ITS REAR END.
MOST
OFTEN THIS FLUID IS A MASS OF HOT GASES PRODUCED BY A CHEMICAL REACTION INSIDE THE ROCKET ’S BODY, AND THIS BACKWARD MOTION CREATES AN EQUAL AND OPPOSITE REACTION FROM THE ATMOSPHERE, PROPELLING THE ROCKET FORWARD. (Corbis. Reproduced by permission.)
maneuvering. In addition to guided or unguided, ballistic or aerodynamic, missiles can be classified in terms of source and target: surface-to-surface, air-to-air, and so on. By the 1970s, the United States had developed an extraordinarily sophisticated surface-to-air missile, the Stinger. Stingers proved a decisive factor in the AfghanSoviet War (1979-89), when U.S.-supplied Afghan guerrillas used them against Soviet aircraft. In the period from the late 1940s to the late 1980s, the United States, the Soviet Union, and other smaller nuclear powers stockpiled these warheads, which were most effective precisely
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because they were never used. Thus, U.S. President Ronald Reagan played an important role in ending the Cold War, because his weapons buildup forced the Soviets to spend money they did not have on building their own arsenal. During the aftermath of the Cold War, America and the newly democratized Russian Federation worked to reduce their nuclear stockpiles. Ironically, this was also the period when sophisticated missiles such as the Patriot began gaining widespread use in the Persian Gulf War and later conflicts. Certain properties unite the many varieties of rocket that have existed across time and
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Projectile Motion
KEY TERMS ACCELERATION:
A change in velocity
parabola there is a proportional relation-
over a given time period. AERODYNAMIC: BALLISTICS:
a result, between any two points on the
Relating to airflow.
The study of projectile
ship between x and y values. PROJECTILE:
Any object that has
been thrown, shot, or launched.
motion. The force that opposes the for-
DRAG:
ward motion of an object in airflow. In
SPECIFIC IMPULSE:
A measure of
rocket fuel efficiency—specifically, the mass that can be lifted by a particular type
most cases, its opposite is lift.
of fuel for each pound of fuel consumer FIRST LAW OF MOTION:
A principle,
formulated by Sir Isaac Newton (16421727), which states that an object at rest
(that is, the rocket and its contents) per second of operation time. Figures for specific impulse are rendered in seconds.
will remain at rest, and an object in motion will remain in motion, at a constant velocity unless or until outside forces act upon it. FRICTION:
Any force that resists the
SPEED:
The rate at which the position
of an object changes over a given period of time. Unlike velocity, direction is not a component of speed.
motion of body in relation to another with which it is in contact.
A princi-
ple, which like the first law of motion was
The tendency of an object in
formulated by Sir Isaac Newton. The third
motion to remain in motion, and of an
law states that when one object exerts a
object at rest to remain at rest.
force on another, the second object exerts
INERTIA:
LAMINAR:
A term describing a stream-
on the first a force equal in magnitude but
lined flow, in which all particles move at
opposite in direction.
the same speed and in the same direction.
TRAJECTORY:
Its opposite is turbulent flow.
in motion, a parabola upward and across
LIFT:
An aerodynamic force perpendi-
The path of a projectile
space.
cular to the direction of the wind. In most
TURBULENT:
cases, its opposite is drag.
highly irregular form of flow, in which a
A term describing a
A measure of inertia, indicating
fluid is subject to continual changes in
the resistance of an object to a change in its
speed and direction. Its opposite is laminar
motion—including a change in velocity.
flow.
MASS:
PARABOLA:
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THIRD LAW OF MOTION:
A curve generated by a
VELOCITY:
The speed of an object in a
point moving such that its distance from a
particular direction.
fixed point on one axis is equal to its dis-
VISCOSITY:
tance from a fixed line on the other axis. As
fluid that makes it resistant to flow.
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The internal friction in a
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space—including the relatively harmless fireworks used in Fourth of July and New Year’s Eve celebrations around the country. One of the key principles that makes rocket propulsion possible is the third law of motion. Sometimes colloquially put as “For every action, there is an equal and opposite reaction,” a more scientifically accurate version of this law would be: “When one object exerts a force on another, the second object exerts on the first a force equal in magnitude but opposite in direction.” In the case of a rocket, propulsion comes by expelling fluid—which in scientific terms can mean a gas as well as a liquid—from its rear. Most often this fluid is a mass of hot gases produced by a chemical reaction inside the rocket’s body, and this backward motion creates an equal and opposite reaction from the rocket, propelling it forward.
along the flight in part to increase specific impulse. This was the case with the Saturn 5 rockets that carried astronauts to the Moon in the period 1969-72, but not with the varieties of space shuttle that have flown regular missions since 1981. The space shuttle is essentially a hybrid of an airplane and rocket, with a physical structure more like that of an aircraft but with rocket power. In fact, the shuttle uses many rockets to maximize efficiency, utilizing no less than 67 rockets—49 of which run on liquid fuel and the rest on solid fuel—at different stages of its flight. WHERE TO LEARN MORE “Aerodynamics in Sports Equipment.” K8AIT Principles of Aeronautics—Advanced (Web site). (March 2, 2001).
Before it undergoes a chemical reaction, rocket fuel may be either in solid or liquid form inside the rocket’s fuel chamber, though it ends up as a gas when expelled. Both solid and liquid varieties have their advantages and disadvantages in terms of safety, convenience, and efficiency in lifting the craft. Scientists calculate efficiency by a number of standards, among them specific impulse, a measure of the mass that can be lifted by a particular type of fuel for each pound of fuel consumed (that is, the rocket and its contents) per second of operation time. Figures for specific impulse are rendered in seconds.
The Physics of Projectile Motion (Web site). (March 2, 2001).
A spacecraft may be divided into segments or stages, which can be released as specific points
Richardson, Hazel. How to Build a Rocket. Illustrated by Scoular Anderson. New York: F. Watts, 2001.
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Projectile Motion
Asimov, Isaac. Exploring Outer Space: Rockets, Probes, and Satellites. Revisions and updates by Francis Reddy. Milwaukee, WI: G. Stevens, 1995. How in the World? Pleasantville, N.Y.: Reader’s Digest, 1990. “Interesting Properties of Projectile of Motion” (Web site). (March 2, 2001). JBM Small Arms Ballistics (Web site). (March 2, 2001).
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TORQUE Torque
CONCEPT Torque is the application of force where there is rotational motion. The most obvious example of torque in action is the operation of a crescent wrench loosening a lug nut, and a close second is a playground seesaw. But torque is also crucial to the operation of gyroscopes for navigation, and of various motors, both internal-combustion and electrical.
HOW IT WORKS Force, which may be defined as anything that causes an object to move or stop moving, is the linchpin of the three laws of motion formulated by Sir Isaac Newton (1642-1727.) The first law states that an object at rest will remain at rest, and an object in motion will remain in motion, unless or until outside forces act upon it. The second law defines force as the product of mass multiplied by acceleration. According to the third law, when one object exerts a force on another, the second object exerts on the first a force equal in magnitude but opposite in direction.
On the other hand, the third law can be demonstrated when there is no apparent movement, as for instance, when a person is sitting on a chair, and the chair exerts an equal and opposite force upward. In such a situation, when all the forces acting on an object are in balance, that object is said to be in a state of equilibrium. Physicists often discuss torque within the context of equilibrium, even though an object experiencing net torque is definitely not in equilibrium. In fact, torque provides a convenient means for testing and measuring the degree of rotational or circular acceleration experienced by an object, just as other means can be used to calculate the amount of linear acceleration. In equilibrium, the net sum of all forces acting on an object should be zero; thus in order to meet the standards of equilibrium, the sum of all torques on the object should also be zero.
REAL-LIFE A P P L I C AT I O N S Seesaws and Wrenches
One way to envision the third law is in terms of an active event—for instance, two balls striking one another. As a result of the impact, each flies backward. Given the fact that the force on each is equal, and that force is the product of mass and acceleration (this is usually rendered with the formula F = ma), it is possible to make some predictions regarding the properties of mass and acceleration in this interchange. For instance, if the mass of one ball is relatively small compared to that of the other, its acceleration will be correspondingly greater, and it will thus be thrown backward faster.
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As for what torque is and how it works, it is best discuss it in relationship to actual objects in the physical world. Two in particular are favorites among physicists discussing torque: a seesaw and a wrench turning a lug nut. Both provide an easy means of illustrating the two ingredients of torque, force and moment arm. In any object experiencing torque, there is a pivot point, which on the seesaw is the balancepoint, and which in the wrench-and-lug nut combination is the lug nut itself. This is the area around which all the forces are directed. In each
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Torque
A
SEESAW ROTATES ON AND OFF THE GROUND DUE TO TORQUE IMBALANCE. (Photograph by Dean Conger/Corbis. Reproduced
by permission.)
case, there is also a place where force is being applied. On the seesaw, it is the seats, each holding a child of differing weight. In the realm of physics, weight is actually a variety of force. Whereas force is equal to mass multiplied by acceleration, weight is equal to mass multiplied by the acceleration due to gravity. The latter is equal to 32 ft (9.8 m)/sec2. This means that for every second that an object experiencing gravitational force continues to fall, its velocity increases at the rate of 32 ft or 9.8 m per second. Thus, the formula for weight is essentially the same as that for force, with a more specific variety of acceleration substituted for the generalized term in the equation for force. As for moment arm, this is the distance from the pivot point to the vector on which force is being applied. Moment arm is always perpendicular to the direction of force. Consider a wrench operating on a lug nut. The nut, as noted earlier, is the pivot point, and the moment arm is the distance from the lug nut to the place where the person operating the wrench has applied force. The torque that the lug nut experiences is the product of moment arm multiplied by force.
force that, when applied to 1 kg of mass, will give it an acceleration of 1 m/sec2). Hence if a person were to a grip a wrench 9 in (23 cm) from the pivot point, the moment arm would be 0.75 ft (0.23 m.) If the person then applied 50 lb (11.24 N) of force, the lug nut would be experiencing 37.5 pound-feet (2.59 N•m) of torque. The greater the amount of torque, the greater the tendency of the object to be put into rotation. In the case of a seesaw, its overall design, in particular the fact that it sits on the ground, means that its board can never undergo anything close to 360° rotation; nonetheless, the board does rotate within relatively narrow parameters. The effects of torque can be illustrated by imagining the clockwise rotational behavior of a seesaw viewed from the side, with a child sitting on the left and a teenager on the right.
In English units, torque is measured in pound-feet, whereas the metric unit is Newtonmeters, or N•m. (One newton is the amount of
Suppose the child weighs 50 lb (11.24 N) and sits 3 ft (0.91 m) from the pivot point, giving her side of the seesaw a torque of 150 pound-feet (10.28 N•m). On the other side, her teenage sister weighs 100 lb (22.48 N) and sits 6 ft (1.82 m) from the center, creating a torque of 600 poundfeet (40.91 N•m). As a result of the torque imbalance, the side holding the teenager will rotate clockwise, toward the ground, causing the child’s side to also rotate clockwise—off the ground.
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Torque
TORQUE, ALONG WITH ANGULAR MOMENTUM, IS THE LEADING FACTOR DICTATING THE MOTION OF A GYROSCOPE. HERE, A WOMAN RIDES INSIDE A GIANT GYROSCOPE AT AN AMUSEMENT PARK. (Photograph by Richard Cummins/Corbis. Reproduced by permission.)
In order for the two to balance one another
but a more likely remedy is a change in position,
and therefore, of moment arm. Since the teenager weighs exactly twice as much as the child, the moment arm on the child’s side must be exactly twice as long as that on the teenager’s.
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perfectly, the torque on each side has to be adjusted. One way would be by changing weight,
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Hence, a remedy would be for the two to switch positions with regard to the pivot point. The child would then move out an additional 3 ft (.91 m), to a distance of 6 ft (1.83 m) from the pivot, and the teenager would cut her distance from the pivot point in half, to just 3 ft (.91 m). In fact, however, any solution that gave the child a moment arm twice as long as that of the teenager would work: hence, if the teenager sat 1 ft (.3 m) from the pivot point, the child should be at 2 ft (.61 m) in order to maintain the balance, and so on. On the other hand, there are many situations in which you may be unable to increase force, but can increase moment arm. Suppose you were trying to disengage a particularly stubborn lug nut, and after applying all your force, it still would not come loose. The solution would be to increase moment arm, either by grasping the wrench further from the pivot point, or by using a longer wrench. For the same reason, on a door, the knob is placed as far as possible from the hinges. Here the hinge is the pivot point, and the door itself is the moment arm. In some situations of torque, however, moment arm may extend over “empty space,” and for this reason, the handle of a wrench is not exactly the same as its moment arm. If one applies force on the wrench at a 90°angle to the handle, then indeed handle and moment arm are identical; however, if that force were at a 45° angle, then the moment arm would be outside the handle, because moment arm and force are always perpendicular. And if one were to pull the wrench away from the lug nut, then there would be 0° difference between the direction of force and the pivot point—meaning that moment arm (and hence torque) would also be equal to zero.
Gyroscopes A gyroscope consists of a wheel-like disk, called a flywheel, mounted on an axle, which in turn is mounted on a larger ring perpendicular to the plane of the wheel itself. An outer circle on the same plane as the flywheel provides structural stability, and indeed, the gyroscope may include several such concentric rings. Its focal point, however, is the flywheel and the axle. One end of the axle is typically attached to some outside object, while the other end is left free to float.
downward, rotating it on an axis perpendicular to that of the flywheel. This should cause the gyroscope to fall over, but instead it begins to spin a third axis, a horizontal axis perpendicular both to the plane of the flywheel and to the direction of gravity. Thus, it is spinning on three axes, and as a result becomes very stable—that is, very resistant toward outside attempts to upset its balance.
Torque
This in turn makes the gyroscope a valued instrument for navigation: due to its high degree of gyroscopic inertia, it resists changes in orientation, and thus can guide a ship toward its destination. Gyroscopes, rather than magnets, are often the key element in a compass. A magnet will point to magnetic north, some distance from “true north” (that is, the North Pole.) But with a gyroscope whose axle has been aligned with true north before the flywheel is set spinning, it is possible to possess a much more accurate directional indicator. For this reason, gyroscopes are used on airplanes—particularly those flying over the poles— as well as submarines and even the Space Shuttle. Torque, along with angular momentum, is the leading factor dictating the motion of a gyroscope. Think of angular momentum as the momentum (mass multiplied by velocity) that a turning object acquires. Due to a principle known as the conservation of angular momentum, a spinning object has a tendency to reach a constant level of angular momentum, and in order to do this, the sum of the external torques acting on the system must be reduced to zero. Thus angular momentum “wants” or “needs” to cancel out torque. The “right-hand rule” can help you to understand the torque in a system such as the gyroscope. If you extend your right hand, palm downward, your fingers are analogous to the moment arm. Now if you curl your fingers downward, toward the ground, then your fingertips point in the direction of g—that is, gravitational force. At that point, your thumb (involuntarily, due to the bone structure of the hand) points in the direction of the torque vector.
Once the flywheel is set spinning, gravity has a tendency to pull the unattached end of the axle
When the gyroscope starts to spin, the vectors of angular momentum and torque are at odds with one another. Were this situation to persist, it would destabilize the gyroscope; instead, however, the two come into alignment. Using the right-hand rule, the torque vector on a gyroscope is horizontal in direction, and the vector of angular momentum eventually aligns with
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Torque
KEY TERMS A change in velocity over a given time period. ACCELERATION:
EQUILIBRIUM:
balance.
The rate at which the position
of an object changes over a given period of
The product of mass multi-
The tendency of an object in
TORQUE:
The product of moment
arm multiplied by force. VECTOR:
A quantity that possesses
motion to remain in motion, and of an
both magnitude and direction. By contrast,
object at rest to remain at rest.
a scalar quantity is one that possesses only
MASS:
A measure of inertia, indicating
magnitude, with no specific direction.
the resistance of an object to a change in its
VELOCITY:
motion—including a change in velocity.
particular direction.
MOMENT ARM:
For an object experi-
WEIGHT:
The speed of an object in a A measure of the gravitation-
encing torque, moment arm is the distance
al force on an object; the product of mass
from the pivot or balance point to the vec-
multiplied by the acceleration due to
tor on which force is being applied.
gravity.
it. To achieve this, the gyroscope experiences what is known as gyroscopic precession, pivoting along its support post in an effort to bring angular momentum into alignment with torque. Once this happens, there is no net torque on the system, and the conservation of angular momentum is in effect.
that the engine supply enough torque to keep the car running; otherwise it will stall. To allocate torque and speed appropriately, the engine may decrease or increase the number of revolutions per minute to which the rotors are subjected.
An automobile engine produces energy, which the pistons or rotor convert into torque for transmission to the wheels. Though torque is greatest at high speeds, the amount of torque needed to operate a car does not always vary proportionately with speed. At moderate speeds and on level roads, the engine does not need to provide a great deal of torque. But when the car is starting, or climbing a steep hill, it is important
Torque comes from the engine, but it has to be supplied to the transmission. In an automatic transmission, there are two principal components: the automatic gearbox and the torque converter. It is the job of the torque converter to transmit power from the flywheel of the engine to the gearbox, and it has to do so as smoothly as possible. The torque converter consists of three elements: an impeller, which is turned by the engine flywheel; a reactor that passes this motion on to a turbine; and the turbine itself, which turns the input shaft on the automatic gearbox. An infusion of oil to the converter assists the impeller and turbine in synchronizing movement, and this alignment of elements in the torque converter creates a smooth relationship between engine and gearbox. This also leads to an increase in the car’s overall torque—that is, its turning force.
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Torque in Complex Machines Torque is a factor in several complex machines such as the electric motor that—with variations—runs most household appliances. It is especially important to the operation of automobiles, playing a significant role in the engine and transmission.
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SPEED:
time.
plied by acceleration. INERTIA:
the direction of force.
A situation in which
the forces acting upon an object are in
FORCE:
Moment arm is always perpendicular to
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Torque is also important in the operation of electric motors, found in everything from vacuum cleaners and dishwashers to computer printers and videocassette recorders to subway systems and water-pumping stations. Torque in the context of electricity involves reference to a number of concepts beyond the scope of this discussion: current, conduction, magnetic field, and other topics relevant to electromagnetic force. WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991.
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Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998.
Torque
“Rotational Motion.” Physics Department, University of Guelph (Web site). (March 4, 2001). “Rotational Motion—Torque.” Lee College (Web site). (March 4, 2001). Schweiger, Peggy E. “Torque” (Web site). (March 4, 2001). “Torque and Rotational Motion” (Web site). (March 4, 2001).
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S C I E N C E O F E V E RY DAY T H I N G S real-life Physics
F LU I D M E C H A N I C S FLUID MECHANICS AERODYNAMICS BERNOULLI’S PRINCIPLE B U OYA N CY
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Fluid Mechanics
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F LU I D M E C H A N I C S
CONCEPT The term “fluid” in everyday language typically refers only to liquids, but in the realm of physics, fluid describes any gas or liquid that conforms to the shape of its container. Fluid mechanics is the study of gases and liquids at rest and in motion. This area of physics is divided into fluid statics, the study of the behavior of stationary fluids, and fluid dynamics, the study of the behavior of moving, or flowing, fluids. Fluid dynamics is further divided into hydrodynamics, or the study of water flow, and aerodynamics, the study of airflow. Applications of fluid mechanics include a variety of machines, ranging from the waterwheel to the airplane. In addition, the study of fluids provides an understanding of a number of everyday phenomena, such as why an open window and door together create a draft in a room.
HOW IT WORKS The Contrast Between Fluids and Solids To understand fluids, it is best to begin by contrasting their behavior with that of solids. Whereas solids possess a definite volume and a definite shape, these physical characteristics are not so clearly defined for fluids. Liquids, though they possess a definite volume, have no definite shape—a factor noted above as one of the defining characteristics of fluids. As for gases, they have neither a definite shape nor a definite volume.
reduce the size or volume of an object. A solid is highly noncompressible, meaning that it resists compression, and if compressed with a sufficient force, its mechanical properties alter significantly. For example, if one places a drinking glass in a vise, it will resist a small amount of pressure, but a slight increase will cause the glass to break. Fluids vary with regard to compressibility, depending on whether the fluid in question is a liquid or a gas. Most gases tend to be highly compressible—though air, at low speeds at least, is not among them. Thus, gases such as propane fuel can be placed under high pressure. Liquids tend to be noncompressible: unlike a gas, a liquid can be compressed significantly, yet its response to compression is quite different from that of a solid—a fact illustrated below in the discussion of hydraulic presses. One way to describe a fluid is “anything that flows”—a behavior explained in large part by the interaction of molecules in fluids. If the surface of a solid is disturbed, it will resist, and if the force of the disturbance is sufficiently strong, it will deform—as for instance, when a steel plate begins to bend under pressure. This deformation will be permanent if the force is powerful enough, as was the case in the above example of the glass in a vise. By contrast, when the surface of a liquid is disturbed, it tends to flow. M O L E C U LA R B E H AV I O R O F F LU I D S A N D S O L I D S . At the molecu-
One of several factors that distinguishes fluids from solids is their response to compression, or the application of pressure in such a way as to
lar level, particles of solids tend to be definite in their arrangement and close to one another. In the case of liquids, molecules are close in proximity, though not as much so as solid molecules, and the arrangement is random. Thus, with a glass of water, the molecules of glass (which at
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Fluid Mechanics
IN
A WIDE, UNCONSTRICTED REGION, A RIVER FLOWS SLOWLY.
WALLS, AS WITH
WYOMING’S BIGHORN RIVER,
HOWEVER,
IF ITS FLOW IS NARROWED BY CANYON
THEN IT SPEEDS UP DRAMATICALLY. (Photograph by Kevin R. Morris/Corbis.
Reproduced by permission.)
relatively low temperatures is a solid) in the container are fixed in place while the molecules of water contained by the glass are not. If one portion of the glass were moved to another place on the glass, this would change its structure. On the other hand, no significant alteration occurs in the character of the water if one portion of it is moved to another place within the entire volume of water in the glass. As for gas molecules, these are both random in arrangement and far removed in proximity. Whereas solid particles are slow-moving and have a strong attraction to one another, liquid molecules move at moderate speeds and exert a moderate attraction on each other. Gas molecules are extremely fast-moving and exert little or no attraction. Thus, if a solid is released from a container pointed downward, so that the force of gravity moves it, it will fall as one piece. Upon hitting a floor or other surface, it will either rebound, come to a stop, or deform permanently. A liquid, on the other hand, will disperse in response to impact, its force determining the area over which the total volume of liquid is distributed. But for a gas, assuming it is lighter than air, the downward pull of gravity is not even required to disperse it: 96
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once the top on a container of gas is released, the molecules begin to float outward.
Fluids Under Pressure As suggested earlier, the response of fluids to pressure is one of the most significant aspects of fluid behavior and plays an important role within both the statics and dynamics subdisciplines of fluid mechanics. A number of interesting principles describe the response to pressure, on the part of both fluids at rest inside a container, and fluids which are in a state of flow. Within the realm of hydrostatics, among the most important of all statements describing the behavior of fluids is Pascal’s principle. This law is named after Blaise Pascal (1623-1662), a French mathematician and physicist who discovered that the external pressure applied on a fluid is transmitted uniformly throughout its entire body. The understanding offered by Pascal’s principle later became the basis for one of the most important machines ever developed, the hydraulic press. HYDROSTATIC PRESSURE AND BUOYANCY. Some nineteen centuries before
Pascal, the Greek mathematician, physicist, and inventor Archimedes (c. 287-212 B.C.) discovered a precept of fluid statics that had implications at S C I E N C E O F E V E RY DAY T H I N G S
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least as great as those of Pascal’s principle. This was Archimedes’s principle, which explains the buoyancy of an object immersed in fluid. According to Archimedes’s principle, the buoyant force exerted on the object is equal to the weight of the fluid it displaces.
pressure and velocity are inversely related—in other words, as one increases, the other decreases. Hence, he formulated Bernoulli’s principle, which states that for all changes in movement, the sum of static and dynamic pressure in a fluid remains the same.
Buoyancy explains both how a ship floats on water, and how a balloon floats in the air. The pressures of water at the bottom of the ocean, and of air at the surface of Earth, are both examples of hydrostatic pressure—the pressure that exists at any place in a body of fluid due to the weight of the fluid above. In the case of air pressure, air is pulled downward by the force of Earth’s gravitation, and air along the planet’s surface has greater pressure due to the weight of the air above it. At great heights above Earth’s surface, however, the gravitational force is diminished, and thus the air pressure is much smaller.
A fluid at rest exerts pressure—what Bernoulli called “static pressure”—on its container. As the fluid begins to move, however, a portion of the static pressure—proportional to the speed of the fluid—is converted to what Bernoulli called dynamic pressure, or the pressure of movement. In a cylindrical pipe, static pressure is exerted perpendicular to the surface of the container, whereas dynamic pressure is parallel to it.
Water, too, is pulled downward by gravity, and as with air, the fluid at the bottom of the ocean has much greater pressure due to the weight of the fluid above it. Of course, water is much heavier than air, and therefore, water at even a moderate depth in the ocean has enormous pressure. This pressure, in turn, creates a buoyant force that pushes upward. If an object immersed in fluid—a balloon in the air, or a ship on the ocean—weighs less that the fluid it displaces, it will float. If it weighs more, it will sink or fall. The balloon itself may be “heavier than air,” but it is not as heavy as the air it has displaced. Similarly, an aircraft carrier contains a vast weight in steel and other material, yet it floats, because its weight is not as great as that of the displaced water. B E R N O U L L I ’ S P R I N C I P L E . Archimedes and Pascal contributed greatly to what became known as fluid statics, but the father of fluid mechanics, as a larger realm of study, was the Swiss mathematician and physicist Daniel Bernoulli (1700-1782). While conducting experiments with liquids, Bernoulli observed that when the diameter of a pipe is reduced, the water flows faster. This suggested to him that some force must be acting upon the water, a force that he reasoned must arise from differences in pressure.
Fluid Mechanics
According to Bernoulli’s principle, the greater the velocity of flow in a fluid, the greater the dynamic pressure and the less the static pressure. In other words, slower-moving fluid exerts greater pressure than faster-moving fluid. The discovery of this principle ultimately made possible the development of the airplane.
REAL-LIFE A P P L I C AT I O N S Bernoulli’s Principle in Action As fluid moves from a wider pipe to a narrower one, the volume of the fluid that moves a given distance in a given time period does not change. But since the width of the narrower pipe is smaller, the fluid must move faster (that is, with greater dynamic pressure) in order to move the same amount of fluid the same distance in the same amount of time. Observe the behavior of a river: in a wide, unconstricted region, it flows slowly, but if its flow is narrowed by canyon walls, it speeds up dramatically.
Specifically, the slower-moving fluid in the wider area of pipe had a greater pressure than the portion of the fluid moving through the narrower part of the pipe. As a result, he concluded that
Bernoulli’s principle ultimately became the basis for the airfoil, the design of an airplane’s wing when seen from the end. An airfoil is shaped like an asymmetrical teardrop laid on its side, with the “fat” end toward the airflow. As air hits the front of the airfoil, the airstream divides, part of it passing over the wing and part passing under. The upper surface of the airfoil is curved, however, whereas the lower surface is much straighter.
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As a result, the air flowing over the top has a greater distance to cover than the air flowing under the wing. Since fluids have a tendency to compensate for all objects with which they come into contact, the air at the top will flow faster to meet the other portion of the airstream, the air flowing past the bottom of the wing, when both reach the rear end of the airfoil. Faster airflow, as demonstrated by Bernoulli, indicates lower pressure, meaning that the pressure on the bottom of the wing keeps the airplane aloft. C R E AT I N G A D RA F T. Among the most famous applications of Bernoulli’s principle is its use in aerodynamics, and this is discussed in the context of aerodynamics itself elsewhere in this book. Likewise, a number of other applications of Bernoulli’s principle are examined in an essay devoted to that topic. Bernoulli’s principle, for instance, explains why a shower curtain tends to billow inward when the water is turned on; in addition, it shows why an open window and door together create a draft.
Suppose one is in a hotel room where the heat is on too high, and there is no way to adjust the thermostat. Outside, however, the air is cold, and thus, by opening a window, one can presumably cool down the room. But if one opens the window without opening the front door of the room, there will be little temperature change. The only way to cool off will be by standing next to the window: elsewhere in the room, the air will be every bit as stuffy as before. But if the door leading to the hotel hallway is opened, a nice cool breeze will blow through the room. Why? With the door closed, the room constitutes an area of relatively high pressure compared to the pressure of the air outside the window. Because air is a fluid, it will tend to flow into the room, but once the pressure inside reaches a certain point, it will prevent additional air from entering. The tendency of fluids is to move from high-pressure to low-pressure areas, not the other way around. As soon as the door is opened, the relatively high-pressure air of the room flows into the relatively low-pressure area of the hallway. As a result, the air pressure in the room is reduced, and the air from outside can now enter. Soon a wind will begin to blow through the room.
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chamber built for the purpose of examining the characteristics of airflow in contact with solid objects, such as aircraft and automobiles. The wind tunnel represents a safe and judicious use of the properties of fluid mechanics. Its purpose is to test the interaction of airflow and solids in relative motion: in other words, either the aircraft has to be moving against the airflow, as it does in flight, or the airflow can be moving against a stationary aircraft. The first of these choices, of course, poses a number of dangers; on the other hand, there is little danger in exposing a stationary craft to winds at speeds simulating that of the aircraft in flight. The first wind tunnel was built in England in 1871, and years later, aircraft pioneers Orville (1871-1948) and Wilbur (1867-1912) Wright used a wind tunnel to improve their planes. By the late 1930s, the U.S. National Advisory Committee for Aeronautics (NACA) was building wind tunnels capable of creating speeds equal to 300 MPH (480 km/h); but wind tunnels built after World War II made these look primitive. With the development of jet-powered flight, it became necessary to build wind tunnels capable of simulating winds at the speed of sound—760 MPH (340 m/s). By the 1950s, wind tunnels were being used to simulate hypersonic speeds—that is, speeds of Mach 5 (five times the speed of sound) and above. Researchers today use helium to create wind blasts at speeds up to Mach 50.
Fluid Mechanics for Performing Work H Y D RAU L I C P R E SS E S . Though
applications of Bernoulli’s principle are among the most dramatic examples of fluid mechanics in operation, the everyday world is filled with instances of other ideas at work. Pascal’s principle, for instance, can be seen in the operation of any number of machines that represent variations on the idea of a hydraulic press. Among these is the hydraulic jack used to raise a car off the floor of an auto mechanic’s shop.
A W I N D T U N N E L . The above scenario of wind flowing through a room describes a rudimentary wind tunnel. A wind tunnel is a
Beneath the floor of the shop is a chamber containing a quantity of fluid, and at either end of the chamber are two large cylinders side by side. Each cylinder holds a piston, and valves control flow between the two cylinders through the channel of fluid that connects them. In accordance with Pascal’s principle, when one applies force by pressing down the piston in one cylinder
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(the input cylinder), this yields a uniform pressure that causes output in the second cylinder, pushing up a piston that raises the car.
Fluid Mechanics
Another example of a hydraulic press is the hydraulic ram, which can be found in machines ranging from bulldozers to the hydraulic lifts used by firefighters and utility workers to reach heights. In a hydraulic ram, however, the characteristics of the input and output cylinders are reversed from those of a car jack. For the car jack, the input cylinder is long and narrow, while the output cylinder is wide and short. This is because the purpose of a car jack is to raise a heavy object through a relatively short vertical range of movement—just high enough so that the mechanic can stand comfortably underneath the car. In the hydraulic ram, the input or master cylinder is short and squat, while the output or slave cylinder is tall and narrow. This is because the hydraulic ram, in contrast to the car jack, carries a much lighter cargo (usually just one person) through a much greater vertical range—for instance, to the top of a tree or building. PU M P S . A pump is a device made for
moving fluid, and it does so by utilizing a pressure difference, causing the fluid to move from an area of higher pressure to one of lower pressure. Its operation is based on aspects both of Pascal’s and Bernoulli’s principles—though, of course, humans were using pumps thousands of years before either man was born. A siphon hose used to draw gas from a car’s fuel tank is a very simple pump. Sucking on one end of the hose creates an area of low pressure compared to the relatively high-pressure area of the gas tank. Eventually, the gasoline will come out of the low-pressure end of the hose. The piston pump, slightly more complex, consists of a vertical cylinder along which a piston rises and falls. Near the bottom of the cylinder are two valves, an inlet valve through which fluid flows into the cylinder, and an outlet valve through which fluid flows out. As the piston moves upward, the inlet valve opens and allows fluid to enter the cylinder. On the downstroke, the inlet valve closes while the outlet valve opens, and the pressure provided by the piston forces the fluid through the outlet valve.
PUMPS
FOR
GROUND
DRAWING
ARE
USABLE
UNDOUBTEDLY
WATER
THE
FROM
OLDEST
THE
PUMPS
KNOWN. (Photograph by Richard Cummins/Corbis. Reproduced by
permission.)
by providing a series of controlled explosions created by the spark plug’s ignition of the gas. In another variety of piston pump—the kind used to inflate a basketball or a bicycle tire—air is the fluid being pumped. Then there is a pump for water. Pumps for drawing usable water from the ground are undoubtedly the oldest known variety, but there are also pumps designed to remove water from areas where it is undesirable; for example, a bilge pump, for removing water from a boat, or the sump pump used to pump flood water out of a basement.
One of the most obvious applications of the piston pump is in the engine of an automobile. In this case, of course, the fluid being pumped is gasoline, which pushes the pistons up and down
F LU I D P O W E R. For several thousand years, humans have used fluids—in particular water—to power a number of devices. One of the great engineering achievements of ancient times was the development of the waterwheel, which included a series of buckets along the rim that made it possible to raise water from the river below and disperse it to other points. By about 70 B.C., Roman engineers recognized that they could use the power of water itself to turn wheels and grind grain. Thus, the waterwheel became one of the first mechanisms in which an inanimate
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Fluid Mechanics
KEY TERMS An area of fluid
AERODYNAMICS:
dynamics devoted to studying the proper-
fluid mechanics are fluid statics and fluid dynamics.
ties and characteristics of airflow.
An area of fluid
FLUID STATICS:
A rule
ARCHIMEDES’S PRINCIPLE:
of physics stating that the buoyant force of
mechanics devoted to studying the behavior of stationary fluids.
an object immersed in fluid is equal to the weight of the fluid displaced by the object.
An area of fluid
It is named after the Greek mathematician,
dynamics devoted to studying the proper-
physicist, and inventor, Archimedes (c.
ties and characteristics of water flow.
287-212 B.C.), who first identified it.
HYDROSTATIC
BERNOULLI’S PRINCIPLE:
A prop-
osition, credited to Swiss mathematician and physicist Daniel Bernoulli (17001782), which maintains that slower-moving fluid exerts greater pressure than fastermoving fluid. BUOYANCY:
explained by Archimedes’s principle. COMPRESSION:
To reduce in size or
volume by applying pressure. FLUID:
PRESSURE:
The
pressure that exists at any place in a body of fluid due to the weight of the fluid above. PASCAL’S PRINCIPLE:
A statement,
formulated by French mathematician and physicist Blaise Pascal (1623-1662), which holds that the external pressure applied on
The tendency of an object
immersed in a fluid to float. This can be
a fluid is transmitted uniformly throughout the entire body of that fluid. PRESSURE:
The ratio of force to sur-
face area, when force is applied in a direction perpendicular to that surface.
Any substance, whether gas or A machine that converts the
liquid, that conforms to the shape of its
TURBINE:
container.
kinetic energy (the energy of movement)
FLUID DYNAMICS:
An area of fluid
mechanics devoted to studying of the behavior of moving, or flowing, fluids.
in fluids to useable mechanical energy by passing the stream of fluid through a series of fixed and moving fans or blades.
Fluid dynamics is further divided into
WIND TUNNEL:
hydrodynamics and aerodynamics.
the purpose of examining the characteris-
A chamber built for
The study of
tics of airflow in relative motion against
the behavior of gases and liquids at rest
solid objects such as aircraft and auto-
and in motion. The major divisions of
mobiles.
FLUID MECHANICS:
The water clock, too, was another ingenious use of water developed by the ancients. It did not use water for power; rather, it relied on gravity— a concept only dimly understood by ancient peo-
ples—to move water from one chamber of the clock to another, thus, marking a specific interval of time. The earliest clocks were sundials, which were effective for measuring time, provided the Sun was shining, but which were less useful for measuring periods shorter than an hour. Hence,
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source (as opposed to the effort of humans or animals) created power.
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the development of the hourglass, which used sand, a solid that in larger quantities exhibits the behavior of a fluid. Then, in about 270 B.C., Ctesibius of Alexandria (fl. c. 270-250 B.C.) used gearwheel technology to devise a constant-flow water clock called a “clepsydra.” Use of water clocks prevailed for more than a thousand years, until the advent of the first mechanical clocks. During the medieval period, fluids provided power to windmills and water mills, and at the dawn of the Industrial Age, engineers began applying fluid principles to a number of sophisticated machines. Among these was the turbine, a machine that converts the kinetic energy (the energy of movement) in fluids to useable mechanical energy by passing the stream of fluid through a series of fixed and moving fans or blades. A common house fan is an example of a turbine in reverse: the fan adds energy to the passing fluid (air), whereas a turbine extracts energy from fluids such as air and water. The turbine was developed in the mid-eighteenth century, and later it was applied to the extraction of power from hydroelectric dams, the first of which was constructed in 1894. Today, hydroelectric dams provide electric power to millions of homes around the world. Among the most dramatic examples of fluid mechanics in action, hydroelectric dams are vast in size and equally impressive in the power they can generate using a completely renewable resource: water. A hydroelectric dam forms a huge steel-andconcrete curtain that holds back millions of tons of water from a river or other body. The water
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nearest the top—the “head” of the dam—has enormous potential energy, or the energy that an object possesses by virtue of its position. Hydroelectric power is created by allowing controlled streams of this water to flow downward, gathering kinetic energy that is then transferred to powering turbines, which in turn generate electric power.
Fluid Mechanics
WHERE TO LEARN MORE Aerodynamics for Students (Web site). (April 8, 2001). Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Chahrour, Janet. Flash! Bang! Pop! Fizz!: Exciting Science for Curious Minds. Illustrated by Ann Humphrey Williams. Hauppauge, N.Y.: Barron’s, 2000. “Educational Fluid Mechanics Sites.” Virginia Institute of Technology (Web site). (April 8, 2001). Fleisher, Paul. Liquids and Gases: Principles of Fluid Mechanics. Minneapolis, MN: Lerner Publications, 2002. Institute of Fluid Mechanics (Web site). (April 8, 2001). K8AIT Principles of Aeronautics Advanced Text (web site). (February 19, 2001). Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998. Sobey, Edwin J. C. Wacky Water Fun with Science: Science You Can Float, Sink, Squirt, and Sail. Illustrated by Bill Burg. New York: McGraw-Hill, 2000. Wood, Robert W. Mechanics Fundamentals. Illustrated by Bill Wright. Philadelphia: Chelsea House, 1997.
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AERODYNAMICS Aerodynamics
CONCEPT Though the term “aerodynamics” is most commonly associated with airplanes and the overall science of flight, in fact, its application is much broader. Simply put, aerodynamics is the study of airflow and its principles, and applied aerodynamics is the science of improving manmade objects such as airplanes and automobiles in light of those principles. Aside from the obvious application to these heavy forms of transportation, aerodynamic concepts are also reflected in the simplest of manmade flying objects—and in the natural model for all studies of flight, a bird’s wings.
HOW IT WORKS All physical objects on Earth are subject to gravity, but gravity is not the only force that tends to keep them pressed to the ground. The air itself, though it is invisible, operates in such a way as to prevent lift, much as a stone dropped into the water will eventually fall to the bottom. In fact, air behaves much like water, though the downward force is not as great due to the fact that air’s pressure is much less than that of water. Yet both are media through which bodies travel, and air and water have much more in common with one another than either does with a vacuum. Liquids such as water and gasses such as air are both subject to the principles of fluid dynamics, a set of laws that govern the motion of liquids and vapors when they come in contact with solid surfaces. In fact, there are few significant differences—for the purposes of the present discussion—between water and air with regard to their behavior in contact with solid surfaces.
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When a person gets into a bathtub, the water level rises uniformly in response to the fact that a solid object is taking up space. Similarly, air currents blow over the wings of a flying aircraft in such a way that they meet again more or less simultaneously at the trailing edge of the wing. In both cases, the medium adjusts for the intrusion of a solid object. Hence within the parameters of fluid dynamics, scientists typically use the term “fluid” uniformly, even when describing the movement of air. The study of fluid dynamics in general, and of air flow in particular, brings with it an entire vocabulary. One of the first concepts of importance is viscosity, the internal friction in a fluid that makes it resistant to flow and resistant to objects flowing through it. As one might suspect, viscosity is a far greater factor with water than with air, the viscosity of which is less than two percent that of water. Nonetheless, near a solid surface—for example, the wing of an airplane— viscosity becomes a factor because air tends to stick to that surface. Also significant are the related aspects of density and compressibility. At speeds below 220 MPH (354 km/h), the compressibility of air is not a significant factor in aerodynamic design. However, as air flow approaches the speed of sound—660 MPH (1,622 km/h)—compressibility becomes a significant factor. Likewise temperature increases greatly when airflow is supersonic, or faster than the speed of sound. All objects in the air are subject to two types of airflow, laminar and turbulent. Laminar flow is smooth and regular, always moving at the same speed and in the same direction. This type of airflow is also known as streamlined flow, and under these conditions every particle of fluid that
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passes a particular point follows a path identical to all particles that passed that point earlier. This may be illustrated by imagining a stream flowing around a twig.
Aerodynamics
By contrast, in turbulent flow the air is subject to continual changes in speed and direction—as for instance when a stream flows over shoals of rocks. Whereas the mathematical model of laminar airflow is rather straightforward, conditions are much more complex in turbulent flow, which typically occurs in the presence either of obstacles or of high speeds. Absent the presence of viscosity, and thus in conditions of perfect laminar flow, an object behaves according to Bernoulli’s principle, sometimes known as Bernoulli’s equation. Named after the Swiss mathematician and physicist Daniel Bernoulli (1700-1782), this proposition goes to the heart of that which makes an airplane fly. While conducting experiments concerning the conservation of energy in liquids, Bernoulli observed that when the diameter of a pipe is reduced, the water flows faster. This suggested to him that some force must be acting upon the water, a force that he reasoned must arise from differences in pressure. Specifically, the slowermoving fluid had a greater pressure than the portion of the fluid moving through the narrower part of the pipe. As a result, he concluded that pressure and velocity are inversely related. Bernoulli’s principle states that for all changes in movement, the sum of static and dynamic pressure in a fluid remain the same. A fluid at rest exerts static pressure, which is the same as what people commonly mean when they say “pressure,” as in “water pressure.” As the fluid begins to move, however, a portion of the static pressure—proportional to the speed of the fluid—is converted to what scientists call dynamic pressure, or the pressure of movement. The greater the speed, the greater the dynamic pressure and the less the static pressure. Bernoulli’s findings would prove crucial to the design of aircraft in the twentieth century, as engineers learned how to use currents of faster and slower air for keeping an airplane aloft. Very close to the surface of an object experiencing airflow, however, the presence of viscosity plays havoc with the neat proportions of the Bernoulli’s principle. Here the air sticks to the object’s surface, slowing the flow of nearby air and creating a “boundary layer” of slow-moving
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A
TYPICAL PAPER AIRPLANE HAS LOW ASPECT RATIO
WINGS, A TERM THAT REFERS TO THE SIZE OF THE WINGSPAN COMPARED TO THE CHORD.
IN
SUBSONIC
FLIGHT, HIGHER ASPECT RATIOS ARE USUALLY PREFERRED. (Photograph by Bruce Burkhardt/Corbis. Reproduced by per-
mission.)
air. At the beginning of the flow—for instance, at the leading edge of an airplane’s wing—this boundary layer describes a laminar flow; but the width of the layer increases as the air moves along the surface, and at some point it becomes turbulent. These and a number of other factors contribute to the coefficients of drag and lift. Simply put, drag is the force that opposes the forward motion of an object in airflow, whereas lift is a force perpendicular to the direction of the wind, which keeps the object aloft. Clearly these concepts can be readily applied to the operation of an airplane, but they also apply in the case of an automobile, as will be shown later.
REAL-LIFE A P P L I C AT I O N S How a Bird Flies—and Why a Human Being Cannot Birds are exquisitely designed (or adapted) for flight, and not simply because of the obvious fact
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Aerodynamics
BIRDS
LIKE THESE FAIRY TERNS ARE SUPREME EXAMPLES OF AERODYNAMIC PRINCIPLES, FROM THEIR LOW BODY
WEIGHT AND LARGE STERNUM AND PECTORALIS MUSCLES TO THEIR LIGHTWEIGHT FEATHERS. (Corbis. Reproduced by per-
mission.)
that they have wings. Thanks to light, hollow bones, their body weight is relatively low, giving them the advantage in overcoming gravity and remaining aloft. Furthermore, a bird’s sternum or breast bone, as well as its pectoralis muscles (those around the chest) are enormous in proportion to its body size, thus helping it to achieve the thrust necessary for flight. And finally, the bird’s lightweight feathers help to provide optimal lift and minimal drag. A bird’s wing is curved along the top, a crucial aspect of its construction. As air passes over the leading edge of the wing, it divides, and because of the curve, the air on top must travel a greater distance before meeting the air that flowed across the bottom. The tendency of airflow, as noted earlier, is to correct for the presence of solid objects. Therefore, in the absence of outside factors such as viscosity, the air on top “tries” to travel over the wing in the same amount of time that it takes the air below to travel under the wing. As shown by Bernoulli, the fast-moving air above the wing exerts less pressure than the slowmoving air below it; hence there is a difference in pressure between the air below and the air above, and this keeps the wing aloft.
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When a bird beats its wings, its downstrokes propel it, and as it rises above the ground, the force of aerodynamic lift helps push its wings upward in preparation for the next downstroke. However, to reduce aerodynamic drag during the upstroke, the bird folds its wings, thus decreasing its wingspan. Another trick that birds execute instinctively is the moving of their wings forward and backward in order to provide balance. They also “know” how to flap their wings in a direction almost parallel to the ground when they need to fly slowly or hover. Witnessing the astonishing aerodynamic feats of birds, humans sought the elusive goal of flight from the earliest of times. This was symbolized by the Greek myth of Icarus and Daedalus, who escaped from a prison in Crete by constructing a set of bird-like wings and flying away. In the world of physical reality, however, the goal would turn out to be unattainable as long as humans attempted to achieve flight by imitating birds. As noted earlier, a bird’s physiology is quite different from that of a human being. There is simply no way that a human can fly by flapping his arms—nor will there ever be a man strong enough to do so, no matter how apparently well-
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designed his mechanical wings are. Indeed, to be capable of flying like a bird, a man would have to have a chest so enormous in proportion to his body that he would be hideous in appearance. Not realizing this, humans for centuries attempted to fly like birds—with disastrous results. An English monk named Eilmer (b. 980) attempted to fly off the tower of Malmesbury Abbey with a set of wings attached to his arms and feet. Apparently Eilmer panicked after gliding some 600 ft (about 200 m) and suddenly plummeted to earth, breaking both of his legs. At least he lived; more tragic was the case of Abul Qasim Ibn Firnas (d. 873), an inventor from Cordoba in Arab Spain who devised and demonstrated a glider. Much of Cordoba’s population came out to see him demonstrate his flying machine, but after covering just a short distance, the craft fell to earth. Severely wounded, Ibn Firnas died shortly afterward. The first real progress in the development of flying machines came when designers stopped trying to imitate birds and instead used the principle of buoyancy. Hence in 1783, the French brothers Jacques-Etienne and Joseph-Michel Montgolfier constructed the first practical balloon. Balloons and their twentieth-century descendant, the dirigible, had a number of obvious drawbacks, however. Without a motor, a balloon could not be guided, and even with a motor, dirigibles proved highly dangerous. At that stage, most dirigibles used hydrogen, a gas that is cheap and plentiful, but extremely flammable. After the Hindenburg exploded in 1937, the age of passenger travel aboard airships was over. However, the German military continued to use dirigibles for observation purposes, as did the United States forces in World War II. Today airships, the most famous example being the Goodyear Blimp, are used not only for observation but for advertising. Scientists working in rain forests, for instance, use dirigibles to glide above the forest canopy; as for the Goodyear Blimp, it provides television networks with “eye in the sky” views of large sporting events. The first man to make a serious attempt at creating a heavier-than-air flying machine (as opposed to a balloon, which uses gases that are lighter than air) was Sir George Cayley (17731857), who in 1853 constructed a glider. It is interesting to note that in creating this, the foreS C I E N C E O F E V E RY DAY T H I N G S
runner of the modern airplane, Cayley went back to an old model: the bird. After studying the physics of birds’ flight for many years, he equipped his glider with an extremely wide wingspan, used the lightest possible materials in its construction, and designed it with exceptionally smooth surfaces to reduce drag.
Aerodynamics
The only thing that in principle differentiated Cayley’s craft from a modern airplane was its lack of an engine. In those days, the only possible source of power was a steam engine, which would have added far too much weight to his aircraft. However, the development of the internalcombustion engine in the nineteenth century overcame that obstacle, and in 1903 Orville and Wilbur Wright achieved the dream of flight that had intrigued and eluded human beings for centuries.
Airplanes: Getting Aloft, Staying Aloft, and Remaining Stable Once engineers and pilots took to the air, they encountered a number of factors that affect flight. In getting aloft and staying aloft, an aircraft is subject to weight, lift, drag, and thrust. As noted earlier, the design of an airplane wing takes advantage of Bernoulli’s principle to give it lift. Seen from the end, the wing has the shape of a long teardrop lying on its side, with the large end forward, in the direction of airflow, and the narrow tip pointing toward the rear. (Unlike a teardrop, however, an airplane’s wing is asymmetrical, and the bottom side is flat.) This cross-section is known as an airfoil, and the greater curvature of its upper surface in comparison to the lower side is referred to as the airplane’s camber. The front end of the airfoil is also curved, and the chord line is an imaginary straight line connecting the spot where the air hits the front—known as the stagnation point— to the rear, or trailing edge, of the wing. Again in accordance with Bernoulli’s principle, the shape of the airflow facilitates the spread of laminar flow around it. The slower-moving currents beneath the airfoil exert greater pressure than the faster currents above it, giving lift to the aircraft. Another parameter influencing the lift coefficient (that is, the degree to which the aircraft experiences lift) is the size of the wing: the longer the wing, the greater the total force exerted VOLUME 2: REAL-LIFE PHYSICS
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beneath it, and the greater the ratio of this pressure to that of the air above. The size of a modern aircraft’s wing is actually somewhat variable, due to the presence of flaps at the trailing edge. With regard to the flaps, however, it should be noted that they have different properties at different stages of flight: in takeoff, they provide lift, but in stable flight they increase drag, and for that reason the pilot retracts them. In preparing for landing, as the aircraft slows and descends, the extended flaps then provide stability and assist in the decrease of speed. Speed, too, encourages lift: the faster the craft, the faster the air moves over the wing. The pilot affects this by increasing or decreasing the power of the engine, thus regulating the speed with which the plane’s propellers turn. Another highly significant component of lift is the airfoil’s angle of attack—the orientation of the airfoil with regard to the air flow, or the angle that the chord line forms with the direction of the air stream. Up to a point, increasing the angle of attack provides the aircraft with extra lift because it moves the stagnation point from the leading edge down along the lower surface; this increases the low-pressure area of the upper surface. However, if the pilot increases the angle of attack too much, this affects the boundary layer of slowmoving air, causing the aircraft to go into a stall. Together the engine provides the propellers with power, and this gives the aircraft thrust, or propulsive force. In fact, the propeller blades constitute miniature wings, pivoted at the center and powered by the engine to provide rotational motion. As with the wings of the aircraft, the blades have a convex forward surface and a narrow trailing edge. Also like the aircraft wings, their angle of attack (or pitch) is adjusted at different points for differing effects. In stable flight, the pilot increases the angle of attack for the propeller blades sharply as against airflow, whereas at takeoff and landing the pitch is dramatically reduced. During landing, in fact, the pilot actually reverses the direction of the propeller blades, turning them into a brake on the aircraft’s forward motion—and producing that lurching sensation that a passenger experiences as the aircraft slows after touching down.
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preparing to land—drag. This apparent inconsistency results from the fact that the characteristics of air flow change drastically from situation to situation, and in fact, air never behaves as perfectly as it does in a textbook illustration of Bernoulli’s principle. Not only is the aircraft subject to air viscosity—the air’s own friction with itself—it also experiences friction drag, which results from the fact that no solid can move through a fluid without experiencing a retarding force. An even greater drag factor, accounting for one-third of that which an aircraft experiences, is induced drag. The latter results because air does not flow in perfect laminar streams over the airfoil; rather, it forms turbulent eddies and currents that act against the forward movement of the plane. In the air, an aircraft experiences forces that tend to destabilize flight in each of three dimensions. Pitch is the tendency to rotate forward or backward; yaw, the tendency to rotate on a horizontal plane; and roll, the tendency to rotate vertically on the axis of its fuselage. Obviously, each of these is a terrifying prospect, but fortunately, pilots have a solution for each. To prevent pitching, they adjust the angle of attack of the horizontal tail at the rear of the craft. The vertical rear tail plays a part in preventing yawing, and to prevent rolling, the pilot raises the tips of the main wings so that the craft assumes a V-shape when seen from the front or back. The above factors of lift, drag, thrust, and weight, as well as the three types of possible destabilization, affect all forms of heavier-thanair flying machines. But since the 1944 advent of jet engines, which travel much faster than pistondriven engines, planes have flown faster and faster, and today some craft such as the Concorde are capable of supersonic flight. In these situations, air compressibility becomes a significant issue.
By this point there have been several examples regarding the use of the same technique alternately to provide lift or—when slowing or
Sound is transmitted by the successive compression and expansion of air. But when a plane is traveling at above Mach 1.2—the Mach number indicates the speed of an aircraft in relation to the speed of sound—there is a significant discrepancy between the speed at which sound is traveling away from the craft, and the speed at which the craft is moving away from the sound. Eventually the compressed sound waves build up, resulting in a shock wave.
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Down on the ground, the shock wave manifests as a “sonic boom”; meanwhile, for the aircraft, it can cause sudden changes in pressure, density, and temperature, as well as an increase in drag and a loss of stability. To counteract this effect, designers of supersonic and hypersonic (Mach 5 and above) aircraft are altering wing design, using a much narrower airfoil and sweptback wings. One of the pioneers in this area is Richard Whitcomb of the National Aeronautics and Space Administration (NASA). Whitcomb has designed a supercritical airfoil for a proposed hypersonic plane, which would ascend into outer space in the course of a two-hour flight—all the time needed for it to travel from Washington, D.C., to Tokyo, Japan. Before the craft can become operational, however, researchers will have to figure out ways to control temperatures and keep the plane from bursting into flame as it reenters the atmosphere. Much of the research for improving the aerodynamic qualities of such aircraft takes place in wind tunnels. First developed in 1871, these use powerful fans to create strong air currents, and over the years the top speed in wind tunnels has been increased to accommodate testing on supersonic and hypersonic aircraft. Researchers today use helium to create wind blasts at speeds up to Mach 50.
Thrown and Flown: The Aerodynamics of Small Objects Long before engineers began to dream of sending planes into space for transoceanic flight—about 14,000 years ago, in fact—many of the features that make an airplane fly were already present in the boomerang. It might seem backward to move from a hypersonic jet to a boomerang, but in fact, it is easier to appreciate the aerodynamics of small objects, including the kite and even the paper airplane, once one comprehends the larger picture.
intelligent than Europeans. In fact, as Diamond showed, an individual would actually have to be smarter to figure out how to survive on the limited range of plants and animals available in Australia prior to the introduction of Eurasian flora and fauna. Hence the wonder of the boomerang, one of the most ingenious inventions ever fashioned by humans in a “primitive” state.
Aerodynamics
Thousands of years before Bernoulli, the boomerang’s designers created an airfoil consistent with Bernoulli’s principle. The air below exerts more pressure than the air above, and this, combined with the factors of gyroscopic stability and gyroscopic precession, gives the boomerang flight. Gyroscopic stability can be illustrated by spinning a top: the action of spinning itself keeps the top stable. Gyroscopic precession is a much more complex process: simply put, the leading wing of the boomerang—the forward or upward edge as it spins through the air—creates more lift than the other wing. At this point it should be noted that, contrary to the popular image, a boomerang travels on a plane perpendicular to that of the ground, not parallel. Hence any thrower who knows what he or she is doing tosses the boomerang not with a side-arm throw, but overhand. And of course a boomerang does not just sail through the air; a skilled thrower can make it come back as if by magic. This is because the force of the increased lift that it experiences in flight, combined with gyroscopic precession, turns it around. As noted earlier, in different situations the same force that creates lift can create drag, and as the boomerang spins downward the increasing drag slows it. Certainly it takes great skill for a thrower to make a boomerang come back, and for this reason, participants in boomerang competitions often attach devices such as flaps to increase drag on the return cycle.
There is a certain delicious irony in the fact that the first manmade object to take flight was constructed by people who never advanced beyond the Stone Age until the nineteenth century, when the Europeans arrived in Australia. As the ethnobotanist Jared Diamond showed in his groundbreaking work Guns, Germs, and Steel: The Fates of Human Societies (1997), this was not because the Aborigines of Australia were less
Another very early example of an aerodynamically sophisticated humanmade device— though it is quite recent compared to the boomerang—is the kite, which first appeared in China in about 1000 B.C. The kite’s design borrows from avian anatomy, particularly the bird’s light, hollow bones. Hence a kite, in its simplest form, consists of two crossed strips of very light wood such as balsa, with a lightweight fabric stretched over them.
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Kites can come in a variety of shapes, though for many years the well-known diamond shape has been the most popular, in part because its aerodynamic qualities make it easiest for the novice kite-flyer to handle. Like birds and boomerangs, kites can “fly” because of the physical laws embodied in Bernoulli’s principle: at the best possible angle of attack, the kite experiences a maximal ratio of pressure from the slowermoving air below as against the faster-moving air above. For centuries, when the kite represented the only way to put a humanmade object many hundreds of feet into the air, scientists and engineers used them for a variety of experiments. Of course, the most famous example of this was Benjamin Franklin’s 1752 experiment with electricity. More significant to the future of aerodynamics were investigations made half a century later by Cayley, who recognized that the kite, rather than the balloon, was an appropriate model for the type of heavier-than-air flight he intended. In later years, engineers built larger kites capable of lifting men into the air, but the advent of the airplane rendered kites obsolete for this purpose. However, in the 1950s an American engineer named Francis Rogallo invented the flexible kite, which in turn spawned the delta wing kite used by hang gliders. During the 1960s, Domina Jolbert created the parafoil, an even more efficient device, which took nonmechanized human flight perhaps as far as it can go. Akin to the kite, glider, and hang glider is that creation of childhood fancy, the paper airplane. In its most basic form—and paper airplane enthusiasts are capable of fairly complex designs—a paper airplane is little more than a set of wings. There are a number or reasons for this, not least the fact that in most cases, a person flying a paper airplane is not as concerned about pitch, yaw, and roll as a pilot flying with several hundred passengers on board would be. However, when fashioning a paper airplane it is possible to add a number of design features, for instance by folding flaps upward at the tail. These become the equivalent of the elevator, a control surface along the horizontal edge of a real aircraft’s tail, which the pilot rotates upward to provide stability. But as noted by Ken Blackburn, author of several books on paper airplanes, it is not necessarily the case that an airplane must
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have a tail; indeed, some of the most sophisticated craft in the sky today—including the fearsome B-2 “Stealth” bomber—do not have tails. A typical paper airplane has low aspect ratio wings, a term that refers to the size of the wingspan compared to the chord line. In subsonic flight, higher aspect ratios are usually preferred, and this is certainly the case with most “real” gliders; hence their wings are longer, and their chord lines shorter. But there are several reasons why this is not the case with a paper airplane. First of all, as Blackburn noted wryly on his Web site, “Paper is a lousy building material. There is a reason why real airplanes are not made of paper.” He stated the other factors governing paper airplanes’ low aspect ratio in similarly whimsical terms. First, “Low aspect ratio wings are easier to fold....”; second, “Paper airplane gliding performance is not usually very important....”; and third, “Low-aspect ratio wings look faster, especially if they are swept back.” The reason why low-aspect ratio wings look faster, Blackburn suggested, is that people see them on jet fighters and the Concorde, and assume that a relatively narrow wing span with a long chord line yields the fastest speeds. And indeed they do—but only at supersonic speeds. Below the speed of sound, high-aspect ratio wings are best for preventing drag. Furthermore, as Blackburn went on to note, low-aspect ratio wings help the paper airplane to withstand the relatively high launch speeds necessary to send them into longer glides. In fact, a paper airplane is not subject to anything like the sort of design constraints affecting a real craft. All real planes look somewhat similar, because the established combinations, ratios, and dimensions of wings, tails, and fuselage work best. Certainly there is a difference in basic appearance between subsonic and supersonic aircraft—but again, all supersonic jets have more or less the same low-aspect, swept wing. “With paper airplanes,” Blackburn wrote, “it’s easy to make airplanes that don’t look like real airplanes” since “The mission of a paper airplane is [simply] to provide a good time for the pilot.”
Aerodynamics on the Ground The preceding discussions of aerodynamics in action have concerned the behavior of objects off the ground. But aerodynamics is also a factor in
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wheeled transport on Earth’s surface, whether by bicycle, automobile, or some other variation.
Aerodynamics
On a bicycle, the rider accounts for 65-80% of the drag, and therefore his or her position with regard to airflow is highly important. Thus, from as early as the 1890s, designers of racing bikes have favored drop handlebars, as well as a seat and frame that allow a crouched position. Since the 1980s, bicycle designers have worked to eliminate all possible extra lines and barriers to airflow, including the crossbar and chainstays. A typical bicycle’s wheel contains 32 or 36 cylindrical spokes, and these can affect aerodynamics adversely. As the wheel rotates, the airflow behind the spoke separates, creating turbulence and hence drag. For this reason, some of the most advanced bicycles today use either aerodynamic rims, which reduce the length of the spokes, three-spoke aerodynamic wheels, or even solid wheels. The rider’s gear can also serve to impede or enhance his velocity, and thus modern racing helmets have a streamlined shape—rather like that of an airfoil. The best riders, such as those who compete in the Olympics or the Tour de France, have bikes custom-designed to fit their own body shape. One interesting aspect of aerodynamics where it concerns bicycle racing is the phenomenon of “drafting.” Riders at the front of a pack, like riders pedaling alone, consume 30-40% more energy than do riders in the middle of a pack. The latter are benefiting from the efforts of bicyclists in front of them, who put up most of the wind resistance. The same is true for bicyclists who ride behind automobiles or motorcycles. The use of machine-powered pace vehicles to help in achieving extraordinary speeds is far from new. Drafting off of a railroad car with specially designed aerodynamic shields, a rider in 1896 was able to exceed 60 MPH (96 km/h), a then unheard-of speed. Today the record is just under 167 MPH (267 km/h). Clearly one must be a highly skilled, powerful rider to approach anything like this speed; but design factors also come into play, and not just in the case of the pace vehicle. Just as supersonic jets are quite different from ordinary planes, super high-speed bicycles are not like the average bike; they are designed in such a way that they must be moving faster than 60 MPH before the rider can even pedal.
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A
PROFESSIONAL BICYCLE RACER’S STREAMLINED HEL-
MET AND CROUCHED POSITION HELP TO IMPROVE AIRFLOW, THUS INCREASING SPEED. (Photograph by Ronnen
Eshel/Corbis. Reproduced by permission.)
With regard to automobiles, as noted earlier, aerodynamics has a strong impact on body design. For this reason, cars over the years have become steadily more streamlined and aerodynamic in appearance, a factor that designers balance with aesthetic appeal. Today’s Chrysler PT Cruiser, which debuted in 2000, may share outward features with 1930s and 1940s cars, but the PT Cruiser’s design is much more sound aerodynamically—not least because a modern vehicle can travel much, much faster than the cars driven by previous generations. Nowhere does the connection between aerodynamics and automobiles become more crucial than in the sport of auto racing. For race-car drivers, drag is always a factor to be avoided and counteracted by means ranging from drafting to altering the body design to reduce the airflow under the vehicle. However, as strange as it may seem, a car—like an airplane—is also subject to lift. It was noted earlier that in some cases lift can be undesirable in an airplane (for instance, when trying to land), but it is virtually always undesirable in an automobile. The greater the speed, the greater the lift force, which increases
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Aerodynamics
KEY TERMS AERODYNAMICS:
The study of air
flow and its principles. Applied aerodynamics is the science of improving manmade objects in light of those principles.
Its opposite is turbulent flow. LIFT: An aerodynamic force perpendicu-
lar to the direction of the wind. For an air-
AIRFOIL: The design of an airplane’s
craft, lift is the force that raises it off the
wing when seen from the end, a shape
ground and keeps it aloft.
intended to maximize the aircraft’s response to airflow. ANGLE OF ATTACK: The orientation of
the airfoil with regard to the airflow, or the angle that the chord line forms with the direction of the air stream. BERNOULLI’S PRINCIPLE: A proposi-
tion, credited to Swiss mathematician and physicist Daniel Bernoulli (1700-1782),
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the same speed and in the same direction.
PITCH: The tendency of an aircraft in
flight to rotate forward or backward; see also yaw and roll. ROLL: The tendency of an aircraft in
flight to rotate vertically on the axis of its fuselage; see also pitch and yaw. STAGNATION POINT: The spot where
airflow hits the leading edge of an airfoil.
which maintains that slower-moving fluid
SUPERSONIC: Faster than Mach 1, or
exerts greater pressure than faster-moving
the speed of sound—660 MPH (1,622
fluid.
km/h). Speeds above Mach 5 are referred to
CAMBER: The enhanced curvature on the
as hypersonic.
upper surface of an airfoil.
TURBULENT: A term describing a highly
CHORD LINE: The distance, along an
irregular form of flow, in which a fluid is
imaginary straight line, from the stagna-
subject to continual changes in speed and
tion point of an airfoil to the rear, or trail-
direction. Its opposite is laminar flow.
ing edge.
VISCOSITY: The internal friction in a
DRAG: The force that opposes the forward
fluid that makes it resistant to flow.
motion of an object in airflow.
YAW: The tendency of an aircraft in flight
LAMINAR: A term describing a stream-
to rotate on a horizontal plane; see also
lined flow, in which all particles move at
Pitch and Roll.
the threat of instability. For this reason, builders of race cars design their vehicles for negative lift: hence a typical family car has a lift coefficient of about 0.03, whereas a race car is likely to have a coefficient of -3.00.
not wrap around the vehicle’s rear end. Instead, the spoiler creates a downward force to stabilize the rear, and it may help to decrease drag by reducing the separation of airflow (and hence the creation of turbulence) at the rear window.
Among the design features most often used to reduce drag while achieving negative lift is a rear-deck spoiler. The latter has an airfoil shape, but its purpose is different: to raise the rear stagnation point and direct air flow so that it does
Similar in concept to a spoiler, though somewhat different in purpose, is the aerodynamically curved shield that sits atop the cab of most modern eighteen-wheel transport trucks. The purpose of the shield becomes apparent when the
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truck is moving at high speeds: wind resistance becomes strong, and if the wind were to hit the truck’s trailer head-on, it would be as though the air were pounding a brick wall. Instead, the shield scoops air upward, toward the rear of the truck. At the rear may be another panel, patented by two young engineers in 1994, that creates a dragreducing vortex between panel and truck. WHERE TO LEARN MORE Cockpit Physics (Department of Physics, United States Air Force Academy web site.). (February 19, 2001). K8AIT Principles of Aeronautics Advanced Text. (web site). (February 19, 2001).
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Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998.
Aerodynamics
Blackburn, Ken. Paper Airplane Aerodynamics. (web site). (February 19, 2001). Schrier, Eric and William F. Allman. Newton at the Bat: The Science in Sports. New York: Charles Scribner’s Sons, 1984. Smith, H. C. The Illustrated Guide to Aerodynamics. Blue Ridge Summit, PA: Tab Books, 1992. Stever, H. Guyford, James J. Haggerty, and the Editors of Time-Life Books. Flight. New York: Time-Life Books, 1965. Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.
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BERNOULLI’S PRINCIPLE
Bernoulli’s Principle
CONCEPT Bernoulli’s principle, sometimes known as Bernoulli’s equation, holds that for fluids in an ideal state, pressure and density are inversely related: in other words, a slow-moving fluid exerts more pressure than a fast-moving fluid. Since “fluid” in this context applies equally to liquids and gases, the principle has as many applications with regard to airflow as to the flow of liquids. One of the most dramatic everyday examples of Bernoulli’s principle can be found in the airplane, which stays aloft due to pressure differences on the surface of its wing; but the truth of the principle is also illustrated in something as mundane as a shower curtain that billows inward.
HOW IT WORKS The Swiss mathematician and physicist Daniel Bernoulli (1700-1782) discovered the principle that bears his name while conducting experiments concerning an even more fundamental concept: the conservation of energy. This is a law of physics that holds that a system isolated from all outside factors maintains the same total amount of energy, though energy transformations from one form to another take place. For instance, if you were standing at the top of a building holding a baseball over the side, the ball would have a certain quantity of potential energy—the energy that an object possesses by virtue of its position. Once the ball is dropped, it immediately begins losing potential energy and gaining kinetic energy—the energy that an object possesses by virtue of its motion. Since the total energy must remain constant, potential and
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kinetic energy have an inverse relationship: as the value of one variable decreases, that of the other increases in exact proportion. The ball cannot keep falling forever, losing potential energy and gaining kinetic energy. In fact, it can never gain an amount of kinetic energy greater than the potential energy it possessed in the first place. At the moment before the ball hits the ground, its kinetic energy is equal to the potential energy it possessed at the top of the building. Correspondingly, its potential energy is zero—the same amount of kinetic energy it possessed before it was dropped. Then, as the ball hits the ground, the energy is dispersed. Most of it goes into the ground, and depending on the rigidity of the ball and the ground, this energy may cause the ball to bounce. Some of the energy may appear in the form of sound, produced as the ball hits bottom, and some will manifest as heat. The total energy, however, will not be lost: it will simply have changed form. Bernoulli was one of the first scientists to propose what is known as the kinetic theory of gases: that gas, like all matter, is composed of tiny molecules in constant motion. In the 1730s, he conducted experiments in the conservation of energy using liquids, observing how water flows through pipes of varying diameter. In a segment of pipe with a relatively large diameter, he observed, water flowed slowly, but as it entered a segment of smaller diameter, its speed increased. It was clear that some force had to be acting on the water to increase its speed. Earlier, Robert Boyle (1627-1691) had demonstrated that pressure and volume have an inverse relationship,
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and Bernoulli seems to have applied Boyle’s findings to the present situation. Clearly the volume of water flowing through the narrower pipe at any given moment was less than that flowing through the wider one. This suggested, according to Boyle’s law, that the pressure in the wider pipe must be greater. As fluid moves from a wider pipe to a narrower one, the volume of that fluid that moves a given distance in a given time period does not change. But since the width of the narrower pipe is smaller, the fluid must move faster in order to achieve that result. One way to illustrate this is to observe the behavior of a river: in a wide, unconstricted region, it flows slowly, but if its flow is narrowed by canyon walls (for instance), then it speeds up dramatically. The above is a result of the fact that water is a fluid, and having the characteristics of a fluid, it adjusts its shape to fit that of its container or other solid objects it encounters on its path. Since the volume passing through a given length of pipe during a given period of time will be the same, there must be a decrease in pressure. Hence Bernoulli’s conclusion: the slower the rate of flow, the higher the pressure, and the faster the rate of flow, the lower the pressure. Bernoulli published the results of his work in Hydrodynamica (1738), but did not present his ideas or their implications clearly. Later, his friend the German mathematician Leonhard Euler (1707-1783) generalized his findings in the statement known today as Bernoulli’s principle.
The Venturi Tube Also significant was the work of the Italian physicist Giovanni Venturi (1746-1822), who is credited with developing the Venturi tube, an instrument for measuring the drop in pressure that takes place as the velocity of a fluid increases. It consists of a glass tube with an inward-sloping area in the middle, and manometers, devices for measuring pressure, at three places: the entrance, the point of constriction, and the exit. The Venturi meter provided a consistent means of demonstrating Bernoulli’s principle.
viscosity, the internal friction in a fluid that makes it resistant to flow. In 1904, the German physicist Ludwig Prandtl (1875-1953) was conducting experiments in liquid flow, the first effort in well over a century to advance the findings of Bernoulli and others. Observing the flow of liquid in a tube, Prandtl found that a tiny portion of the liquid adheres to the surface of the tube in the form of a thin film, and does not continue to move. This he called the viscous boundary layer.
Bernoulli’s Principle
Like Bernoulli’s principle itself, Prandtl’s findings would play a significant part in aerodynamics, or the study of airflow and its principles. They are also significant in hydrodynamics, or the study of water flow and its principles, a discipline Bernoulli founded.
Laminar vs. Turbulent Flow Air and water are both examples of fluids, substances which—whether gas or liquid—conform to the shape of their container. The flow patterns of all fluids may be described in terms either of laminar flow, or of its opposite, turbulent flow. Laminar flow is smooth and regular, always moving at the same speed and in the same direction. Also known as streamlined flow, it is characterized by a situation in which every particle of fluid that passes a particular point follows a path identical to all particles that passed that point earlier. A good illustration of laminar flow is what occurs when a stream flows around a twig. By contrast, in turbulent flow, the fluid is subject to continual changes in speed and direction—as, for instance, when a stream flows over shoals of rocks. Whereas the mathematical model of laminar flow is rather straightforward, conditions are much more complex in turbulent flow, which typically occurs in the presence of obstacles or high speeds.
Like many propositions in physics, Bernoulli’s principle describes an ideal situation in the absence of other forces. One such force is
Turbulent flow makes it more difficult for two streams of air, separated after hitting a barrier, to rejoin on the other side of the barrier; yet that is their natural tendency. In fact, if a single air current hits an airfoil—the design of an airplane’s wing when seen from the end, a streamlined shape intended to maximize the aircraft’s response to airflow—the air that flows over the top will “try” to reach the back end of the airfoil at the same time as the air that flows over the
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Bernoulli’s Principle
A
KITE’S DESIGN, PARTICULARLY ITS USE OF LIGHTWEIGHT FABRIC STRETCHED OVER TWO CROSSED STRIPS OF VERY
LIGHT WOOD, MAKES IT WELL-SUITED FOR FLIGHT, BUT WHAT KEEPS IT IN THE AIR IS A DIFFERENCE IN AIR PRESSURE.
AT
THE BEST POSSIBLE ANGLE OF ATTACK, THE KITE EXPERIENCES AN IDEAL RATIO OF PRESSURE FROM THE SLOW-
ER-MOVING AIR BELOW VERSUS THE FASTER-MOVING AIR ABOVE, AND THIS GIVES IT LIFT. (Roger Ressmeyer/Corbis. Repro-
duced by permission.)
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bottom. In order to do so, it will need to speed up—and this, as will be shown below, is the basis for what makes an airplane fly.
When viscosity is absent, conditions of perfect laminar flow exist: an object behaves in complete alignment with Bernoulli’s principle. Of
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Bernoulli’s Principle
THE
BOOMERANG, DEVELOPED BY
AUSTRALIA’S ABORIGINAL PEOPLE, FLIES THROUGH THE AIR ON A PLANE PERAS IT FLIES, THE BOOMERANG BECOMES BOTH A GYROSCOPE ROLE GIVES IT AERODYNAMIC LIFT. (Bettmann/Corbis. Reproduced by permission.)
PENDICULAR TO THE GROUND, RATHER THAN PARALLEL. AND AN AIRFOIL, AND THIS DUAL
course, though ideal conditions seldom occur in the real world, Bernoulli’s principle provides a guide for the behavior of planes in flight, as well as a host of everyday things.
REAL-LIFE A P P L I C AT I O N S Flying Machines For thousands of years, human beings vainly sought to fly “like a bird,” not realizing that this is literally impossible, due to differences in physiognomy between birds and homo sapiens. No man has ever been born (or ever will be) who possesses enough strength in his chest that he could flap a set of attached wings and lift his body off the ground. Yet the bird’s physical structure proved highly useful to designers of practical flying machines. A bird’s wing is curved along the top, so that when air passes over the wing and divides, the curve forces the air on top to travel a greater distance than the air on the bottom. The tendency of airflow, as noted earlier, is to correct for the presence of solid objects and to return to its original pattern as quickly as possible. Hence, when
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the air hits the front of the wing, the rate of flow at the top increases to compensate for the greater distance it has to travel than the air below the wing. And as shown by Bernoulli, fast-moving fluid exerts less pressure than slow-moving fluid; therefore, there is a difference in pressure between the air below and the air above, and this keeps the wing aloft. Only in 1853 did Sir George Cayley (17731857) incorporate the avian airfoil to create history’s first workable (though engine-less) flying machine, a glider. Much, much older than Cayley’s glider, however, was the first manmade flying machine built “according to Bernoulli’s principle”—only it first appeared in about 12,000 B.C., and the people who created it had had little contact with the outside world until the late eighteenth century A.D. This was the boomerang, one of the most ingenious devices ever created by a stone-age society—in this case, the Aborigines of Australia. Contrary to the popular image, a boomerang flies through the air on a plane perpendicular to the ground, rather than parallel. Hence, any thrower who properly knows how tosses the boomerang not with a side-arm throw, but overhand. As it flies, the boomerang becomes
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both a gyroscope and an airfoil, and this dual role gives it aerodynamic lift. Like the gyroscope, the boomerang imitates a top; spinning keeps it stable. It spins through the air, its leading wing (the forward or upward wing) creating more lift than the other wing. As an airfoil, the boomerang is designed so that the air below exerts more pressure than the air above, which keeps it airborne. Another very early example of a flying machine using Bernoulli’s principles is the kite, which first appeared in China in about 1000 B.C. The kite’s design, particularly its use of lightweight fabric stretched over two crossed strips of very light wood, makes it well-suited for flight, but what keeps it in the air is a difference in air pressure. At the best possible angle of attack, the kite experiences an ideal ratio of pressure from the slower-moving air below versus the fastermoving air above, and this gives it lift. Later Cayley studied the operation of the kite, and recognized that it—rather than the balloon, which at first seemed the most promising apparatus for flight—was an appropriate model for the type of heavier-than-air flying machine he intended to build. Due to the lack of a motor, however, Cayley’s prototypical airplane could never be more than a glider: a steam engine, then state-of-the-art technology, would have been much too heavy. Hence, it was only with the invention of the internal-combustion engine that the modern airplane came into being. On December 17, 1903, at Kitty Hawk, North Carolina, Orville (1871-1948) and Wilbur (1867-1912) Wright tested a craft that used a 25-horsepower engine they had developed at their bicycle shop in Ohio. By maximizing the ratio of power to weight, the engine helped them overcome the obstacles that had dogged recent attempts at flight, and by the time the day was over, they had achieved a dream that had eluded men for more than four millennia.
Again, in accordance with Bernoulli’s principle, the shape of the airflow facilitates the spread of laminar flow around it. The slower-moving currents beneath the airfoil exert greater pressure than the faster currents above it, giving lift to the aircraft. Of course, the aircraft has to be moving at speeds sufficient to gain momentum for its leap from the ground into the air, and here again, Bernoulli’s principle plays a part. Thrust comes from the engines, which run the propellers—whose blades in turn are designed as miniature airfoils to maximize their power by harnessing airflow. Like the aircraft wings, the blades’ angle of attack—the angle at which airflow hits it. In stable flight, the pilot greatly increases the angle of attack (also called pitched), whereas at takeoff and landing, the pitch is dramatically reduced.
Drawing Fluids Upward: Atomizers and Chimneys A number of everyday objects use Bernoulli’s principle to draw fluids upward, and though in terms of their purposes, they might seem very different—for instance, a perfume atomizer vs. a chimney—they are closely related in their application of pressure differences. In fact, the idea behind an atomizer for a perfume spray bottle can also be found in certain garden-hose attachments, such as those used to provide a high-pressure car wash.
As noted earlier, an airfoil has a streamlined design. Its shape is rather like that of an elongat-
The air inside the perfume bottle is moving relatively slowly; therefore, according to Bernoulli’s principle, its pressure is relatively high, and it exerts a strong downward force on the perfume itself. In an atomizer there is a narrow tube running from near the bottom of the bottle to the top. At the top of the perfume bottle, it opens inside another tube, this one perpendicular to the first tube. At one end of the horizontal tube is a simple squeeze-pump which causes air to flow quickly through it. As a result, the pressure
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Within fifty years, airplanes would increasingly obtain their power from jet rather than internal-combustion engines. But the principle that gave them flight, and the principle that kept them aloft once they were airborne, reflected back to Bernoulli’s findings of more than 160 years before their time. This is the concept of the airfoil.
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ed, asymmetrical teardrop lying on its side, with the large end toward the direction of airflow, and the narrow tip pointing toward the rear. The greater curvature of its upper surface in comparison to the lower side is referred to as the airplane’s camber. The front end of the airfoil is also curved, and the chord line is an imaginary straight line connecting the spot where the air hits the front—known as the stagnation point— to the rear, or trailing edge, of the wing.
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toward the top of the bottle is reduced, and the perfume flows upward along the vertical tube, drawn from the area of higher pressure at the bottom. Once it is in the upper tube, the squeezepump helps to eject it from the spray nozzle.
true. There is little variation in tones on a Hoover bugle: increasing the velocity results in a frequency twice that of the original, but it is difficult to create enough speed to generate a third tone.
A carburetor works on a similar principle, though in that case the lower pressure at the top draws air rather than liquid. Likewise a chimney draws air upward, and this explains why a windy day outside makes for a better fire inside. With wind blowing over the top of the chimney, the air pressure at the top is reduced, and tends to draw higher-pressure air from down below.
Spin, Curve, and Pull: The Counterintuitive Principle
The upward pull of air according to the Bernoulli principle can also be illustrated by what is sometimes called the “Hoover bugle”—a name perhaps dating from the Great Depression, when anything cheap or contrived bore the appellation “Hoover” as a reflection of popular dissatisfaction with President Herbert Hoover. In any case, the Hoover bugle is simply a long corrugated tube that, when swung overhead, produces musical notes. You can create a Hoover bugle using any sort of corrugated tube, such as vacuum-cleaner hose or swimming-pool drain hose, about 1.8 in (4 cm) in diameter and 6 ft (1.8 m) in length. To operate it, you should simply hold the tube in both hands, with extra length in the leading hand—that is, the right hand, for most people. This is the hand with which to swing the tube over your head, first slowly and then faster, observing the changes in tone that occur as you change the pace. The vacuum hose of a Hoover tube can also be returned to a version of its original purpose in an illustration of Bernoulli’s principle. If a piece of paper is torn into pieces and placed on a table, with one end of the tube just above the paper and the other end spinning in the air, the paper tends to rise. It is drawn upward as though by a vacuum cleaner—but in fact, what makes it happen is the pressure difference created by the movement of air. In both cases, reduced pressure draws air from the slow-moving region at the bottom of the tube. In the case of the Hoover bugle, the corrugations produce oscillations of a certain frequency. Slower speeds result in slower oscillations and hence lower frequency, which produces a lower tone. At higher speeds, the opposite is
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Bernoulli’s Principle
There are several other interesting illustrations— sometimes fun and in one case potentially tragic—of Bernoulli’s principle. For instance, there is the reason why a shower curtain billows inward once the shower is turned on. It would seem logical at first that the pressure created by the water would push the curtain outward, securing it to the side of the bathtub. Instead, of course, the fast-moving air generated by the flow of water from the shower creates a center of lower pressure, and this causes the curtain to move away from the slower-moving air outside. This is just one example of the ways in which Bernoulli’s principle creates results that, on first glance at least, seem counterintuitive— that is, the opposite of what common sense would dictate. Another fascinating illustration involves placing two empty soft drink cans parallel to one another on a table, with a couple of inches or a few centimeters between them. At that point, the air on all sides has the same slow speed. If you were to blow directly between the cans, however, this would create an area of low pressure between them. As a result, the cans push together. For ships in a harbor, this can be a frightening prospect: hence, if two crafts are parallel to one another and a strong wind blows between them, there is a possibility that they may behave like the cans. Then there is one of the most illusory uses of Bernoulli’s principle, that infamous baseball pitcher’s trick called the curve ball. As the ball moves through the air toward the plate, its velocity creates an air stream moving against the trajectory of the ball itself. Imagine it as two lines, one curving over the ball and one curving under, as the ball moves in the opposite direction. In an ordinary throw, the effects of the airflow would not be particularly intriguing, but in this case, the pitcher has deliberately placed a “spin” on the ball by the manner in which he has thrown it. How pitchers actually produce spin is a complex subject unto itself, involving grip,
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Bernoulli’s Principle
KEY TERMS AERODYNAMICS:
The study of air-
INVERSE RELATIONSHIP:
A situa-
flow and its principles. Applied aerody-
tion involving two variables, in which one
namics is the science of improving man-
of the two increases in direct proportion to
made objects in light of those principles.
the decrease in the other.
AIRFOIL:
The design of an airplane’s
wing when seen from the end, a shape
KINETIC ENERGY:
The energy that
an object possesses by virtue of its motion.
intended to maximize the aircraft’s LAMINAR: A term describing a stream-
response to airflow. ANGLE OF ATTACK: The orientation of
the airfoil with regard to the airflow, or the angle that the chord line forms with the
lined flow, in which all particles move at the same speed and in the same direction. Its opposite is turbulent flow. LIFT: An aerodynamic force perpendicu-
direction of the air stream. BERNOULLI’S PRINCIPLE: A proposi-
lar to the direction of the wind. For an air-
tion, credited to Swiss mathematician and
craft, lift is the force that raises it off the
physicist Daniel Bernoulli (1700-1782),
ground and keeps it aloft.
which maintains that slower-moving fluid
MANOMETERS:
exerts greater pressure than faster-moving
ing pressure in conjunction with a Venturi
fluid.
tube.
CAMBER: The enhanced curvature on the
upper surface of an airfoil.
Devices for measur-
POTENTIAL ENERGY:
The energy
that an object possesses by virtue of its
CHORD LINE: The distance, along an
position.STAGNATION POINT: The spot
imaginary straight line, from the stagna-
where airflow hits the leading edge of an
tion point of an airfoil to the rear, or trail-
airfoil.
ing edge. CONSERVATION OF ENERGY:
A
law of physics which holds that within a system isolated from all other outside factors, the total amount of energy remains
irregular form of flow, in which a fluid is subject to continual changes in speed and direction. Its opposite is laminar flow. An instrument, con-
the same, though transformations of ener-
VENTURI TUBE:
gy from one form to another take place.
sisting of a glass tube with an inward-slop-
Any substance, whether gas or
ing area in the middle, for measuring the
liquid, that conforms to the shape of its
drop in pressure that takes place as the
container.
velocity of a fluid increases.
FLUID:
HYDRODYNAMICS:
The study of
water flow and its principles.
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TURBULENT: A term describing a highly
VISCOSITY: The internal friction in a
fluid that makes it resistant to flow.
wrist movement, and other factors, and in any case, the fact of the spin is more important than the way in which it was achieved.
If the direction of airflow is from right to left, the ball, as it moves into the airflow, is spinning clockwise. This means that the air flowing
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over the ball is moving in a direction opposite to the spin, whereas that flowing under it is moving in the same direction. The opposite forces produce a drag on the top of the ball, and this cuts down on the velocity at the top compared to that at the bottom of the ball, where spin and airflow are moving in the same direction. Thus the air pressure is higher at the top of the ball, and as per Bernoulli’s principle, this tends to pull the ball downward. The curve ball— of which there are numerous variations, such as the fade and the slider—creates an unpredictable situation for the batter, who sees the ball leave the pitcher’s hand at one altitude, but finds to his dismay that it has dropped dramatically by the time it crosses the plate. A final illustration of Bernoulli’s often counterintuitive principle neatly sums up its effects on the behavior of objects. To perform the experiment, you need only an index card and a flat surface. The index card should be folded at the ends so that when the card is parallel to the surface, the ends are perpendicular to it. These folds should be placed about half an inch (about one centimeter) from the ends. At this point, it would be handy to have an unsuspecting person—someone who has not studied Bernoulli’s principle—on the scene, and challenge him or her to raise the card by blowing under it. Nothing could seem easier, of course: by
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blowing under the card, any person would naturally assume, the air will lift it. But of course this is completely wrong according to Bernoulli’s principle. Blowing under the card, as illustrated, will create an area of high velocity and low pressure. This will do nothing to lift the card: in fact, it only pushes the card more firmly down on the table.
Bernoulli’s Principle
WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. “Bernoulli’s Principle: Explanations and Demos.” (Web site). (February 22, 2001). Cockpit Physics (Department of Physics, United States Air Force Academy. Web site.). (February 19, 2001). K8AIT Principles of Aeronautics Advanced Text. (Web site). (February 19, 2001). Schrier, Eric and William F. Allman. Newton at the Bat: The Science in Sports. New York: Charles Scribner’s Sons, 1984. Smith, H. C. The Illustrated Guide to Aerodynamics. Blue Ridge Summit, PA: Tab Books, 1992. Stever, H. Guyford, James J. Haggerty, and the Editors of Time-Life Books. Flight. New York: Time-Life Books, 1965.
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B U O YA N C Y Buoyancy
CONCEPT The principle of buoyancy holds that the buoyant or lifting force of an object submerged in a fluid is equal to the weight of the fluid it has displaced. The concept is also known as Archimedes’s principle, after the Greek mathematician, physicist, and inventor Archimedes (c. 287-212 B.C.), who discovered it. Applications of Archimedes’s principle can be seen across a wide vertical spectrum: from objects deep beneath the oceans to those floating on its surface, and from the surface to the upper limits of the stratosphere and beyond.
HOW IT WORKS Archimedes Discovers Buoyancy There is a famous story that Sir Isaac Newton (1642-1727) discovered the principle of gravity when an apple fell on his head. The tale, an exaggerated version of real events, has become so much a part of popular culture that it has been parodied in television commercials. Almost equally well known is the legend of how Archimedes discovered the concept of buoyancy. A native of Syracuse, a Greek colony in Sicily, Archimedes was related to one of that city’s kings, Hiero II (308?-216 B.C.). After studying in Alexandria, Egypt, he returned to his hometown, where he spent the remainder of his life. At some point, the royal court hired (or compelled) him to set about determining the weight of the gold in the king’s crown. Archimedes was in his bath pondering this challenge when suddenly it occurred to him that the buoyant force of a sub-
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merged object is equal to the weight of the fluid displaced by it. He was so excited, the legend goes, that he jumped out of his bath and ran naked through the streets of Syracuse shouting “Eureka!” (I have found it). Archimedes had recognized a principle of enormous value—as will be shown—to shipbuilders in his time, and indeed to shipbuilders of the present. Concerning the history of science, it was a particularly significant discovery; few useful and enduring principles of physics date to the period before Galileo Galilei (1564-1642.) Even among those few ancient physicists and inventors who contributed work of lasting value—Archimedes, Hero of Alexandria (c. 65-125 A.D.), and a few others—there was a tendency to miss the larger implications of their work. For example, Hero, who discovered steam power, considered it useful only as a toy, and as a result, this enormously significant discovery was ignored for seventeen centuries. In the case of Archimedes and buoyancy, however, the practical implications of the discovery were more obvious. Whereas steam power must indeed have seemed like a fanciful notion to the ancients, there was nothing farfetched about oceangoing vessels. Shipbuilders had long been confronted with the problem of how to keep a vessel afloat by controlling the size of its load on the one hand, and on the other hand, its tendency to bob above the water. Here, Archimedes offered an answer.
Buoyancy and Weight Why does an object seem to weigh less underwater than above the surface? How is it that a ship
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made of steel, which is obviously heavier than water, can float? How can we determine whether a balloon will ascend in the air, or a submarine will descend in the water? These and other questions are addressed by the principle of buoyancy, which can be explained in terms of properties— most notably, gravity—unknown to Archimedes.
solid object of exactly the same size. The solid object will experience exactly the same degree of pressure as the imaginary “bag” did—and hence, it will also experience the same buoyant force pushing it up from the bottom. This means that buoyant force is equal to the weight—Vdg—of displaced fluid.
To understand the factors at work, it is useful to begin with a thought experiment. Imagine a certain quantity of fluid submerged within a larger body of the same fluid. Note that the terms “liquid” or “water” have not been used: not only is “fluid” a much more general term, but also, in general physical terms and for the purposes of the present discussion, there is no significant difference between gases and liquids. Both conform to the shape of the container in which they are placed, and thus both are fluids.
Buoyancy is always a double-edged proposition. If the buoyant force on an object is greater than the weight of that object—in other words, if the object weighs less than the amount of water it has displaced—it will float. But if the buoyant force is less than the object’s weight, the object will sink. Buoyant force is not the same as net force: if the object weighs more than the water it displaces, the force of its weight cancels out and in fact “overrules” that of the buoyant force.
To return to the thought experiment, what has been posited is in effect a “bag” of fluid—that is, a “bag” made out of fluid and containing fluid no different from the substance outside the “bag.” This “bag” is subjected to a number of forces. First of all, there is its weight, which tends to pull it to the bottom of the container. There is also the pressure of the fluid all around it, which varies with depth: the deeper within the container, the greater the pressure. Pressure is simply the exertion of force over a two-dimensional area. Thus it is as though the fluid is composed of a huge number of twodimensional “sheets” of fluid, each on top of the other, like pages in a newspaper. The deeper into the larger body of fluid one goes, the greater the pressure; yet it is precisely this increased force at the bottom of the fluid that tends to push the “bag” upward, against the force of gravity. Now consider the weight of this “bag.” Weight is a force—the product of mass multiplied by acceleration—that is, the downward acceleration due to Earth’s gravitational pull. For an object suspended in fluid, it is useful to substitute another term for mass. Mass is equal to volume, or the amount of three-dimensional space occupied by an object, multiplied by density. Since density is equal to mass divided by volume, this means that volume multiplied by density is the same as mass.
Buoyancy
At the heart of the issue is density. Often, the density of an object in relation to water is referred to as its specific gravity: most metals, which are heavier than water, are said to have a high specific gravity. Conversely, petroleumbased products typically float on the surface of water, because their specific gravity is low. Note the close relationship between density and weight where buoyancy is concerned: in fact, the most buoyant objects are those with a relatively high volume and a relatively low density. This can be shown mathematically by means of the formula noted earlier, whereby density is equal to mass divided by volume. If Vd = V(m/V), an increase in density can only mean an increase in mass. Since weight is the product of mass multiplied by g (which is assumed to be a constant figure), then an increase in density means an increase in mass and hence, an increase in weight—not a good thing if one wants an object to float.
REAL-LIFE A P P L I C AT I O N S Staying Afloat
We have established that the weight of the fluid “bag” is Vdg, where V is volume, d is density, and g is the acceleration due to gravity. Now imagine that the “bag” has been replaced by a
In the early 1800s, a young Mississippi River flatboat operator submitted a patent application describing a device for “buoying vessels over shoals.” The invention proposed to prevent a problem he had often witnessed on the river— boats grounded on sandbars—by equipping the boats with adjustable buoyant air chambers. The young man even whittled a model of his inven-
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tion, but he was not destined for fame as an inventor; instead, Abraham Lincoln (1809-1865) was famous for much else. In fact Lincoln had a sound idea with his proposal to use buoyant force in protecting boats from running aground. Buoyancy on the surface of water has a number of easily noticeable effects in the real world. (Having established the definition of fluid, from this point onward, the fluids discussed will be primarily those most commonly experienced: water and air.) It is due to buoyancy that fish, human swimmers, icebergs, and ships stay afloat. Fish offer an interesting application of volume change as a means of altering buoyancy: a fish has an internal swim bladder, which is filled with gas. When it needs to rise or descend, it changes the volume in its swim bladder, which then changes its density. The examples of swimmers and icebergs directly illustrate the principle of density—on the part of the water in the first instance, and on the part of the object itself in the second. To a swimmer, the difference between swimming in fresh water and salt water shows that buoyant force depends as much on the density of the fluid as on the volume displaced. Fresh water has a density of 62.4 lb/ft3 (9,925 N/m3), whereas that of salt water is 64 lb/ft3 (10,167 N/m3). For this reason, salt water provides more buoyant force than fresh water; in Israel’s Dead Sea, the saltiest body of water on Earth, bathers experience an enormous amount of buoyant force. Water is an unusual substance in a number of regards, not least its behavior as it freezes. Close to the freezing point, water thickens up, but once it turns to ice, it becomes less dense. This is why ice cubes and icebergs float. However, their low density in comparison to the water around them means that only part of an iceberg stays atop the surface. The submerged percentage of an iceberg is the same as the ratio of the density of ice to that of water: 89%.
For a ship to be seaworthy, it must maintain a delicate balance between buoyancy and stability. A vessel that is too light—that is, too much volume and too little density—will bob on the top of the water. Therefore, it needs to carry a certain amount of cargo, and if not cargo, then water or some other form of ballast. Ballast is a heavy substance that increases the weight of an object experiencing buoyancy, and thereby improves its stability. Ideally, the ship’s center of gravity should be vertically aligned with its center of buoyancy. The center of gravity is the geometric center of the ship’s weight—the point at which weight above is equal to weight below, weight fore is equal to weight aft, and starboard (right-side) weight is equal to weight on the port (left) side. The center of buoyancy is the geometric center of its submerged volume, and in a stable ship, it is some distance directly below center of gravity. Displacement, or the weight of the fluid that is moved out of position when an object is immersed, gives some idea of a ship’s stability. If a ship set down in the ocean causes 1,000 tons (8.896 • 106 N) of water to be displaced, it is said to possess a displacement of 1,000 tons. Obviously, a high degree of displacement is desirable. The principle of displacement helps to explain how an aircraft carrier can remain afloat, even though it weighs many thousands of tons.
Down to the Depths
Because water itself is relatively dense, a highvolume, low-density object is likely to displace a quantity of water more dense—and heavier— than the object itself. By contrast, a steel ball dropped into the water will sink straight to the bottom, because it is a low-volume, high-density object that outweighs the water it displaced.
A submarine uses ballast as a means of descending and ascending underwater: when the submarine captain orders the crew to take the craft down, the craft is allowed to take water into its ballast tanks. If, on the other hand, the command is given to rise toward the surface, a valve will be opened to release compressed air into the tanks. The air pushes out the water, and causes the craft to ascend.
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This brings back the earlier question: how can a ship made out of steel, with a density of 487 lb/ft3 (77,363 N/m3), float on a salt-water ocean with an average density of only about one-eighth that amount? The answer lies in the design of the ship’s hull. If the ship were flat like a raft, or if all the steel in it were compressed into a ball, it would indeed sink. Instead, however, the hollow hull displaces a volume of water heavier than the ship’s own weight: once again, volume has been maximized, and density minimized.
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Buoyancy
Ic 0°
4°
THE
MOLECULAR STRUCTURE OF WATER BEGINS TO EXPAND ONCE IT COOLS BEYOND
TO EXPAND UNTIL IT BECOMES ICE.
FOR
39.4°F (4°C)
AND CONTINUES
THIS REASON, ICE IS LESS DENSE THAN WATER, FLOATS ON THE SURFACE,
AND RETARDS FURTHER COOLING OF DEEPER WATER, WHICH ACCOUNTS FOR THE SURVIVAL OF FRESHWATER PLANT AND ANIMAL LIFE THROUGH THE WINTER.
FOR
THEIR PART, FISH CHANGE THE VOLUME OF THEIR INTERNAL SWIM BLAD-
DER IN ORDER TO ALTER THEIR BUOYANCY.
A submarine is an underwater ship; its streamlined shape is designed to ease its movement. On the other hand, there are certain kinds of underwater vessels, known as submersibles, that are designed to sink—in order to observe or collect data from the ocean floor. Originally, the idea of a submersible was closely linked to that of diving itself. An early submersible was the diving bell, a device created by the noted English astronomer Edmund Halley (1656-1742.) Though his diving bell made it possible for Halley to set up a company in which hired divers salvaged wrecks, it did not permit divers to go beyond relatively shallow depths. First of all, the diving bell received air from the surface: in Halley’s time, no technology existed for taking an oxygen supply below. Nor did it provide substantial protection from the effects of increased pressure at great depths.
ducing two different—but equally frightening— effects. Nitrogen is an inert gas under normal conditions, yet in the high pressure of the ocean depths it turns into a powerful narcotic, causing nitrogen narcosis—often known by the poeticsounding name “rapture of the deep.” Under the influence of this deadly euphoria, divers begin to think themselves invincible, and their altered judgment can put them into potentially fatal situations.
P E R I L S O F T H E D E E P. The most immediate of those effects is, of course, the tendency of an object experiencing such pressure to simply implode like a tin can in a vise. Furthermore, the human body experiences several severe reactions to great depth: under water, nitrogen gas accumulates in a diver’s bodily tissues, pro-
Nitrogen narcosis can occur at depths as shallow as 60 ft (18.29 m), and it can be overcome simply by returning to the surface. However, one should not return to the surface too quickly, particularly after having gone down to a significant depth for a substantial period of time. In such an instance, on returning to the surface nitrogen gas will bubble within the body, producing decompression sickness—known colloquially as “the bends.” This condition may manifest as itching and other skin problems, joint pain, choking, blindness, seizures, unconsciousness, and even permanent neurological defects such as paraplegia.
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French physiologist Paul Bert (1833-1886) first identified the bends in 1878, and in 1907, John Scott Haldane (1860-1936) developed a method for counteracting decompression sickness. He calculated a set of decompression tables that advised limits for the amount of time at given depths. He recommended what he called stage decompression, which means that the ascending diver stops every few feet during ascension and waits for a few minutes at each level, allowing the body tissues time to adjust to the new pressure. Modern divers use a decompression chamber, a sealed container that simulates the stages of decompression. B AT H Y S P H E R E , S C U B A , A N D B AT H Y S CA P H E . In 1930, the American
naturalist William Beebe (1877-1962) and American engineer Otis Barton created the bathysphere. This was the first submersible that provided the divers inside with adequate protection from external pressure. Made of steel and spherical in shape, the bathysphere had thick quartz windows and was capable of maintaining ordinary atmosphere pressure even when lowered by a cable to relatively great depths. In 1934, a bathysphere descended to what was then an extremely impressive depth: 3,028 ft (923 m). However, the bathysphere was difficult to operate and maneuver, and in time it was be replaced by a more workable vessel, the bathyscaphe. Before the bathyscaphe appeared, however, in 1943, two Frenchmen created a means for divers to descend without the need for any sort of external chamber. Certainly a diver with this new apparatus could not go to anywhere near the same depths as those approached by the bathysphere; nonetheless, the new aqualung made it possible to spend an extended time under the surface without need for air. It was now theoretically feasible for a diver to go below without any need for help or supplies from above, because he carried his entire oxygen supply on his back. The name of one of inventors, Emile Gagnan, is hardly a household word; but that of the other— Jacques Cousteau (1910-1997)—certainly is. So, too, is the name of their invention: the self-contained underwater breathing apparatus, better known as scuba. The most important feature of the scuba gear was the demand regulator, which made it possible for the divers to breathe air at the same pressure as their underwater surroundings. This
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in turn facilitated breathing in a more normal, comfortable manner. Another important feature of a modern diver’s equipment is a buoyancy compensation device. Like a ship atop the water, a diver wants to have only so much buoyancy— not so much that it causes him to surface. As for the bathyscaphe—a term whose two Greek roots mean “deep” and “boat”—it made its debut five years after scuba gear. Built by the Swiss physicist and adventurer Auguste Piccard (1884-1962), the bathyscaphe consisted of two compartments: a heavy steel crew cabin that was resistant to sea pressure, and above it, a larger, light container called a float. The float was filled with gasoline, which in this case was not used as fuel, but to provide extra buoyancy, because of the gasoline’s low specific gravity. When descending, the occupants of the bathyscaphe—there could only be two, since the pressurized chamber was just 79 in (2.01 m) in diameter—released part of the gasoline to decrease buoyancy. They also carried iron ballast pellets on board, and these they released when preparing to ascend. Thanks to battery-driven screw propellers, the bathyscaphe was much more maneuverable than the bathysphere had ever been; furthermore, it was designed to reach depths that Beebe and Barton could hardly have conceived. R E AC H I N G N E W D E P T H S . It took several years of unsuccessful dives, but in 1953 a bathyscaphe set the first of many depth records. This first craft was the Trieste, manned by Piccard and his son Jacques, which descended 10,335 ft (3,150 m) below the Mediterranean, off Capri, Italy. A year later, in the Atlantic Ocean off Dakar, French West Africa (now Senegal), French divers Georges Houot and Pierre-Henri Willm reached 13,287 ft (4,063 m) in the FNRS 3.
Then in 1960, Jacques Piccard and United States Navy Lieutenant Don Walsh set a record that still stands: 35,797 ft (10,911 m)—23% greater than the height of Mt. Everest, the world’s tallest peak. This they did in the Trieste some 250 mi (402 km) southeast of Guam at the Mariana Trench, the deepest spot in the Pacific Ocean and indeed the deepest spot on Earth. Piccard and Walsh went all the way to the bottom, a descent that took them 4 hours, 48 minutes. Coming up took 3 hours, 17 minutes. Thirty-five years later, in 1995, the Japanese craft Kaiko also made the Mariana descent and
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confirmed the measurements of Piccard and Walsh. But the achievement of the Kaiko was not nearly as impressive of that of the Trieste’s twoman crew: the Kaiko, in fact, had no crew. By the 1990s, sophisticated remote-sensing technology had made it possible to send down unmanned ocean expeditions, and it became less necessary to expose human beings to the incredible risks encountered by the Piccards, Walsh, and others.
Buoyancy
F I L M I N G T I T A N I C . An example of such an unmanned vessel is the one featured in the opening minutes of the Academy Award-winning motion picture Titanic (1997). The vessel itself, whose sinking in 1912 claimed more than 1,000 lives, rests at such a great depth in the North Atlantic that it is impractical either to raise it, or to send manned expeditions to explore the interior of the wreck. The best solution, then, is a remotely operated vessel of the kind also used for purposes such as mapping the ocean floor, exploring for petroleum and other deposits, and gathering underwater plate technology data.
The craft used in the film, which has “arms” for grasping objects, is of a variety specially designed for recovering items from shipwrecks. For the scenes that showed what was supposed to be the Titanic as an active vessel, director James Cameron used a 90% scale model that depicted the ship’s starboard side—the side hit by the iceberg. Therefore, when showing its port side, as when it was leaving the Southampton, England, dock on April 15, 1912, all shots had to be reversed: the actual signs on the dock were in reverse lettering in order to appear correct when seen in the final version. But for scenes of the wrecked vessel lying at the bottom of the ocean, Cameron used the real Titanic. To do this, he had to use a submersible; but he did not want to shoot only from inside the submersible, as had been done in the 1992 IMAX film Titanica. Therefore, his brother Mike Cameron, in cooperation with Panavision, built a special camera that could withstand 400 atm (3.923 • 107 Pa)—that is, 400 times the air pressure at sea level. The camera was attached to the outside of the submersible, which for these external shots was manned by Russian submarine operators.
THE
DIVERS PICTURED HERE HAVE ASCENDED FROM A
SUNKEN SHIP AND HAVE STOPPED AT THE
10-FT (3-M)
DECOMPRESSION LEVEL TO AVOID GETTING DECOMPRESSION SICKNESS, BETTER KNOWN AS THE “BENDS.” (Photograph, copyright Jonathan Blair/Corbis. Reproduced by permission.)
would have been too dangerous for the humans in the manned craft. Cameron had intended the remotely operated submersible as a mere prop, but in the end its view inside the ruined Titanic added one of the most poignant touches in the entire film. To these he later added scenes involving objects specific to the film’s plot, such as the safe. These he shot in a controlled underwater environment designed to look like the interior of the Titanic.
Into the Skies In the earlier description of Piccard’s bathyscaphe design, it was noted that the craft consisted of two compartments: a heavy steel crew cabin resistant to sea pressure, and above it a larger, light container called a float. If this sounds rather like the structure of a hot-air balloon, there is no accident in that.
Because the special camera only held twelve minutes’ worth of film, it was necessary to make a total of twelve dives. On the last two, a remotely operated submersible entered the wreck, which
In 1931, nearly two decades before the bathyscaphe made its debut, Piccard and another Swiss scientist, Paul Kipfer, set a record of a different kind with a balloon. Instead of going lower
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than anyone ever had, as Piccard and his son Jacques did in 1953—and as Jacques and Walsh did in an even greater way in 1960—Piccard and Kipfer went higher than ever, ascending to 55,563 ft (16,940 m). This made them the first two men to penetrate the stratosphere, which is the next atmospheric layer above the troposphere, a layer approximately 10 mi (16.1 km) high that covers the surface of Earth. Piccard, without a doubt, experienced the greatest terrestrial altitude range of any human being over a lifetime: almost 12.5 mi (20.1 km) from his highest high to his lowest low, 84% of it above sea level and the rest below. His career, then, was a tribute to the power of buoyant force—and to the power of overcoming buoyant force for the purpose of descending to the ocean depths. Indeed, the same can be said of the Piccard family as a whole: not only did Jacques set the world’s depth record, but years later, Jacques’s son Bertrand took to the skies for another record-setting balloon flight. In 1999, Bertrand Piccard and British balloon instructor Brian Wilson became the first men to circumnavigate the globe in a balloon, the Breitling Orbiter 3. The craft extended 180 ft (54.86) from the top of the envelope—the part of the balloon holding buoyant gases—to the bottom of the gondola, the part holding riders. The pressurized cabin had one bunk in which one pilot could sleep while the other flew, and up front was a computerized control panel which allowed the pilot to operate the burners, switch propane tanks, and release empty ones. It took Piccard and Wilson just 20 days to circle the Earth—a far cry from the first days of ballooning two centuries earlier. T H E F I R S T B A L LO O N S . The Piccard family, though Swiss, are francophone; that is, they come from the French-speaking part of Switzerland. This is interesting, because the history of human encounters with buoyancy— below the ocean and even more so in the air— has been heavily dominated by French names. In fact, it was the French brothers, Joseph-Michel (1740-1810) and Jacques-Etienne (1745-1799) Montgolfier, who launched the first balloon in 1783. These two became to balloon flight what two other brothers, the Americans Orville and Wilbur Wright, became with regard to the invention that superseded the balloon twelve decades later: the airplane.
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On that first flight, the Montgolfiers sent up a model 30 ft (9.15 m) in diameter, made of linen-lined paper. It reached a height of 6,000 ft (1,828 m), and stayed in the air for 10 minutes before coming back down. Later that year, the Montgolfiers sent up the first balloon flight with living creatures—a sheep, a rooster, and a duck— and still later in 1783, Jean-François Pilatre de Rozier (1756-1785) became the first human being to ascend in a balloon. Rozier only went up 84 ft (26 m), which was the length of the rope that tethered him to the ground. As the makers and users of balloons learned how to use ballast properly, however, flight times were extended, and balloon flight became ever more practical. In fact, the world’s first military use of flight dates not to the twentieth century but to the eighteenth—1794, specifically, when France created a balloon corps. HOW
A
BALLOON
F L O AT S .
There are only three gases practical for lifting a balloon: hydrogen, helium, and hot air. Each is much less than dense than ordinary air, and this gives them their buoyancy. In fact, hydrogen is the lightest gas known, and because it is cheap to produce, it would be ideal—except for the fact that it is extremely flammable. After the 1937 crash of the airship Hindenburg, the era of hydrogen use for lighter-than-air transport effectively ended. Helium, on the other hand, is perfectly safe and only slightly less buoyant than hydrogen. This makes it ideal for balloons of the sort that children enjoy at parties; but helium is expensive, and therefore impractical for large balloons. Hence, hot air—specifically, air heated to a temperature of about 570°F (299°C), is the only truly viable option. Charles’s law, one of the laws regarding the behavior of gases, states that heating a gas will increase its volume. Gas molecules, unlike their liquid or solid counterparts, are highly nonattractive—that is, they tend to spread toward relatively great distances from one another. There is already a great deal of empty space between gas molecules, and the increase in volume only increases the amount of empty space. Hence, density is lowered, and the balloon floats. A I R S H I P S . Around the same time the Montgolfier brothers launched their first balloons, another French designer, Jean-BaptisteMarie Meusnier, began experimenting with a
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Buoyancy
ONCE CONSIDERED OBSOLETE, BLIMPS ARE ENJOYING A RENAISSANCE AMONG SCIENTISTS AND GOVERNMENT AGENCIES. THE BLIMP PICTURED HERE, THE AEROSTAT BLIMP, IS EQUIPPED WITH RADAR FOR DRUG ENFORCEMENT AND INSTRUMENTS FOR WEATHER OBSERVATION. (Corbis. Reproduced by permission.)
more streamlined, maneuverable model. Early balloons, after all, could only be maneuvered along one axis, up and down: when it came to moving sideways or forward and backward, they were largely at the mercy of the elements. It was more than a century before Meusnier’s idea—the prototype for an airship— became a reality. In 1898, Alberto SantosDumont of Brazil combined a balloon with a propeller powered by an internal-combustion instrument, creating a machine that improved on the balloon, much as the bathyscaphe later improved on the bathysphere. Santos-Dumont’s airship was non-rigid, like a balloon. It also used hydrogen, which is apt to contract during descent and collapse the envelope. To counter this problem, Santos-Dumont created the ballonet, an internal airbag designed to provide buoyancy and stabilize flight.
tions. Yet Zeppelin’s earliest launches, in the decade that followed 1898, were fraught with a number of problems—not least of which were disasters caused by the flammability of hydrogen. Zeppelin was finally successful in launching airships for public transport in 1911, and the quarter-century that followed marked the golden age of airship travel. Not that all was “golden” about this age: in World War I, Germany used airships as bombers, launching the first London blitz in May 1915. By the time Nazi Germany initiated the more famous World War II London blitz 25 years later, ground-based anti-aircraft technology would have made quick work of any zeppelin; but by then, airplanes had long since replaced airships.
One of the greatest figures in the history of lighter-than-air flight—a man whose name, along with blimp and dirigible, became a synonym for the airship—was Count Ferdinand von Zeppelin (1838-1917). It was he who created a lightweight structure of aluminum girders and rings that made it possible for an airship to remain rigid under varying atmospheric condi-
During the 1920s, though, airships such as the Graf Zeppelin competed with airplanes as a mode of civilian transport. It is a hallmark of the perceived safety of airships over airplanes at the time that in 1928, the Graf Zeppelin made its first transatlantic flight carrying a load of passengers. Just a year earlier, Charles Lindbergh had made the first-ever solo, nonstop transatlantic flight in an airplane. Today this would be the equivalent of someone flying to the Moon, or perhaps even Mars, and there was no question of carrying pas-
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Buoyancy
KEY TERMS ARCHIMEDES’S PRINCIPLE:
A rule
MASS:
of physics which holds that the buoyant
the resistance of an object to a change in its
force of an object immersed in fluid is
motion. For an object immerse in fluid,
equal to the weight of the fluid displaced
mass is equal to volume multiplied by
by the object. It is named after the Greek
density.
mathematician, physicist, and inventor Archimedes (c. 287-212 B.C.), who first identified it.
The exertion of force
PRESSURE:
over a two-dimensional area; hence the formula for pressure is force divided by
A heavy substance that, by
area. The British system of measures typi-
increasing the weight of an object experi-
cally reckons pressure in pounds per
encing buoyancy, improves its stability.
square inch. In metric terms, this is meas-
BALLAST:
BUOYANCY:
The tendency of an object
immersed in a fluid to float. This can be explained by Archimedes’s principle. Mass divided by volume.
DENSITY:
ured in terms of newtons (N) per square meter, a figure known as a pascal (Pa.) SPECIFIC GRAVITY:
The density of
an object or substance relative to the densi-
A measure of the
ty of water; or more generally, the ratio
weight of the fluid that has had to be
between the densities of two objects or
moved out of position so that an object can
substances.
be immersed. If a ship set down in the
VOLUME:
ocean causes 1,000 tons of water to be dis-
dimensional space occupied by an object.
placed, it is said to possess a displacement
Volume is usually measured in cubic units.
DISPLACEMENT:
of 1,000 tons. WEIGHT:
The
amount
of
three-
A force equal to mass multi-
Any substance, whether gas or
plied by the acceleration due to gravity (32
liquid, that conforms to the shape of its
ft/9.8 m/sec2). For an object immersed in
container.
fluid, weight is the same as volume multi-
FLUID:
FORCE:
The product of mass multi-
plied by acceleration.
sengers. Furthermore, Lindbergh was celebrated as a hero for the rest of his life, whereas the passengers aboard the Graf Zeppelin earned no more distinction for bravery than would pleasureseekers aboard a cruise.
plied by density multiplied by gravitational acceleration.
the leading contender in the realm of flight technology.
few years, airships constituted the luxury liners of the skies; but the Hindenburg crash signaled the end of relatively widespread airship transport. In any case, by the time of the 1937 Hindenburg crash, lighter-than-air transport was no longer
Ironically enough, by 1937 the airplane had long since proved itself more viable—even though it was actually heavier than air. The principles that make an airplane fly have little to do with buoyancy as such, and involve differences in pressure rather than differences in density. Yet the replacement of lighter-than-air craft on the cutting edge of flight did not mean that balloons and airships were relegated to the museum; instead, their purposes changed.
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T H E L I M I TAT I O N S O F L I G H T E R - T H A N - A I R T RA N S P O RT. For a
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A measure of inertia, indicating
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The airship enjoyed a brief resurgence of interest during World War II, though purely as a surveillance craft for the United States military. In the period after the war, the U.S. Navy hired the Goodyear Tire and Rubber Company to produce airships, and as a result of this relationship Goodyear created the most visible airship since the Graf Zeppelin and the Hindenburg: the Goodyear Blimp. B L I M P S A N D B A L LO O N S : O N T H E C U T T I N G E D G E ? . The blimp,
known to viewers of countless sporting events, is much better-suited than a plane or helicopter to providing TV cameras with an aerial view of a stadium—and advertisers with a prominent billboard. Military forces and science communities have also found airships useful for unexpected purposes. Their virtual invisibility with regard to radar has reinvigorated interest in blimps on the part of the U.S. Department of Defense, which has discussed plans to use airships as radar platforms in a larger Strategic Air Initiative. In addition, French scientists have used airships for studying rain forest treetops or canopies. Balloons have played a role in aiding space exploration, which is emblematic of the relationship between lighter-than-air transport and more advanced means of flight. In 1961, Malcolm D. Ross and Victor A. Prother of the U.S. Navy set the balloon altitude record with a height of 113,740 ft (34,668 m.) The technology that enabled their survival at more than 21 mi (33.8 km) in the air was later used in creating life-support systems for astronauts. Balloon astronomy provides some of the clearest images of the cosmos: telescopes mounted on huge, unmanned balloons at elevations as high as 120,000 ft (35,000 m)—far above the dust
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and smoke of Earth—offer high-resolution images. Balloons have even been used on other planets: for 46 hours in 1985, two balloons launched by the unmanned Soviet expedition to Venus collected data from the atmosphere of that planet.
Buoyancy
American scientists have also considered a combination of a large hot-air balloon and a smaller helium-filled balloon for gathering data on the surface and atmosphere of Mars during expeditions to that planet. As the air balloon is heated by the Sun’s warmth during the day, it would ascend to collect information on the atmosphere. (In fact the “air” heated would be from the atmosphere of Mars, which is composed primarily of carbon dioxide.) Then at night when Mars cools, the air balloon would lose its buoyancy and descend, but the helium balloon would keep it upright while it collected data from the ground. WHERE TO LEARN MORE “Buoyancy” (Web site). (March 12, 2001). “Buoyancy” (Web site). (March 12, 2001). “Buoyancy Basics” Nova/PBS (Web site). (March 12, 2001). Challoner, Jack. Floating and Sinking. Austin, TX: Raintree Steck-Vaughn, 1997. Cobb, Allan B. Super Science Projects About Oceans. New York: Rosen, 2000. Gibson, Gary. Making Things Float and Sink. Illustrated by Tony Kenyon. Brookfield, CT: Copper Beeck Brooks, 1995. Taylor, Barbara. Liquid and Buoyancy. New York: Warwick Press, 1990.
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S C I E N C E O F E V E RY DAY T H I N G S real-life Physics
S TAT I C S S TAT I C S A N D E Q U I L I B R I U M PRESSURE ELASTICITY
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Statics and Equilibrium
S TAT I C S A N D EQUILIBRIUM
CONCEPT Statics, as its name suggests, is the study of bodies at rest. Those bodies may be acted upon by a variety of forces, but as long as the lines of force meet at a common point and their vector sum is equal to zero, the body itself is said to be in a state of equilibrium. Among the topics of significance in the realm of statics is center of gravity, which is relatively easy to calculate for simple bodies, but much more of a challenge where aircraft or ships are concerned. Statics is also applied in analysis of stress on materials—from a picture frame to a skyscraper.
HOW IT WORKS Equilibrium and Vectors Essential to calculations in statics is the use of vectors, or quantities that have both magnitude and direction. By contrast, a scalar has only magnitude. If one says that a certain piece of property has an area of one acre, there is no directional component. Nor is there a directional component involved in the act of moving the distance of 1 mi (1.6 km), since no statement has been made as to the direction of that mile. On the other hand, if someone or something experiences a displacement, or change in position, of 1 mi to the northeast, then what was a scalar description has been placed in the language of vectors. Not only are mass and speed (as opposed to velocity) considered scalars; so too is time. This might seem odd at first glance, but—on Earth at least, and outside any special circumstances posed by quantum mechanics—time can only move forward. Hence, direction is not a factor. By
S C I E N C E O F E V E RY DAY T H I N G S
contrast, force, equal to mass multiplied by acceleration, is a vector. So too is weight, a specific type of force equal to mass multiplied by the acceleration due to gravity (32 ft or [9.8 m] / sec2). Force may be in any direction, but the direction of weight is always downward along a vertical plane. V E C T O R S U M S . Adding scalars is simple, since it involves mere arithmetic. The addition of vectors is more challenging, and usually requires drawing a diagram, for instance, if trying to obtain a vector sum for the velocity of a car that has maintained a uniform speed, but has changed direction several times.
One would begin by representing each vector as an arrow on a graph, with the tail of each vector at the head of the previous one. It would then be possible to draw a vector from the tail of the first to the head of the last. This is the sum of the vectors, known as a resultant, which measures the net change. Suppose, for instance, that a car travels north 5 mi (8 km), east 2 mi (3.2 km), north 3 mi (4.8 km), east 3 mi, and finally south 3 mi. One must calculate its net displacement—in other words, not the sum of all the miles it has traveled, but the distance and direction between its starting point and its end point. First, one draws the vectors on a piece of graph paper, using a logical system that treats the y axis as the north-south plane, and the x axis as the east-west plane. Each vector should be in the form of an arrow pointing in the appropriate direction. Having drawn all the vectors, the only remaining one is between the point where the car’s journey ends and the starting point—that is, the resultant. The number of sides to the
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resulting shape is always one more than the number of vectors being added; the final side is the resultant. In this particular case, the answer is fairly easy. Because the car traveled north 5 mi and ultimately moved east by 5 mi, returning to a position of 5 mi north, the segment from the resultant forms the hypotenuse of an equilateral (that is, all sides equal) right triangle. By applying the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides, one quickly arrives at a figure of 7.07 m (11.4 km) in a northeasterly direction. This is the car’s net displacement.
Calculating Force and Tension in Equilibrium Using vector sums, it is possible to make a number of calculations for objects in equilibrium, but these calculations are somewhat more challenging than those in the car illustration. One form of equilibrium calculation involves finding tension, or the force exerted by a supporting object on an object in equilibrium—a force that is always equal to the amount of weight supported. (Another way of saying this is that if the tension on the supporting object is equal to the weight it supports, then the supported object is in equilibrium.) In calculations for tension, it is best to treat the supporting object—whether it be a rope, picture hook, horizontal strut or some other item— as though it were weightless. One should begin by drawing a free-body diagram, a sketch showing all the forces acting on the supported object. It is not necessary to show any forces (other than weight) that the object itself exerts, since those do not contribute to its equilibrium. R E S O LV I N G X A N D Y C O M P O N E N T S . As with the distance vector graph
discussed above, next one must equate these forces to the x and y axes. The distance graph example involved only segments already parallel to x and y, but suppose—using the numbers already discussed—the graph had called for the car to move in a perfect 45°-angle to the northeast along a distance of 7.07 mi. It would then have been easy to resolve this distance into an x component (5 mi east) and a y component (5 mi north)—which are equal to the other two sides of the equilateral triangle.
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This resolution of x and y components is more challenging for calculations involving equilibrium, but once one understands the principle involved, it is easy to apply. For example, imagine a box suspended by two ropes, neither of which is at a 90°-angle to the box. Instead, each rope is at an acute angle, rather like two segments of a chain holding up a sign. The x component will always be the product of tension (that is, weight) multiplied by the cosine of the angle. In a right triangle, one angle is always equal to 90°, and thus by definition, the other two angles are acute, or less than 90°. The angle of either rope is acute, and in fact, the rope itself may be considered the hypotenuse of an imaginary triangle. The base of the triangle is the x axis, and the angle between the base and the hypotenuse is the one under consideration. Hence, we have the use of the cosine, which is the ratio between the adjacent leg (the base) of the triangle and the hypotenuse. Regardless of the size of the triangle, this figure is a constant for any particular angle. Likewise, to calculate the y component of the angle, one uses the sine, or the ratio between the opposite side and the hypotenuse. Keep in mind, once again, that the adjacent leg for the angle is by definition the same as the x axis, just as the opposite leg is the same as the y axis. The cosine (abbreviated cos), then, gives the x component of the angle, as the sine (abbreviated sin) does the y component.
REAL-LIFE A P P L I C AT I O N S Equilibrium and Center of Gravity in Real Objects Before applying the concept of vector sums to matters involving equilibrium, it is first necessary to clarify the nature of equilibrium itself—what it is and what it is not. Earlier it was stated that an object is in equilibrium if the vector sum of the forces acting on it are equal to zero—as long as those forces meet at a common point. This is an important stipulation, because it is possible to have lines of force that cancel one another out, but nonetheless cause an object to move. If a force of a certain magnitude is applied to the right side of an object, and a line of force of equal magnitude meets it exactly from the left, then the object is in equilibrium. But if the line of
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force from the right is applied to the top of the object, and the line of force from the left to the bottom, then they do not meet at a common point, and the object is not in equilibrium. Instead, it is experiencing torque, which will cause it to rotate.
Statics and Equilibrium
VA R I E T I E S O F E Q U I L I B R I U M .
There are two basic conditions of equilibrium. The term “translational equilibrium” describes an object that experiences no linear (straightline) acceleration; on the other hand, an object experiencing no rotational acceleration (a component of torque) is said to be in rotational equilibrium. Typically, an object at rest in a stable situation experiences both linear and rotational equilibrium. But equilibrium itself is not necessarily stable. An empty glass sitting on a table is in stable equilibrium: if it were tipped over slightly— that is, with a force below a certain threshold— then it would return to its original position. This is true of a glass sitting either upright or upsidedown. Now imagine if the glass were somehow propped along the edge of a book sitting on the table, so that the bottom of the glass formed the hypotenuse of a triangle with the table as its base and the edge of the book as its other side. The glass is in equilibrium now, but unstable equilibrium, meaning that a slight disturbance—a force from which it could recover in a stable situation—would cause it to tip over. If, on the other hand, the glass were lying on its side, then it would be in a state of neutral equilibrium. In this situation, the application of force alongside the glass will not disturb its equilibrium. The glass will not attempt to seek stable equilibrium, nor will it become more unstable; rather, all other things being equal, it will remain neutral. C E N T E R O F G RAV I T Y. Center of gravity is the point in an object at which the weight below is equal to the weight above, the weight in front equal to the weight behind, and the weight to the left equal to the weight on the right. Every object has just one center of gravity, and if the object is suspended from that point, it will not rotate.
A
GLASS SITTING ON A TABLE IS IN A STATE OF STABLE
EQUILIBRIUM. (Photograph by John Wilkes Studio/Corbis. Repro-
duced by permission.)
ing bell in an Olympic competition, the swimmer’s center of gravity is to the front—some distance from his or her chest. This is appropriate, since the objective is to get into the water as quickly as possible once the race starts. By contrast, a sprinter’s stance places the center of gravity well within the body, or at least firmly surrounded by the body—specifically, at the place where the sprinter’s rib cage touches the forward knee. This, too, fits with the needs of the athlete in the split-second following the starting gun. The sprinter needs to have as much traction as possible to shoot forward, rather than forward and downward, as the swimmer does.
Tension Calculations
One interesting aspect of an object’s center of gravity is that it does not necessarily have to be within the object itself. When a swimmer is poised in a diving stance, as just before the start-
In the earlier discussion regarding the method of calculating tension in equilibrium, two of the three steps of this process were given: first, draw a free-body diagram, and second, resolve the forces into x and y components. The third step is to set the force components along each axis equal to zero—since, if the object is truly in equilibrium, the sum of forces will indeed equal zero. This makes it possible, finally, to solve the equations for the net tension.
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Statics and Equilibrium
IN
THE STARTING BLOCKS, A SPRINTER’S CENTER OF GRAVITY IS ALIGNED ALONG THE RIB CAGE AND FORWARD KNEE,
THUS MAXIMIZING THE RUNNER’S ABILITY TO SHOOT FORWARD OUT OF THE BLOCKS. (Photograph by Ronnen Eshel/Corbis.
Reproduced by permission.)
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Imagine a picture that weighs 100 lb (445 N) suspended by a wire, the left side of which may be called segment A, and the right side segment B. The wire itself is not perfectly centered on the picture-hook: A is at a 30° angle, and B on a 45° angle. It is now possible to find the tension on both.
However, the y-force formula is somewhat different than for x: since weight is exerted along the y axis, it must be subtracted. Thus, the formula for the y component of force is Fy = TAy + TBy–w = 0. (Note that the y components of both A and B are positive: by definition, this must be so for an object suspended from some height.)
First, one can resolve the horizontal components by the formula Fx = TBx + TAx = 0, meaning that the x component of force is equal to the product of tension for the x component of B, added to the product of tension for the x component of A, which in turn is equal to zero. Given the 30°-angle of A, Ax = 0.866, which is the cosine of 30°. Bx is equal to cos 45°, which equals 0.707. (Recall the earlier discussion of distance, in which a square with sides 5 mi long was described: its hypotenuse was 7.07 mi, and 5/7.07 = 0.707.)
Substituting the value for TB obtained above, (1.22)TA, makes it possible to complete the equation. Since the sine of 30° is 0.5, and the sine of 45° is 0.707—the same value as its cosine—one can state the equation thus: TA(0.5) + (1.22)TA(0.707)–100 lb = 0. This can be restated as TA(0.5 + (1.22 • 0.707)) = TA(1.36) = 100 lb. Hence, TA = (100 lb/1.36) = 73.53 lb. Since TB = (1.22)TA, this yields a value of 89.71 lb for TB. Note that TA and TB actually add up to considerably more than 100 lb. This, however, is known as an algebraic sum—which is very similar to an arithmetic sum, inasmuch as algebra is simply a generalization of arithmetic. What is important here, however, is the vector sum, and the vector sum of TA and TB equals 100 lb.
Because A goes off to the left from the point at which the picture is attached to the wire, this places it on the negative portion of the x axis. Therefore, the formula can now be restated as TB(0.707)–TA(0.866) = 0. Solving for TB reveals that it is equal to TA(0.866/0.707) = (1.22)TA. This will be substituted for TB in the formula for the total force along the y component.
lengthy calculation for center of gravity, we will explain the principles behind such calculations.
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C A L C U L AT I N G CENTER OF G RAV I T Y. Rather than go through another
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It is easy to calculate the center of gravity for a regular shape, such as a cube or sphere—assuming, of course, that the mass and therefore the weight is evenly distributed throughout the object. In such a case, the center of gravity is the geometric center. For an irregular object, however, center of gravity must be calculated. An analogy regarding United States demographics may help to highlight the difference between geometric center and center of gravity. The geographic center of the U.S., which is analogous to geometric center, is located near the town of Castle Rock in Butte County, South Dakota. (Because Alaska and Hawaii are so far west of the other 48 states—and Alaska, with its great geographic area, is far to the north—the data is skewed in a northwestward direction. The geographic center of the 48 contiguous states is near Lebanon, in Smith County, Kansas.) The geographic center, like the geometric center of an object, constitutes a sort of balance point in terms of physical area: there is as much U.S. land to the north of Castle Rock, South Dakota, as to the south, and as much to the east as to the west. The population center is more like the center of gravity, because it is a measure, in some sense, of “weight” rather than of volume— though in this case concentration of people is substituted for concentration of weight. Put another way, the population center is the balance point of the population, if it were assumed that every person weighed the same amount. Naturally, the population center has been shifting westward ever since the first U.S. census in 1790, but it is still skewed toward the east: though there is far more U.S. land west of the Mississippi River, there are still more people east of it. Hence, according to the 1990 U.S. census, the geographic center is some 1,040 mi (1,664 km) in a southeastward direction from the population center: just northwest of Steelville, Missouri, and a few miles west of the Mississippi. The United States, obviously, is an “irregular object,” and calculations for either its geographic or its population center represent the mastery of numerous mathematical principles. How, then, does one find the center of gravity for a much smaller irregular object? There are a number of methods, all rather complex. To measure center of gravity in purely physical terms, there are a variety of techniques relat-
S C I E N C E O F E V E RY DAY T H I N G S
ing to the shape of the object to be measured. There is also a mathematical formula, which involves first treating the object as a conglomeration of several more easily measured objects. Then the x components for the mass of each “sub-object” can be added, and divided by the combined mass of the object as a whole. The same can be done for the y components.
Statics and Equilibrium
Using Equilibrium Calculations One reason for making center of gravity calculations is to ensure that the net force on an object passes through that center. If it does not, the object will start to rotate—and for an airplane, for instance, this could be disastrous. Hence, the builders and operators of aircraft make exceedingly detailed, complicated calculations regarding center of gravity. The same is true for shipbuilders and shipping lines: if a ship’s center of gravity is not vertically aligned with the focal point of the buoyant force exerted on it by the water, it may well sink. In the case of ships and airplanes, the shapes are so irregular that center of gravity calculations require intensive analyses of the many components. Hence, a number of companies that supply measurement equipment to the aerospace and maritime industries offer center of gravity measurement instruments that enable engineers to make the necessary calculations. On dry ground, calculations regarding equilibrium are likewise quite literally a life and death matter. In the earlier illustration, the object in equilibrium was merely a picture hanging from a wire—but what if it were a bridge or a building? The results of inaccurate estimates of net force could affect the lives of many people. Hence, structural engineers make detailed analyses of stress, once again using series of calculations that make the picture-frame illustration above look like the simplest of all arithmetic problems.
WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. “Determining Center of Gravity” National Aeronautics and Space Administration (Web site). (March 19, 2001).
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Statics and Equilibrium
KEY TERMS A change in velocity.
ACCELERATION:
SCALAR:
The point on
only magnitude, with no specific direction.
an object at which the total weights on
Mass, time, and speed are all scalars. The
either side of all axes (x, y, and z) are iden-
opposite of a scalar is a vector.
tical. Each object has just one center of
SINE:
gravity, and if it is suspended from that
in a right triangle, the sine (abbreviated
point, it will be in a state of perfect rota-
sin) is the ratio between the opposite leg
tional equilibrium.
and the hypotenuse. Regardless of the size
CENTER OF GRAVITY:
COSINE:
For an acute (less than 90°)
angle in a right triangle, the cosine (abbre-
For an acute (less than 90°) angle
of the triangle, this figure is a constant for any particular angle.
viated cos) is the ratio between the adjacent leg and the hypotenuse. Regardless of the size of the triangle, this figure is a constant for any particular angle.
EQUILIBRIUM:
STATICS:
The study of bodies at rest.
Those bodies may be acted upon by a variety of forces, but as long as the vector sum for all those lines of force is equal to zero,
Change in position.
DISPLACEMENT:
A state in which vector
the body itself is said to be in a state of equilibrium.
sum for all lines of force on an object is equal to zero. An object that experiences no linear acceleration is said to be in translational equilibrium, and one that experiences no rotational acceleration is referred
TENSION:
The force exerted by a sup-
porting object on an object in equilibrium—a force that is always equal to the amount of weight supported. A quantity that possesses
to as being in rotational equilibrium. An
VECTOR:
object may also be in stable, unstable, or
both magnitude and direction. Force is a
neutral equilibrium.
vector; so too is acceleration, a component
FORCE:
The product of mass multi-
FREE-BODY
of force; and likewise weight, a variety of force. The opposite of a vector is a scalar.
plied by acceleration. DIAGRAM:
A sketch
VECTOR SUM:
A calculation, made by
showing all the outside forces acting on an
different methods according to the factor
object in equilibrium.
being analyzed—for instance, velocity or
HYPOTENUSE:
In a right triangle, the
side opposite the right angle. RESULTANT:
The sum of two or more
force—that yields the net result of all the vectors applied in a particular situation. VELOCITY:
The speed of an object in a
vectors, which measures the net change in
particular direction. Velocity is thus a vec-
distance and direction.
tor quantity.
RIGHT TRIANGLE:
138
A quantity that possesses
A triangle that
WEIGHT:
A measure of the gravitation-
includes a right (90°) angle. The other
al force on an object; the product of mass
two angles are, by definition, acute, or less
multiplied by the acceleration due to
than 90°.
gravity.
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“Equilibrium and Statics” (Web site). (March 19, 2001). “Exploratorium Snack: Center of Gravity.” The Exploratorium (Web site). (March 19, 2001). Faivre d’Arcier, Marima. What Is Balance? Illustrated by Volker Theinhardt. New York: Viking Kestrel, 1986. Taylor, Barbara. Weight and Balance. Photographs by Peter Millard. New York: F. Watts, 1990.
S C I E N C E O F E V E RY DAY T H I N G S
“Where Is Your Center of Gravity?” The K-8 Aeronautics Internet Textbook (Web site). (March 19, 2001).
Statics and Equilibrium
Wood, Robert W. Mechanics Fundamentals. Illustrated by Bill Wright. Philadelphia, PA: Chelsea House, 1997. Zubrowski, Bernie. Mobiles: Building and Experimenting with Balancing Toys. Illustrated by Roy Doty. New York: Morrow Junior Books, 1993.
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PRESSURE Pressure
CONCEPT Pressure is the ratio of force to the surface area over which it is exerted. Though solids exert pressure, the most interesting examples of pressure involve fluids—that is, gases and liquids—and in particular water and air. Pressure plays a number of important roles in daily life, among them its function in the operation of pumps and hydraulic presses. The maintenance of ordinary air pressure is essential to human health and well-being: the body is perfectly suited to the ordinary pressure of the atmosphere, and if that pressure is altered significantly, a person may experience harmful or even fatal side-effects.
HOW IT WORKS Force and Surface Area When a force is applied perpendicular to a surface area, it exerts pressure on that surface equal to the ratio of F to A, where F is the force and A the surface area. Hence, the formula for pressure (p) is p = F/A. One interesting consequence of this ratio is the fact that pressure can increase or decrease without any change in force—in other words, if the surface becomes smaller, the pressure becomes larger, and vice versa. If one cheerleader were holding another cheerleader on her shoulders, with the girl above standing on the shoulder blades of the girl below, the upper girl’s feet would exert a certain pressure on the shoulders of the lower girl. This pressure would be equal to the upper girl’s weight (F, which in this case is her mass multiplied by the downward acceleration due to gravity) divided by the surface area of her feet. Suppose, then, that
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the upper girl executes a challenging acrobatic move, bringing her left foot up to rest against her right knee, so that her right foot alone exerts the full force of her weight. Now the surface area on which the force is exerted has been reduced to half its magnitude, and thus the pressure on the lower girl’s shoulder is twice as great. For the same reason—that is, that reduction of surface area increases net pressure—a welldelivered karate chop is much more effective than an open-handed slap. If one were to slap a board squarely with one’s palm, the only likely result would be a severe stinging pain on the hand. But if instead one delivered a blow to the board, with the hand held perpendicular—provided, of course, one were an expert in karate— the board could be split in two. In the first instance, the area of force exertion is large and the net pressure to the board relatively small, whereas in the case of the karate chop, the surface area is much smaller—and hence, the pressure is much larger. Sometimes, a greater surface area is preferable. Thus, snowshoes are much more effective for walking in snow than ordinary shoes or boots. Ordinary footwear is not much larger than the surface of one’s foot, perfectly appropriate for walking on pavement or grass. But with deep snow, this relatively small surface area increases the pressure on the snow, and causes one’s feet to sink. The snowshoe, because it has a surface area significantly larger than that of a regular shoe, reduces the ratio of force to surface area and therefore, lowers the net pressure. The same principle applies with snow skis and water skis. Like a snowshoe, a ski makes it possible for the skier to stay on the surface of the
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snow, but unlike a snowshoe, a ski is long and thin, thus enabling the skier to glide more effectively down a snow-covered hill. As for skiing on water, people who are experienced at this sport can ski barefoot, but it is tricky. Most beginners require water skis, which once again reduce the net pressure exerted by the skier’s weight on the surface of the water.
Pressure
Measuring Pressure Pressure is measured by a number of units in the English and metric—or, as it is called in the scientific community, SI—systems. Because p = F/A, all units of pressure represent some ratio of force to surface area. The principle SI unit is called a pascal (Pa), or 1 N/m2. A newton (N), the SI unit of force, is equal to the force required to accelerate 1 kilogram of mass at a rate of 1 meter per second squared. Thus, a Pascal is equal to the pressure of 1 newton over a surface area of 1 square meter. In the English or British system, pressure is measured in terms of pounds per square inch, abbreviated as lbs./in2. This is equal to 6.89 • 103 Pa, or 6,890 Pa. Scientists—even those in the United States, where the British system of units prevails—prefer to use SI units. However, the British unit of pressure is a familiar part of an American driver’s daily life, because tire pressure in the United States is usually reckoned in terms of pounds per square inch. (The recommended tire pressure for a mid-sized car is typically 30-35 lb/in2.) Another important measure of pressure is the atmosphere (atm), which the average pressure exerted by air at sea level. In English units, this is equal to 14.7 lbs./in2, and in SI units to 1.013 • 105 Pa—that is, 101,300 Pa. There are also two other specialized units of pressure measurement in the SI system: the bar, equal to 105 Pa, and the torr, equal to 133 Pa. Meteorologists, scientists who study weather patterns, use the millibar (mb), which, as its name implies, is equal to 0.001 bars. At sea level, atmospheric pressure is approximately 1,013 mb. T H E B A R O M E T E R. The torr, once known as the “millimeter of mercury,” is equal to the pressure required to raise a column of mercury (chemical symbol Hg) 1 mm. It is named for the Italian physicist Evangelista Torricelli (1608-1647), who invented the barometer, an instrument for measuring atmospheric pressure.
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IN
THE INSTANCE OF ONE CHEERLEADER STANDING ON
ANOTHER’S EXERT
SHOULDERS,
DOWNWARD
SHOULDERS.
THE
THE
PRESSURE
CHEERLEADER’S ON
HER
FEET
PARTNER’S
PRESSURE IS EQUAL TO THE GIRL’S
WEIGHT DIVIDED BY THE SURFACE AREA OF HER FEET.
(Photograph by James L. Amos/Corbis. Reproduced by permission.)
The barometer, constructed by Torricelli in 1643, consisted of a long glass tube filled with mercury. The tube was open at one end, and turned upside down into a dish containing more mercury: hence, the open end was submerged in mercury while the closed end at the top constituted a vacuum—that is, an area in which the pressure is much lower than 1 atm. The pressure of the surrounding air pushed down on the surface of the mercury in the bowl, while the vacuum at the top of the tube provided an area of virtually no pressure, into which the mercury could rise. Thus, the height to which the mercury rose in the glass tube represented normal air pressure (that is, 1 atm.) Torricelli discovered that at standard atmospheric pressure, the column of mercury rose to 760 millimeters. The value of 1 atm was thus established as equal to the pressure exerted on a column of mercury 760 mm high at a temperature of 0°C (32°F). Furthermore, Torricelli’s invention eventually became a fixture both of scientific labora-
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both cases, the force is always perpendicular to the walls.
Pressure
In each of these three characteristics, it is assumed that the container is finite: in other words, the fluid has nowhere else to go. Hence, the second statement: the external pressure exerted on the fluid is transmitted uniformly. Note that the preceding statement was qualified by the term “external”: the fluid itself exerts pressure whose force component is equal to its weight. Therefore, the fluid on the bottom has much greater pressure than the fluid on the top, due to the weight of the fluid above it.
THE
AIR PRESSURE ON TOP OF
MOUNT EVEREST,
THE
WORLD’S TALLEST PEAK, IS VERY LOW, MAKING BREATHING DIFFICULT.
MOST CLIMBERS WHO ATTEMPT TO SCALE EVEREST THUS CARRY OXYGEN TANKS WITH THEM. SHOWN HERE IS JIM WHITTAKER, THE FIRST AMERICAN TO CLIMB EVEREST. (Photograph by Galen Rowell/Corbis. Reproduced by permission.)
tories and of households. Since changes in atmospheric pressure have an effect on weather patterns, many home indoor-outdoor thermometers today also include a barometer.
Pressure and Fluids In terms of physics, both gases and liquids are referred to as fluids—that is, substances that conform to the shape of their container. Air pressure and water pressure are thus specific subjects under the larger heading of “fluid pressure.” A fluid responds to pressure quite differently than a solid does. The density of a solid makes it resistant to small applications of pressure, but if the pressure increases, it experiences tension and, ultimately, deformation. In the case of a fluid, however, stress causes it to flow rather than to deform.
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Third, the pressure on any small surface of the fluid is the same, regardless of that surface’s orientation. In other words, an area of fluid perpendicular to the container walls experiences the same pressure as one parallel or at an angle to the walls. This may seem to contradict the first principle, that the force is perpendicular to the walls of the container. In fact, force is a vector quantity, meaning that it has both magnitude and direction, whereas pressure is a scalar, meaning that it has magnitude but no specific direction.
REAL-LIFE A P P L I C AT I O N S Pascal’s Principle and the Hydraulic Press The three characteristics of fluid pressure described above have a number of implications and applications, among them, what is known as Pascal’s principle. Like the SI unit of pressure, Pascal’s principle is named after Blaise Pascal (1623-1662), a French mathematician and physicist who formulated the second of the three statements: that the external pressure applied on a fluid is transmitted uniformly throughout the entire body of that fluid. Pascal’s principle became the basis for one of the important machines ever developed, the hydraulic press.
There are three significant characteristics of the pressure exerted on fluids by a container. First of all, a fluid in a container experiencing no external motion exerts a force perpendicular to the walls of the container. Likewise, the container walls exert a force on the fluid, and in
A simple hydraulic press of the variety used to raise a car in an auto shop typically consists of two large cylinders side by side. Each cylinder contains a piston, and the cylinders are connected at the bottom by a channel containing fluid. Valves control flow between the two cylinders. When one applies force by pressing down the piston in one cylinder (the input cylinder), this yields a uniform pressure that causes output in
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the second cylinder, pushing up a piston that raises the car. In accordance with Pascal’s principle, the pressure throughout the hydraulic press is the same, and will always be equal to the ratio between force and pressure. As long as that ratio is the same, the values of F and A may vary. In the case of an auto-shop car jack, the input cylinder has a relatively small surface area, and thus, the amount of force that must be applied is relatively small as well. The output cylinder has a relatively large surface area, and therefore, exerts a relatively large force to lift the car. This, combined with the height differential between the two cylinders (discussed in the context of mechanical advantage elsewhere in this book), makes it possible to lift a heavy automobile with a relatively small amount of effort. T H E H Y D RAU L I C RA M . The car
jack is a simple model of the hydraulic press in operation, but in fact, Pascal’s principle has many more applications. Among these is the hydraulic ram, used in machines ranging from bulldozers to the hydraulic lifts used by firefighters and utility workers to reach heights. In a hydraulic ram, however, the characteristics of the input and output cylinders are reversed from those of a car jack. The input cylinder, called the master cylinder, has a large surface area, whereas the output cylinder (called the slave cylinder) has a small surface area. In addition—though again, this is a factor related to mechanical advantage rather than pressure, per se—the master cylinder is short, whereas the slave cylinder is tall. Owing to the larger surface area of the master cylinder compared to that of the slave cylinder, the hydraulic ram is not considered efficient in terms of mechanical advantage: in other words, the force input is much greater than the force output. Nonetheless, the hydraulic ram is as wellsuited to its purpose as a car jack. Whereas the jack is made for lifting a heavy automobile through a short vertical distance, the hydraulic ram carries a much lighter cargo (usually just one person) through a much greater vertical range— to the top of a tree or building, for instance.
Exploiting Pressure Differences
tainer, a pump allows the fluid to escape. Specifically, the pump utilizes a pressure difference, causing the fluid to move from an area of higher pressure to one of lower pressure. A very simple example of this is a siphon hose, used to draw petroleum from a car’s gas tank. Sucking on one end of the hose creates an area of low pressure compared to the relatively high-pressure area of the gas tank. Eventually, the gasoline will come out of the low-pressure end of the hose. (And with luck, the person siphoning will be able to anticipate this, so that he does not get a mouthful of gasoline!)
Pressure
The piston pump, more complex, but still fairly basic, consists of a vertical cylinder along which a piston rises and falls. Near the bottom of the cylinder are two valves, an inlet valve through which fluid flows into the cylinder, and an outlet valve through which fluid flows out of it. On the suction stroke, as the piston moves upward, the inlet valve opens and allows fluid to enter the cylinder. On the downstroke, the inlet valve closes while the outlet valve opens, and the pressure provided by the piston on the fluid forces it through the outlet valve. One of the most obvious applications of the piston pump is in the engine of an automobile. In this case, of course, the fluid being pumped is gasoline, which pushes the pistons by providing a series of controlled explosions created by the spark plug’s ignition of the gas. In another variety of piston pump—the kind used to inflate a basketball or a bicycle tire—air is the fluid being pumped. Then there is a pump for water, which pumps drinking water from the ground It may also be used to remove desirable water from an area where it is a hindrance, for instance, in the bottom of a boat. BERNOULLI’S
PRINCIPLE.
Though Pascal provided valuable understanding with regard to the use of pressure for performing work, the thinker who first formulated general principles regarding the relationship between fluids and pressure was the Swiss mathematician and physicist Daniel Bernoulli (1700-1782). Bernoulli is considered the father of fluid mechanics, the study of the behavior of gases and liquids at rest and in motion.
PU M P S . A pump utilizes Pascal’s principle, but instead of holding fluid in a single con-
While conducting experiments with liquids, Bernoulli observed that when the diameter of a pipe is reduced, the water flows faster. This suggested to him that some force must be acting
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upon the water, a force that he reasoned must arise from differences in pressure. Specifically, the slower-moving fluid in the wider area of pipe had a greater pressure than the portion of the fluid moving through the narrower part of the pipe. As a result, he concluded that pressure and velocity are inversely related—in other words, as one increases, the other decreases. Hence, he formulated Bernoulli’s principle, which states that for all changes in movement, the sum of static and dynamic pressure in a fluid remain the same. A fluid at rest exerts static pressure, which is commonly meant by “pressure,” as in “water pressure.” As the fluid begins to move, however, a portion of the static pressure—proportional to the speed of the fluid—is converted to what is known as dynamic pressure, or the pressure of movement. In a cylindrical pipe, static pressure is exerted perpendicular to the surface of the container, whereas dynamic pressure is parallel to it. According to Bernoulli’s principle, the greater the velocity of flow in a fluid, the greater the dynamic pressure and the less the static pressure: in other words, slower-moving fluid exerts greater pressure than faster-moving fluid. The discovery of this principle ultimately made possible the development of the airplane. As fluid moves from a wider pipe to a narrower one, the volume of that fluid that moves a given distance in a given time period does not change. But since the width of the narrower pipe is smaller, the fluid must move faster (that is, with greater dynamic pressure) in order to move the same amount of fluid the same distance in the same amount of time. One way to illustrate this is to observe the behavior of a river: in a wide, unconstricted region, it flows slowly, but if its flow is narrowed by canyon walls, then it speeds up dramatically. Bernoulli’s principle ultimately became the basis for the airfoil, the design of an airplane’s wing when seen from the end. An airfoil is shaped like an asymmetrical teardrop laid on its side, with the “fat” end toward the airflow. As air hits the front of the airfoil, the airstream divides, part of it passing over the wing and part passing under. The upper surface of the airfoil is curved, however, whereas the lower surface is much straighter.
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under the wing. Since fluids have a tendency to compensate for all objects with which they come into contact, the air at the top will flow faster to meet with air at the bottom at the rear end of the wing. Faster airflow, as demonstrated by Bernoulli, indicates lower pressure, meaning that the pressure on the bottom of the wing keeps the airplane aloft.
Buoyancy and Pressure One hundred and twenty years before the first successful airplane flight by the Wright brothers in 1903, another pair of brothers—the Montgolfiers of France—developed another means of flight. This was the balloon, which relied on an entirely different principle to get off the ground: buoyancy, or the tendency of an object immersed in a fluid to float. As with Bernoulli’s principle, however, the concept of buoyancy is related to pressure. In the third century B.C., the Greek mathematician, physicist, and inventor Archimedes (c. 287-212 B.C.) discovered what came to be known as Archimedes’s principle, which holds that the buoyant force of an object immersed in fluid is equal to the weight of the fluid displaced by the object. This is the reason why ships float: because the buoyant, or lifting, force of them is less than equal to the weight of the water they displace. The hull of a ship is designed to displace or move a quantity of water whose weight is greater than that of the vessel itself. The weight of the displaced water—that is, its mass multiplied by the downward acceleration caused by gravity—is equal to the buoyant force that the ocean exerts on the ship. If the ship weighs less than the water it displaces, it will float; but if it weighs more, it will sink. The factors involved in Archimedes’s principle depend on density, gravity, and depth rather than pressure. However, the greater the depth within a fluid, the greater the pressure that pushes against an object immersed in the fluid. Moreover, the overall pressure at a given depth in a fluid is related in part to both density and gravity, components of buoyant force.
As a result, the air flowing over the top has a greater distance to cover than the air flowing
The pressure that a fluid exerts on the bottom of its container is equal to dgh, where d is density, g the acceleration due to gravity, and h the depth of the container. For any portion of the fluid, h is equal to its depth within the container, meaning that
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P R E SS U R E
AND
DEPTH.
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Pressure
THIS
YELLOW DIVING SUIT, CALLED A
“NEWT
SUIT,” IS SPECIALLY DESIGNED TO WITHSTAND THE ENORMOUS WATER
PRESSURE THAT EXISTS AT LOWER DEPTHS OF THE OCEAN. (Photograph by Amos Nachoum/Corbis. Reproduced by permission.)
the deeper one goes, the greater the pressure. Furthermore, the total pressure within the fluid is equal to dgh + pexternal, where pexternal is the pressure exerted on the surface of the fluid. In a piston-and-cylinder assembly, this pressure comes from the piston, but in water, the pressure comes from the atmosphere. In this context, the ocean may be viewed as a type of “container.” At its surface, the air exerts downward pressure equal to 1 atm. The density of the water itself is uniform, as is the downward acceleration due to gravity; the only variable, then, is h, or the distance below the surface. At the deepest reaches of the ocean, the pressure is incredibly great—far more than any human being could endure. This vast amount of pressure pushes upward, resisting the downward pressure of objects on its surface. At the same time, if a boat’s weight is dispersed properly along its hull, the ship maximizes area and minimizes force, thus exerting a downward pressure on the surface of the water that is less than the upward pressure of the water itself. Hence, it floats.
water, but to float in the sky with a craft lighter than air. The particulars of this achievement are discussed elsewhere, in the context of buoyancy; but the topic of lighter-than-air flight suggests another concept that has been alluded to several times throughout this essay: air pressure. Just as water pressure is greatest at the bottom of the ocean, air pressure is greatest at the surface of the Earth—which, in fact, is at the bottom of an “ocean” of air. Both air and water pressure are examples of hydrostatic pressure—the pressure that exists at any place in a body of fluid due to the weight of the fluid above. In the case of air pressure, air is pulled downward by the force of Earth’s gravitation, and air along the surface has greater pressure due to the weight (a function of gravity) of the air above it. At great heights above Earth’s surface, however, the gravitational force is diminished, and, thus, the air pressure is much smaller.
A I R P R E SS U R E . The Montgolfiers used the principle of buoyancy not to float on the
In ordinary experience, a person’s body is subjected to an impressive amount of pressure. Given the value of atmospheric pressure discussed earlier, if one holds out one’s hand—assuming that the surface is about 20 in2 (0.129 m2)—the force of the air resting on it is nearly 300 lb (136 kg)! How is it, then, that one’s
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THE RESPONSE TO CHANGES I N A I R P R E SS U R E . The human body is,
Pressure
KEY TERMS ATMOSPHERE: A measure of pressure, abbreviated “atm” and equal to the average pressure exerted by air at sea level. In English units, this is equal to 14.7 pounds per square inch, and in SI units to 101,300 pascals.
An instrument measuring atmospheric pressure. BAROMETER:
for
BUOYANCY: The tendency of an object immersed in a fluid to float.
Any substance, whether gas or liquid, that conforms to the shape of its container. FLUID:
The study of the behavior of gases and liquids at rest and in motion. FLUID MECHANICS:
HYDROSTATIC PRESSURE: the pressure that exists at any place in a body of fluid due to the weight of the fluid above.
The principle SI or metric unit of pressure, abbreviated “Pa” and equal to 1 N/m2. PASCAL:
A statement, formulated by French mathematician and physicist Blaise Pascal (1623-1662), which holds that the external pressure applied on a fluid is transmitted uniformly throughout the entire body of that fluid. PASCAL’S PRINCIPLE:
PRESSURE: The ratio of force to surface area, when force is applied in a direction perpendicular to that surface. The formula for pressure (p) is p = F/A, where F is force and A the surface area.
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in fact, suited to the normal air pressure of 1 atm, and if that external pressure is altered, the body undergoes changes that may be harmful or even fatal. A minor example of this is the “popping” in the ears that occurs when one drives through the mountains or rides in an airplane. With changes in altitude come changes in pressure, and thus, the pressure in the ears changes as well. As noted earlier, at higher altitudes, the air pressure is diminished, which makes it harder to breathe. Because air is a gas, its molecules have a tendency to be non-attractive: in other words, when the pressure is low, they tend to move away from one another, and the result is that a person at a high altitude has difficulty getting enough air into his or her lungs. Runners competing in the 1968 Olympics at Mexico City, a town in the mountains, had to train in high-altitude environments so that they would be able to breathe during competition. For baseball teams competing in Denver, Colorado (known as “the Mile-High City”), this disadvantage in breathing is compensated by the fact that lowered pressure and resistance allows a baseball to move more easily through the air. If a person is raised in such a high-altitude environment, of course, he or she becomes used to breathing under low air pressure conditions. In the Peruvian Andes, for instance, people spend their whole lives at a height more than twice as great as that of Denver, but a person from a lowaltitude area should visit such a locale only after taking precautions. At extremely great heights, of course, no human can breathe: hence airplane cabins are pressurized. Most planes are equipped with oxygen masks, which fall from the ceiling if the interior of the cabin experiences a pressure drop. Without these masks, everyone in the cabin would die.
hand is not crushed by all this weight? The reason is that the human body itself is under pressure, and that the interior of the body exerts a pressure equal to that of the air.
B LO O D P R E SS U R E . Another aspect of pressure and the human body is blood pressure. Just as 20/20 vision is ideal, doctors recommend a target blood pressure of “120 over 80”—but what does that mean? When a person’s blood pressure is measured, an inflatable cuff is wrapped around the upper arm at the same level as the heart. At the same time, a stethoscope is placed along an artery in the lower arm to monitor the sound of the blood flow. The cuff is inflated to stop the blood flow, then the pressure
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is released until the blood just begins flowing again, producing a gurgling sound in the stethoscope. The pressure required to stop the blood flow is known as the systolic pressure, which is equal to the maximum pressure produced by the heart. After the pressure on the cuff is reduced until the blood begins flowing normally—which is reflected by the cessation of the gurgling sound in the stethoscope—the pressure of the artery is measured again. This is the diastolic pressure, or the pressure that exists within the artery between strokes of the heart. For a healthy person, systolic pressure should be 120 torr, and diastolic pressure 80 torr.
Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. “Blood Pressure” (Web site). (April 7, 2001). Clark, John Owen Edward. The Atmosphere. New York: Gloucester Press, 1992. Cobb, Allan B. Super Science Projects About Oceans. New York: Rosen, 2000. “The Physics of Underwater Diving: Pressure Lesson” (Web site). (April 7, 2001). Provenzo, Eugene F. and Asterie Baker Provenzo. 47 Easy-to-Do Classic Experiments. Illustrations by Peter A. Zorn, Jr. New York: Dover Publications, 1989.
WHERE TO LEARN MORE
“Understanding Air Pressure” USA Today (Web site). (April 7, 2001).
“Atmospheric Pressure: The Force Exerted by the Weight of Air” (Web site). (April 7, 2001).
Zubrowski, Bernie. Balloons: Building and Experimenting with Inflatable Toys. Illustrated by Roy Doty. New York: Morrow Junior Books, 1990.
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ELASTICITY Elasticity
CONCEPT Unlike fluids, solids do not respond to outside force by flowing or easily compressing. The term elasticity refers to the manner in which solids respond to stress, or the application of force over a given unit area. An understanding of elasticity—a concept that carries with it a rather extensive vocabulary of key terms—helps to illuminate the properties of objects from steel bars to rubber bands to human bones.
HOW IT WORKS Characteristics of a Solid A number of parameters distinguish solids from fluids, a term that in physics includes both gases and liquids. Solids possess a definite volume and a definite shape, whereas gases have neither; liquids have no definite shape. At the molecular level, particles of solids tend to be precise in their arrangement and close to one another. Liquid molecules are close in proximity (though not as much so as solid molecules), and their arrangement is random, while gas molecules are both random in arrangement and far removed in proximity. Gas molecules are extremely fast-moving, and exert little or no attraction toward one another. Liquid molecules move at moderate speeds and exert a moderate attraction, but solid particles are slow-moving, and have a strong attraction to one another.
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nal pressure uniformly. If one applies pressure to a quantity of water in a closed container, the pressure is equal everywhere in the water. By contrast, if one places a champagne glass upright in a vise and applies pressure until it breaks, chances are that the stem or the base of the glass will be unaffected, because the pressure is not distributed equally throughout the glass. If the surface of a solid is disturbed, it will resist, and if the force of the disturbance is sufficiently strong, it will deform—for instance, when a steel plate begins to bend under pressure. This deformation will be permanent if the force is powerful enough, as in the above example of the glass in a vise. By contrast, when the surface of a fluid is disturbed, it tends to flow.
Types of Stress Deformation occurs as a result of stress, whether that stress be in the form of tension, compression, or shear. Tension occurs when equal and opposite forces are exerted along the ends of an object. These operate on the same line of action, but away from each other, thus stretching the object. A perfect example of an object under tension is a rope in the middle of a tug-of-war competition. The adjectival form of “tension” is “tensile”: hence the term “tensile stress,” which will be discussed later.
One of several factors that distinguishes solids from fluids is their relative response to pressure. Gases tend to be highly compressible, meaning that they respond well to pressure. Liquids tend to be noncompressible, yet because of their fluid characteristics, they experience exter-
Earlier, stress was defined as the application of force over a given unit area, and in fact, the formula for stress can be written as F/A, where F is force and A area. This is also the formula for pressure, though in order for an object to be under pressure, the force must be applied in a direction perpendicular to—and in the same direction as—its surface. The one form of stress
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that clearly matches these parameters is compression, produced by the action of equal and opposite forces, whose effect is to reduce the length of a material. Thus compression (for example, crushing an aluminum can in one’s hand) is both a form of stress and a form of pressure.
dimension, and k, a constant whose value is related to the nature and size of the object under stress. The harder the material, the higher the value of k; furthermore, the value of k is directly proportional to the object’s cross-sectional area or thickness.
Note that compression was defined as reducing length, yet the example given involved a reduction in what most people would call the “width” or diameter of the aluminum can. In fact, width and height are the same as length, for the purposes of most discussions in physics. Length is, along with time, mass, and electric current, one of the fundamental units of measure used to express virtually all other physical quantities. Width and height are simply length expressed in terms of other planes, and within the subject of elasticity, it is not important to distinguish between these varieties of length. (By contrast, when discussing gravitational attraction—which is always vertical—it is obviously necessary to distinguish between “vertical length,” or height, and horizontal length.)
The elastic limit of a given solid is the maximum stress to which it can be subjected without experiencing permanent deformation. Elastic limit will be discussed in the context of several examples below; for now, it is important merely to know that Hooke’s law is applicable only as long as the material in question has not reached its elastic limit. The same is true for any modulus of elasticity, or the ratio between a particular type of applied stress and the strain that results. (The term “modulus,” whose plural is “moduli,” is Latin for “small measure.”)
The third variety of stress is shear, which occurs when a solid is subjected to equal and opposite forces that do not act along the same line, and which are parallel to the surface area of the object. If a thick hardbound book is lying flat, and a person places a finger on the spine and pushes the front cover away from the spine so that the covers and pages no longer constitute parallel planes, this is an example of shear. Stress resulting from shear is called shearing stress.
Hooke’s Law and Elastic Limit To sum up the three varieties of stress, tension stretches an object, compression shrinks it, and shear twists it. In each case, the object is deformed to some degree. This deformation is expressed in terms of strain, or the ratio between change in dimension and the original dimensions of the object. The formula for strain is δL/Lo, where δL is the change in length (δ, the Greek letter delta, means “change” in scientific notation) and Lo the original length.
Elasticity
Moduli of Elasticity In cases of tension or compression, the modulus of elasticity is Young’s modulus. Named after English physicist Thomas Young (1773-1829), Young’s modulus is simply the ratio between F/A and δL/Lo—in other words, stress divided by strain. There are also moduli describing the behavior of objects exposed to shearing stress (shear modulus), and of objects exposed to compressive stress from all sides (bulk modulus). Shear modulus is the relationship of shearing stress to shearing strain. This can be expressed as the ratio between F/A and φ. The latter symbol, the Greek letter phi, stands for the angle of shear—that is, the angle of deformation along the sides of an object exposed to shearing stress. The greater the amount of surface area A, the less that surface will be displaced by the force F. On the other hand, the greater the amount of force in proportion to A, the greater the value of φ, which measures the strain of an object exposed to shearing stress. (The value of φ, however, will usually be well below 90°, and certainly cannot exceed that magnitude.)
Hooke’s law, formulated by English physicist Robert Hooke (1635-1703), relates strain to stress. Hooke’s law can be stated in simple terms as “the strain is proportional to the stress,” and can also be expressed in a formula, F = ks, where F is the applied force, s, the resulting change in
With tensile and compressive stress, A is a surface perpendicular to the direction of applied force, but with shearing stress, A is parallel to F. Consider again the illustration used above, of a thick hardbound book lying flat. As noted, when one pushes the front cover from the side so that the covers and pages no longer constitute parallel planes, this is an example of shear. If one pulled the spine and the long end of the pages away
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Elasticity
THE
MACHINE PICTURED HERE ROLLS OVER STEEL IN ORDER TO BEND IT INTO PIPES.
BECAUSE
OF ITS ELASTIC
NATURE, STEEL CAN BE BENT WITHOUT BREAKING. (Photograph by Vince Streano/Corbis. Reproduced by permission.)
from one another, that would be tensile stress, whereas if one pushed in on the sides of the pages and spine, that would be compressive stress. Shearing stress, by contrast, would stress only the front cover, which is analogous to A for any object under shearing stress. The third type of elastic modulus is bulk modulus, which occurs when an object is subjected to compression from all sides—that is, volume stress. Bulk modulus is the relationship of volume stress to volume strain, expressed as the ratio between F/A and δV/Vo, where δV is the change in volume and Vo is the original volume.
REAL-LIFE A P P L I C AT I O N S Elastic and Plastic Deformation As noted earlier, the elastic limit is the maximum stress to which a given solid can be subjected without experiencing permanent deformation, referred to as plastic deformation. Plastic deformation describes a permanent change in shape or size as a result of stress; by contrast, elastic deformation is only a temporary change in dimension.
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A classic example of elastic deformation, and indeed, of highly elastic behavior, is a rubber band: it can be deformed to a length many times its original size, but upon release, it returns to its original shape. Examples of plastic deformation, on the other hand, include the bending of a steel rod under tension or the breaking of a glass under compression. Note that in the case of the steel rod, the object is deformed without rupturing—that is, without breaking or reducing to pieces. The breaking of the glass, however, is obviously an instance of rupturing.
Metals and Elasticity Metals, in fact, exhibit a number of interesting characteristics with regard to elasticity. With the notable exception of cast iron, metals tend to possess a high degree of ductility, or the ability to be deformed beyond their elastic limits without experiencing rupture. Up to a certain point, the ratio of tension to elongation for metals is high: in other words, a high amount of tension produces only a small amount of elongation. Beyond the elastic limit, however, the ratio is much lower: that is, a relatively small amount of tension produces a high degree of elongation. Because of their ductility, metals are highly malleable, and, therefore, capable of experienc-
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Elasticity
RUBBER BANDS, LIKE THE ONES SHOWN HERE FORMED INTO MATION. (Photograph by Matthew Klein/Corbis. Reproduced by permission.)
ing mechanical deformation through metallurgical processes, such as forging, rolling, and extrusion. Cold extrusion involves the application of high pressure—that is, a high bulk modulus—to a metal without heating it, and is used on materials such as tin, zinc, and copper to change their shape. Hot extrusion, on the other hand, involves heating a metal to a point of extremely high malleability, and then reshaping it. Metals may also be melted for the purposes of casting, or pouring the molten material into a mold. U LT I M AT E S T R E N GT H . The ten-
sion that a material can withstand is called its ultimate strength, and due to their ductile properties, most metals possess a high value of ultimate strength. It is possible, however, for a metal to break down due to repeated cycles of stress that are well below the level necessary to rupture it. This occurs, for instance, in metal machines such as automobile engines that experience a high frequency of stress cycles during operation. The high ultimate strength of metals, both in tension and compression, makes them useful in a number of structural capacities. Steel has an ultimate compressive strength 25 times as great as concrete, and an ultimate tensile strength 250 times as great. For this reason, when concrete is poured for building bridges or other large struc-
S C I E N C E O F E V E RY DAY T H I N G S
A BALL, ARE A CLASSIC EXAMPLE OF ELASTIC DEFOR-
tures, steel rods are inserted in the concrete. Called “rebar” (for “reinforced bars”), the steel rods have ridges along them in order to bond more firmly with the concrete as it dries. As a result, reinforced concrete has a much greater ability than plain concrete to withstand tension and compression.
Steel Bars and Rubber Bands Under Stress CRYSTALLINE MATERIALS. Metals are crystalline materials, meaning that they are composed of solids called crystals. Particles of crystals are highly ordered, with a definite geometric arrangement repeated in all directions, rather like a honeycomb. (It should be noted, however, that the crystals are not necessarily as uniform in size as the “cells” of the honeycomb.) The atoms of a crystal are arranged in orderly rows, bound to one another by strongly attractive forces that act like microscopic springs.
Just as a spring tends to return to its original length, the highly attractive atoms in a steel bar, when it is stretched, tend to restore it to its original dimensions. Likewise, it takes a great deal of force to pull apart the atoms. When the metal is subjected to plastic deformation, the atoms move
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are flexible, and tend to rotate, producing kinks along the length of the molecule.
Elasticity
When a piece of rubber is subjected to tension, as, for instance, if one pulls a rubber band by the ends, the kinks and loops in the elastomers straighten. Once the stress is released, however, the elastomers immediately return to their original shape. The more “kinky” the polymers, the higher the elastic modulus, and hence, the more capable the item is of stretching and rebounding. It is interesting to note that steel and rubber, materials that are obviously quite different, are both useful in part for the same reason: their high elastic modulus when subjected to tension, and their strength under stress. But a rubber band exhibits behaviors under high temperatures that are quite different from that of a metal: when heated, rubber contracts. It does so quite suddenly, in fact, suggesting that the added energy of the heat allows the bonds in the elastomers to begin rotating again, thus restoring the kinked shape of the molecules. A
HUMAN BONE HAS A GREATER
“ULTIMATE
STRENGTH”
THAN THAT OF CONCRETE. (Ecoscene/Corbis. Reproduced by per-
Bones
mission.)
to new positions and form new bonds. The atoms are incapable of forming bonds; however, when the metal has been subjected to stress exceeding its ultimate strength, at that point, the metal breaks.
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The tensile strength in bone fibers comes from the protein collagen, while the compressive strength is largely due to the presence of inorganic (non-living) salt crystals. It may be hard to believe, but bone actually has an ultimate strength—both in tension and compression— greater than that of concrete!
The crystalline structure of metal influences its behavior under high temperatures. Heat causes atoms to vibrate, and in the case of metals, this means that the “springs” are stretching and compressing. As temperature increases, so do the vibrations, thus increasing the average distance between atoms. For this reason, under extremely high temperature, the elastic modulus of the metal decreases, and the metal becomes less resistant to stress.
The ultimate strength of most materials is rendered in factors of 108 N/m2—that is, 100,000,000 newtons (the metric unit of force) per square meter. For concrete under tensile stress, the ultimate strength is 0.02, whereas for bone, it is 1.3. Under compressive stress, the values are 0.2 and 1.7, respectively. In fact, the ultimate tensile strength of bone is close to that of cast iron (1.7), though the ultimate compressive strength of cast iron (5.5) is much higher than for bone.
P O LY M E R S A N D E L A S T O M E R S . Rubber is so elastic in behavior that in
everyday life, the term “elastic” is most often used for objects containing rubber: the waistband on a pair of underwear, for instance. The long, thin molecules of rubber, which are arranged side-byside, are called “polymers,” and the super-elastic polymers in rubber are called “elastomers.” The chemical bonds between the atoms in a polymer
Even with these figures, it may be hard to understand how bone can be stronger than concrete, but that is largely because the volume of concrete used in most situations is much greater than the volume of any bone in the body of a human being. By way of explanation, consider a piece of concrete no bigger than a typical bone: under relatively small amounts of stress, it would crumble.
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Elasticity
KEY TERMS ANGLE OF SHEAR:
The angle of
HOOKE’S LAW:
A principle of elastic-
deformation on the sides of an object
ity formulated by English physicist Robert
exposed to shearing stress. Its symbol is f
Hooke (1635-1703), who discovered that
(the Greek letter phi), and its value will
strain is proportional to stress. Hooke’s law
usually be well below 90°.
can be written as a formula, F = ks, where
The modulus of
BULK MODULUS:
elasticity for a material subjected to compression on all surfaces—that is, volume stress. Bulk modulus is the relationship of volume stress to volume strain, expressed as the ratio between F/A and dV/Vo, where
F is the applied force, s the resulting change in dimension, and k a constant whose value is related to the nature and size of the object being subjected to stress. Hooke’s law applies only when the elastic limit has
dV is the change in volume and Vo is the
not been exceeded.
original volume.
LENGTH:
In discussions of elasticity,
A form of stress
“length” refers to an object’s dimensions on
produced by the action of equal and oppo-
any given plane, thus, it can be used not
site forces, whose effect is to reduce the
only to refer to what is called length in
length of a material. Compression is a form
everyday language, but also to width or
COMPRESSION:
of pressure. When compressive stress is applied to all surfaces of a material, this is
MODULUS OF ELASTICITY:
known as volume stress. DUCTILITY:
height.
A property whereby a
The
ratio between a type of applied stress (that
material is capable of being deformed far
is, tension, compression, and shear) and
beyond its elastic limit without experienc-
the strain that results in the object to which
ing rupture—that is, without breaking.
stress has been applied. Elastic moduli—
Most metals other than cast iron are high-
including Young’s modulus, shearing mod-
ly ductile.
ulus, and bulk modulus—are applicable
ELASTIC DEFORMATION:
A tempo-
rary change in shape or size experienced by
only as long as the object’s elastic limit has not been reached.
a solid subjected to stress. Elastic deformation is thus less severe than plastic deformation.
PLASTIC DEFORMATION:
A perma-
nent change in shape or size experienced by a solid subjected to stress. Plastic defor-
ELASTIC LIMIT:
The maximum stress
to which a given solid can be subjected without experiencing plastic deforma-
mation is thus more severe than elastic deformation. The ratio of force to sur-
tion—that is, without being permanently
PRESSURE:
deformed.
face area, when force is applied in a direc-
ELASTICITY:
The response of solids to
stress.
S C I E N C E O F E V E RY DAY T H I N G S
tion perpendicular to, and in the same direction as, that surface.
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Elasticity
KEY TERMS A form of stress resulting
area. Thus, it is similar to pressure, and
from equal and opposite forces that do not
indeed, compression is a form of pressure.
SHEAR:
act along the same line. If a thick hard-
TENSION:
A form of stress produced
bound book is lying flat, and one pushes
by a force which acts to stretch a material.
the front cover from the side so that the
The adjectival form of “tension” is “ten-
covers and pages no longer constitute par-
sile”: hence the terms “tensile stress” and
allel planes, this is an example of shear.
“tensile strain.”
SHEAR MODULUS:
The modulus of
ULTIMATE STRENGTH:
The tension
elasticity for an object exposed to shearing
that a material can withstand without rup-
stress. It is expressed as the ratio between
turing. Due to their high levels of ductility,
F/A and φ, where φ (the Greek letter phi)
most metals have a high value of ultimate
stands for the angle of shear.
strength.
STRAIN:
The ratio between the change
VOLUME STRESS:
The stress that
in dimension experienced by an object that
occurs in a material when it is subjected to
has been subjected to stress, and the origi-
compression from all sides. The modus of
nal dimensions of the object. The formula
elasticity for volume stress is the bulk mod-
for strain is dL/Lo, where dL is the change
ulus.
in length and Lo the original length. Hooke’s law, as well as the various moduli of elasticity, relates strain to stress.
YOUNG’S MODULUS:
A modulus of
elasticity describing the relationship between stress to strain for objects under
In general terms, stress is any
either tension or compression. Named
attempt to deform a solid. Types of stress
after English physicist Thomas Young
include tension, compression, and shear.
(1773-1829), Young’s modulus is simply
More specifically, stress is the ratio of force
the ratio between F/A and δL/Lo—in other
to unit area, F/A, where F is force and A
words, stress divided by strain.
STRESS:
WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. “Dictionary of Metallurgy” Steelmill.com: The Polish Steel Industry Directory (Web site). (April 9, 2001).
154
CONTINUED
Gibson, Gary. Making Shapes. Illustrated by Tony Kenyon. Brookfield, CT: Copper Beech Books, 1996. “Glossary of Materials Testing Terms” (Web site). (April 9, 2001). Goodwin, Peter H. Engineering Projects for Young Scientists. New York: Franklin Watts, 1987.
“Engineering Processes.” eFunda.com (Web site). (April 9, 2001).
Johnston, Tom. The Forces with You! Illustrated by Sarah Pooley. Milwaukee, WI: Gareth Stevens Publishing, 1988.
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WORK AND ENERGY M E C H A N I C A L A D VA N TA G E A N D SIMPLE MACHINES ENERGY
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MECHANICAL A D VA N TA G E A N D SIMPLE MACHINES
CONCEPT When the term machine is mentioned, most people think of complex items such as an automobile, but, in fact, a machine is any device that transmits or modifies force or torque for a specific purpose. Typically, a machine increases either the force of the person operating it—an aspect quantified in terms of mechanical advantage—or it changes the distance or direction across which that force can be operated. Even a humble screw is a machine; so too is a pulley, and so is one of the greatest machines ever invented: the wheel. Virtually all mechanical devices are variations on three basic machines: the lever, the inclined plane, and the hydraulic press. From these three, especially the first two, arose literally hundreds of machines that helped define history, and which still permeate daily life.
HOW IT WORKS
Instead, the machines presented for consideration here depend purely on gravitational force and the types of force explainable purely in a gravitational framework. This is the realm of classical physics, a term used to describe the studies of physicists from the time of Galileo Galilei (1564-1642) to the end of the nineteenth century. During this era, physicists were primarily concerned with large-scale interactions that were easily comprehended by the senses, as opposed to the atomic behaviors that have become the subject of modern physics. Late in the classical era, the Scottish physicist James Clerk Maxwell (1831-1879)—building on the work of many distinguished predecessors— identified electromagnetic force. For most of the period, however, the focus was on gravitational force and mechanics, or the study of matter, motion, and forces. Likewise, the majority of machines invented and built during most of the classical period worked according to the mechanical principles of plain gravitational force.
There are four known types of force in the universe: gravitational, electromagnetic, weak nuclear, and strong nuclear. This was the order in which the forces were identified, and the number of machines that use each force descends in the same order. The essay that follows will make little or no reference to nuclear-powered machines. Somewhat more attention will be paid to electrical machines; however, to trace in detail the development of forces in that context would require a new and somewhat cumbersome vocabulary.
This was even true to some extent with the steam engine, first developed late in the seventeenth century and brought to fruition by Scotland’s James Watt (1736-1819.) Yet the steam engine, though it involved ordinary mechanical processes in part, represented a new type of machine, which used thermal energy. This is also true of the internal-combustion engine; yet both steam- and gas-powered engines to some extent borrowed the structure of the hydraulic press, one of the three basic types of machine. Then came the development of electronic power, thanks to Thomas Edison (1847-1931) and others, and machines became increasingly divorced from basic mechanical laws.
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Mechanical Advantage Mechanical Advantage and Simple Machines
A common trait runs through all forms of machinery: mechanical advantage, or the ratio of force output to force input. In the case of the lever, a simple machine that will be discussed in detail below, mechanical advantage is high. In some machines, however, mechanical advantage is actually less than 1, meaning that the resulting force is less than the applied force. This does not necessarily mean that the machine itself has a flaw; on the contrary, it can mean that the machine has a different purpose than that of a lever. One example of this is the screw: a screw with a high mechanical advantage—that is, one that rewarded the user’s input of effort by yielding an equal or greater output— would be useless. In this case, mechanical advantage could only be achieved if the screw backed out from the hole in which it had been placed, and that is clearly not the purpose of a screw. THE
LEVER, LIKE THIS HYDROELECTRIC ENGINE LEVER,
IS A SIMPLE MACHINE THAT PERFECTLY ILLUSTRATES THE CONCEPT OF MECHANICAL ADVANTAGE. (Photograph by E.O.
Hoppe/Corbis. Reproduced by permission.)
The heyday of classical mechanics—when classical studies in mechanics represented the absolute cutting edge of experimentation—was in the period from the beginning of the seventeenth century to the beginning of the nineteenth. One figure held a dominant position in the world of physics during those two centuries, and indeed was the central figure in the history of physics between Galileo and Albert Einstein (1879-1955). This was Sir Isaac Newton (16421727), who discerned the most basic laws of physical reality—laws that govern everyday life, including the operation of simple machines. Newton and his principles are essential to the study that follows, but one other figure deserves “equal billing”: the Greek mathematician, physicist, and inventor Archimedes (c. 287212 B.C.). Nearly 2,000 years before Newton, Archimedes explained and improved a number of basic machines, most notably the lever. Describing the powers of the lever, he is said to have promised, “Give me a lever long enough and a place to stand, and I will move the world.” This he demonstrated, according to one story, by moving a fully loaded ship single-handedly with the use of a lever, while remaining seated some distance away.
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Here a machine offers an improvement in terms of direction rather than force; likewise with scissors or a fishing rod, both of which will be discussed below, an improvement with regard to distance or range of motion is bought at the expense of force. In these and many more cases, mechanical advantage alone does not measure the benefit. Thus, it is important to keep in mind what was previously stated: a machine either increases force output, or changes the force’s distance or direction of operation. Most machines, however, work best when mechanical advantage is maximized. Yet mechanical advantage—whether in theoretical terms or real-life instances—can only go so high, because there are factors that limit it. For one thing, the operator must give some kind of input to yield an output; furthermore, in most situations friction greatly diminishes output. Hence, in the operation of a car, for instance, one-quarter of the vehicle’s energy is expended simply on overcoming the resistance of frictional forces. For centuries, inventors have dreamed of creating a mechanism with an almost infinite mechanical advantage. This is the much-soughtafter “perpetual motion machine,” that would only require a certain amount of initial input; after that, the machine would simply run on its own forever. As output compounded over the years, its ratio to input would become so high that the figure for mechanical advantage would approach infinity.
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A number of factors, most notably the existence of friction, prevent the perpetual motion machine from becoming anything other than a pipe dream. In outer space, however, the nearabsence of friction makes a perpetual motion machine viable: hence, a space probe launched from Earth can travel indefinitely unless or until it enters the gravitational field of some other body in deep space. The concept of a perpetual motion machine, at least on Earth, is only an idealization; yet idealization does have its place in physics. Physicists discuss most concepts in terms of an idealized state. For instance, when illustrating the acceleration due to gravity experienced by a body in free fall, it is customary to treat such an event as though it were taking place under conditions divorced from reality. To consider the effects of friction, air resistance, and other factors on the body’s fall would create an impossibly complicated problem—yet real-world situations are just that complicated. In light of this tendency to discuss physical processes in idealized terms, it should be noted that there are two types of mechanical advantage: theoretical and actual. Efficiency, as applied to machines in its most specific scientific sense, is the ratio of actual to theoretical mechanical advantage. This in some ways resembles the formula for mechanical advantage itself: once again, what is being measured is the relationship between “output” (the real behavior of the machine) and “input” (the planned behavior of the machine).
will henceforth be used as a loose synonym for mechanical advantage—even though the technical definition is rather different.
Mechanical Advantage and Simple Machines
Types of Machines The term “simple machine” is often used to describe the labor-saving devices known to the ancient world, most of which consisted of only one or two essential parts. Historical sources vary regarding the number of simple machines, but among the items usually listed are levers, pulleys, winches, wheels and axles, inclined planes, wedges, and screws. The list, though long, can actually be reduced to just two items: levers and inclined planes. All the items listed after the lever and before the inclined plane—including the wheel and axle—are merely variations on the lever. The same goes for the wedge and the screw, with regard to the inclined plane. In fact, all machines are variants on three basic devices: the lever, the inclined plane, and the hydraulic press. Each transmits or modifies force or torque, producing an improvement in force, distance, or direction. The first two, which will receive more attention here, share several aspects not true of the third. First of all, the lever and the inclined plane originated at the beginning of civilization, whereas the hydraulic press is a much more recent invention.
As with other mechanical processes, the actual mechanical advantage of a machine is a much more complicated topic than the theoretical mechanical advantage. The gulf between the two, indeed, is enormous. It would be almost impossible to address the actual behavior of machines within an environment framework that includes complexities such as friction.
The lever appeared as early as 5000 B.C. in the form of a simple balance scale, and within a few thousand years, workers in the Near East and India were using a crane-like lever called the shaduf to lift containers of water. The shaduf, introduced in Mesopotamia in about 3000 B.C., consisted of a long wooden pole that pivoted on two upright posts. At one end of the lever was a counterweight, and at the other a bucket. The operator pushed down on the pole to fill the bucket with water, and then used the counterweight to assist in lifting the bucket.
Each real-world framework—that is, each physical event in the real world—is just a bit different from every other one, due to the many varieties of factors involved. By contrast, the idealized machines of physics problems behave exactly the same way in one imaginary situation after another, assuming outside conditions are the same. Therefore, the only form of mechanical advantage that a physicist can easily discuss is theoretical. For that reason, the term “efficiency”
The inclined plane made its appearance in the earliest days of civilization, when the Egyptians combined it with rollers in the building of their monumental structures, the pyramids. Modern archaeologists generally believe that Egyptian work gangs raised the huge stone blocks of the pyramids through the use of sloping earthen ramps. These were most probably built up alongside the pyramid itself, and then removed when the structure was completed.
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THE
HYDRAULIC PRESS, LIKE THE LIFT HOLDING UP THIS CAR IN A REPAIR SHOP, IS A RELATIVELY RECENT INVEN-
TION THAT IS USED IN MANY MODERN DEVICES, FROM CAR JACKS TO TOILETS. (Photograph by Charles E. Rotkin/Corbis. Repro-
duced by permission.)
In contrast to the distant origins of the other two machines, the hydraulic press seems like a mere youngster. Also, the first two clearly arose as practical solutions first: by the time Archimedes achieved a conceptual understanding of these machines, they had been in use a long, long time. The hydraulic press, on the other hand, first emerged from the theoretical studies of the brilliant French mathematician and physicist Blaise Pascal (1623-1662.) Nearly 150 years passed before the English inventor Joseph Bramah (1748-1814) developed a workable hydraulic press in 1796, by which time Watt had already introduced his improved steam engine. The Industrial Revolution was almost underway.
REAL-LIFE A P P L I C AT I O N S The Lever In its most basic form, the lever consists of a rigid bar supported at one point, known as the fulcrum. One of the simplest examples of a lever is a crowbar, which one might use to move a heavy object, such as a rock. In this instance, the fulcrum could be the ground, though a more rigid 160
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“artificial” fulcrum (such as a brick) would probably be more effective. As the operator of the crowbar pushes down on its long shaft, this constitutes an input of force, variously termed applied force, effort force, or merely effort. Newton’s third law of motion shows that there is no such thing as an unpaired force in the universe: every input of force in one area will yield an output somewhere else. In this case, the output is manifested by dislodging the stone—that is, the output force, resistance force, or load. Use of the lever gives the operator much greater lifting force than that available to a person who tried to lift with only the strength of his or her own body. Like all machines, the lever links input to output, harnessing effort to yield beneficial results—in this case, by translating the input effort into the output effort of a dislodged stone. Note, however, the statement at the beginning of this paragraph: proper use of a lever actually gives a person much greater force than he or she would possess unaided. How can this be? There is a close relationship between the behavior of the lever and the concept of torque, as, for example, the use of a wrench to remove a lug nut. A wrench, in fact, is a sort of lever (Class
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I—a distinction that will be explored below.) In any object experiencing torque, the distance from the pivot point (the lug nut, in this case), to the area where force is being applied is called the moment arm. On the wrench, this is the distance from the lug nut to the place where the operator is pushing on the wrench handle. Torque is the product of force multiplied by moment arm, and the greater the torque, the greater the tendency of the object to be put into rotation. As with machines in general, the greater the input, the greater the output. The fact that torque is the product of force and moment arm means that if one cannot increase force, it is still possible to gain greater torque by increasing the moment arm. This is the reason why, when one tries and fails to disengage a stubborn lug nut, it is a good idea to get a longer wrench. Likewise with a lever, greater leverage can be gained without applying more force: all one needs is a longer lever arm. As one might suspect, the lever arm is the distance from the force input to the fulcrum, or from the fulcrum to the force output. If a carpenter is using a nail-puller on the head of a hammer to extract a nail from a board, the lever arm of force input would be from the carpenter’s hand gripping the hammer handle to the place where the hammerhead rests against the board. The lever arm of force output would be from the hammerhead to the end of the nail-puller. With a lever, the input force (that of the carpenter’s hand pulling back on the hammer handle) multiplied by the input lever arm is always equal to the output force (that of the nail-puller pulling up the nail) multiplied by the output lever arm. The relationship between input and output force and lever arm then makes it possible to determine a formula for the lever’s mechanical advantage. Since FinLin = FoutLout (where F = force and L = lever arm), it is possible to set up an equation for a lever’s mechanical advantage. Once again, mechanical advantage is always Fout/Fin, but with a lever, it is also Lin/Lout. Hence, the mechanical advantage of a lever is always the same as the inverse ratio of the lever arm. If the input arm is 5 units long and the output arm is 1 unit long, the mechanical advantage will be 5, but if the positions are reversed, it will be 0.2.
tive positions of the input lever arm, the fulcrum, and the output arm or load. In a Class I lever, such as the crowbar and the wrench, the fulcrum is between the input arm and the output arm. By contrast, a Class II lever, for example, a wheelbarrow, places the output force (the load carried in the barrow itself) between the input force (the action of the operator lifting the handles) and the fulcrum, which in this case is the wheel.
Mechanical Advantage and Simple Machines
Finally, there is the Class III lever, which is the reverse of a Class II. Here, the input force is between the output force and the fulcrum. The human arm itself is an example of a Class III lever: if one grasps a weight in one’s hand, one’s bent elbow is the fulcrum, the arm raising the weight is the input force, and the weight held in the hand—now rising—is the output force. The Class III lever has a mechanical advantage of less than 1, but what it loses in force output in gains in range of motion. The world abounds with levers. Among the Class I varieties in common use are a nail puller on a hammerhead, described earlier, as well as postal scales and pliers. A handcart, though it might seem at first like a wheelbarrow, is actually a Class I lever, because the wheel or fulcrum is between the input effort—the force of a person’s hands gripping the handles—and the output, which is the lifting of the load in the handcart itself. Scissors constitute an interesting type of Class I lever, because the force of the output (the cutting blades) is reduced in order to create a greater lever arm for the input, in this case the handles gripped when cutting. A handheld bottle opener provides an excellent illustration of a Class II lever. Here the fulcrum is on the far end of the opener, away from the operator: the top end of the opener ring, which rests atop the bottle cap. The cap itself is the load, and one provides input force by pulling up on the opener handle, thus prying the cap from the bottle with the lower end of the opener ring. Nail clippers represent a type of combination lever: the handle that one operates is a Class II, while the cutting blades are a Class III.
C LASS E S O F L E V E R S . Levers are divided into three classes, depending on the rela-
Whereas Class II levers maximize force at the expense of range of motion, Class III levers operate in exactly the opposite fashion. When using a fishing rod to catch a fish, the fisherman’s left hand (assuming he is right-handed) constitutes the fulcrum as it holds the rod just below the reel assembly. The right hand supplies the effort, jerk-
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ing upward, while the fish is the load. The purpose here is not to raise a heavy object (one reason why a fishing rod may break if one catches too large a fish) but rather to use the increased lever arm for one’s advantage in catching an object at some distance. Similarly, a hammer, which constitutes a Class III lever, with the operator’s wrist as fulcrum, magnifies the motion of the operator’s hand with a hammerhead that cuts a much wider arc.
There is nothing obvious about the wheel, and in fact, it is not nearly as old an invention as most people think. Until the last few centuries, most peoples in sub-Saharan Africa, remote parts of central and northern Asia, the Americas, and the Pacific Islands remained unaware of it. This did not necessarily make them “primitive”: even the Egyptians who built the Great Pyramid of Cheops in about 2550 B.C. had no concept of the wheel.
Many machines that arose in the Industrial Age are a combination of many levers—that is, a compound lever. In a manual typewriter or piano, for instance, each key is a complex assembly of levers designed for a given task. An automobile, too, uses multiple levers—most notably, a special variety known as the wheel and axle.
What the Egyptians did have, however, were rollers—-most often logs, onto which a heavy object was hoisted using a lever. From rollers developed the idea of a sledge, a sled-like device for sliding large loads atop a set of rollers. A sledge appears in a Sumerian illustration from about 3500 B.C., the oldest known representation of a wheel-like object.
T H E W H E E L A N D AX L E . A wheel is a variation on a Class I lever, but it represents such a stunning technological advancement that it deserves to be considered on its own. When driving a car, the driver places input force on the rim of the steering wheel, whose fulcrum is the center of the wheel. The output force is translated along the steering column to the driveshaft.
The combination of wheel and axle overcomes one factor that tends to limit the effectiveness of most levers, regardless of class: limited range of motion. An axle is really a type of wheel, though it has a smaller radius, which means that the output lever arm is correspondingly smaller. Given what was already said about the equation for mechanical advantage in a lever, this presents a very fortunate circumstance. When a wheel turns, it has a relatively large lever arm (the rim), that turns a relatively small lever arm, the axle. Because the product of input force and input lever arm must equal output force multiplied by output lever arm, this means that the output force will be higher than the input force. Therefore, the larger the wheel in proportion to the axle, the greater the mechanical advantage.
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The transformation from the roller-andsledge assembly to wheeled vehicles is not as easy as it might seem, and historians still disagree as to the connection. Whatever the case, it appears that the first true wheels originated in Sumer (now part of Iraq) in about 3500 B.C. These were tripartite wheels, made by attaching three pieces of wood and then cutting out a circle. This made a much more durable wheel than a sawed-off log, and also overcame the fact that few trees are perfectly round. During the early period of wheeled transportation, from 3500 to 2000 B.C., donkeys and oxen rather than horses provided the power, in part because wheeled vehicles were not yet made for the speeds that horses could achieve. Hence, it was a watershed event when wheelmakers began fashioning axles as machines separate from the wheel. Formerly, axles and wheels were made up of a single unit; separating them made carts much more stable, especially when making turns—and, as noted earlier, greatly increased the mechanical advantage of the wheels themselves. Transportation entered a new phase in about 2000 B.C., when improvements in technology made possible the development of spoked wheels. By heat-treating wood, it became possible to bend the material slightly, and to attach spokes between the rim and hub of the wheel. When the wood cooled, the tension created a much stronger wheel—capable of carrying heavier loads faster and over greater distances.
It is for this reason that large vehicles without power steering often have very large steering wheels, which have a larger range of motion and, thus, a greater torque on the axle—that is, the steering column. Some common examples of the wheel-and-axle principle in operation today include a doorknob and a screwdriver; however, long before the development of the wheel and axle, there were wheels alone.
In China during the first century B.C., a new type of wheeled vehicle—identified earlier as a
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Class II lever—was born in the form of the wheelbarrow, or “wooden ox.” The wheelbarrow, whose invention the Chinese attributed to a semi-legendary figure named Ko Yu, was of such value to the imperial army for moving arms and military equipment that China’s rulers kept its design secret for centuries. In Europe, around the same time, chariots were dying out, and it was a long time before the technology of wheeled transport improved. The first real innovation came during the 1500s, with the development of the horsedrawn coach. By 1640, a German family was running a regular stagecoach service, and, in 1667, a new, light, two-wheeled carriage called a cabriolet made its first appearance. Later centuries, of course, saw the development of increasingly more sophisticated varieties of wheeled vehicles powered in turn by human effort (the bicycle), steam (the locomotive), and finally, the internal combustion engine (the automobile.) But the wheel was never just a machine for transport: long before the first wheeled carts came into existence, potters had been using wheels that rotated in place to fashion perfectly round objects, and in later centuries, wheels gained many new applications. By 500 B.C., farmers in Greece and other parts of the Mediterranean world were using rotary mills powered by donkeys. These could grind grain much faster than a person working with a hand-powered grindstone could hope to do, and in time, the Greeks found a means of powering their mills with a force more useful than donkeys: water. The first waterwheels, turned by human or animal power, included a series of buckets along the rim that made it possible to raise water from the river below and disperse it to other points. By about 70 B.C., however, Roman engineers recognized that they could use the power of water itself to turn wheels and grind grain. Thus, the waterwheel became one of the first two rotor mechanisms in which an inanimate source (as opposed to the effort of humans or animals) created power to spin a shaft. In this way, the waterwheel was a prototype for the engine developed many centuries later. Indeed, in the first century A.D., Hero of Alexandria—who discovered the concept of steam power some 1,700 years before anyone took up the idea and put it to use—proposed what has been considered a prototype for the turbine
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engine. However, for a variety of complex reasons, the ancient world was simply not ready for the technological leap portended by such an invention; and so, in terms of significant progress in the development of machines, Europe was asleep for more than a millennium.
Mechanical Advantage and Simple Machines
The other significant form of wheel powered by an “inanimate” source was the windmill, first mentioned in 85 B.C. by Antipater of Thessalonica, who commented on a windmill he saw in northern Greece. In this early version of the windmill, the paddle wheel moved on a horizontal plane. However, the windmill did not take hold in Europe during ancient times, and, in fact, its true origins lie further east, and it did not become widespread until much later. In the seventh century A.D., windmills began to appear in the region of modern Iran and Afghanistan, and the concept spread to the Arab world. Europeans in the Near East during the Crusades (1095-1291) observed the windmill, and brought the idea back to Europe with them. By the twelfth century Europeans had developed the more familiar vertical mill. Finally, there was a special variety of wheel that made its appearance as early as 500 B.C.: the toothed gearwheel. By 300 B.C., it was in use throughout Egypt, and by about 270 B.C., Ctesibius of Alexandria (fl. c. 270-250 B.C.) had applied the gear in devising a constant-flow water clock called a clepsydra. Some 2,100 years after Ctesibius, toothed gears became a critical component of industrialization. The most common type is a spur gear, in which the teeth of the wheel are parallel to the axis of rotation. Helical gears, by contrast, have curved teeth in a spiral pattern at an angle to their rotational axes. This means that several teeth of one gearwheel are always in contact with several teeth of the adjacent wheel, thus providing greater torque. In bevel gears, the teeth are straight, as with a spur gear, but they slope at a 45°-angle relative to their axes so that two gearwheels can fit together at up to 90°-angles to one another without a change in speed. Finally, planetary gears are made such that one or more smaller gearwheels can fit within a larger gearwheel, which has teeth cut on the inside rather than the outside. Similar in concept to the gearwheel is the V belt drive, which consists of two wheels side by side, joined with a belt. Each of the wheels has
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grooves cut in it for holding the belt, making this a modification of the pulley, and the grooves provide much greater gripping power for holding the belt in place. One common example of a V belt drive, combined with gearwheels, is a bicycle chain assembly.
rope runs from the support pulley down to the load-bearing wheel, wraps around that pulley and comes back up to a fixed attachment on the upper pulley. Whereas the upper pulley is fixed, the load-bearing pulley is free to move, and raises the load as the rope is pulled below.
P U L L E Y S . A pulley is essentially a grooved wheel on an axle attached to a frame, which in turn is attached to some form of rigid support such as a ceiling. A rope runs along the grooves of the pulley, and one end is attached to a load while the other is controlled by the operator.
The simplest kind of compound pulley, with just two wheels, has a mechanical advantage of 2. On a theoretical level, at least, it is possible to calculate the mechanical advantage of a compound pulley with more wheels: the number is equal to the segments of rope between the lower pulleys and the upper, or support pulley. In reality, however, friction, which is high as ropes rub against the pulley wheels, takes its toll. Thus mechanical advantage is never as great as it might be.
In several instances, it has been noted that a machine may provide increased range of motion or position rather than power. So, this simplest kind of pulley, known as a single or fixed pulley, only offers the advantage of direction rather than improved force. When using Venetian blinds, there is no increase in force; the advantage of the machine is simply that it allows one to move objects upward and downward. Thus, the theoretical mechanical advantage of a fixed pulley is 1 (or almost certainly less under actual conditions, where friction is a factor). Here it is appropriate to return to Archimedes, whose advancements in the understanding of levers translated to improvements in pulleys. In the case of the lever, it was Archimedes who first recognized that the longer the effort arm, the less effort one had to apply in raising the load. Likewise, with pulleys and related devices— cranes and winches—he explained and improved the way these machines worked. The first crane device dates to about 1000 B.C., but evidence from pictures suggests that pulleys may have been in use as early as seven thousand years before. Several centuries before Archimedes’s time, the Greeks were using compound pulleys that contained several wheels and thus provided the operator with much greater mechanical advantage than a fixed pulley. Archimedes, who was also the first to recognize the relationship between pulleys and levers, created the first fully realized block-and-tackle system using compound pulleys and cranes. In the late modern era, compound pulley systems were used in applications such as elevators and escalators.
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A block-and-tackle, like a compound pulley, uses just one rope with a number of pulley wheels. In a block-and-tackle, however, the wheels are arranged along two axles, each of which includes multiple pulley wheels that are free to rotate along the axle. The upper row is attached to the support, and the lower row to the load. The rope connects them all, running from the first pulley in the upper set to the first in the lower set, then to the second in the upper set, and so on. In theory, at least, the mechanical advantage of a block-and-tackle is equal to the number of wheels used, which must be an even number—but again, friction diminishes the theoretical mechanical advantage.
The Inclined Plane To the contemporary mind, it is difficult enough to think of a lever as a “machine”—but levers at least have more than one part, unlike an inclined plane. The latter, by contrast, is exactly what it seems to be: a ramp. Yet it was just such a ramp structure, as noted earlier, that probably enabled the Egyptians to build the pyramids—a feat of engineering so stunning that even today, some people refuse to believe that the ancient Egyptians could have achieved it on their own.
A compound pulley consists of two or more wheels, with at least one attached to the support while the other wheel or wheels lift the load. A
Surely, as anti-scientific proponents of various fantastic theories often insist, the building of the pyramids could only have been done with machines provided by super-intelligent, extraterrestrial beings. Even in ancient times, the Greek historian Herodotus (c. 484-c. 424 B.C.) speculated that the Egyptians must have used huge cranes that had long since disappeared.
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These bizarre guesses concerning the technology for raising the pyramid’s giant blocks serve to highlight the brilliance of a gloriously simple machine that, in essence, doubles force. If one needs to move a certain weight to a certain height, there are two options. One can either raise the weight straight upward, expending an enormous amount of effort, even with a pulley system; or one can raise the weight gradually along an inclined plane. The inclined plane is a much wiser choice, because it requires half the effort. Why half? Imagine an inclined plane sloping evenly upward to the right. The plane exists in a sort of frame that is equal in both length and height to the dimensions of the plane itself. As we can easily visualize, the plane takes up exactly half of the frame, and this is true whether the slope is more than, less than, or equal to 45°. For any plane in which the slope is more than 45°, however, the mechanical advantage will be less than 1, and it is indeed hard to imagine why anyone would use such a plane unless forced to do so by limitations on their horizontal space—for example, when lifting a heavy object from a narrow canyon. The mechanical advantage of an inclined plane is equal to the ratio between the distance over which input force is applied and the distance of output; or, more simply, the ratio of length to height. If a man is pushing a crate up a ramp 4 ft high and 8 ft long (1.22 m by 2.44 m), 8 ft is the input distance and 4 ft the output distance; hence, the mechanical advantage is 2. If the ramp length were doubled to 16 ft (4.88 m), the mechanical advantage would likewise double to 4, and so on. The concept of work, in terms of physics, has specific properties that are a subject unto themselves; however, it is important here only to recognize that work is the product of force (that is, effort) multiplied by distance. This means that if one increases the distance, a much smaller quantity of force is needed to achieve the same amount of work. On an everyday level, it is easy to see this in action. Walking or running up a gentle hill, obviously, is easier than going up a steep hill. Therefore, if one’s primary purpose is to conserve effort, it is best to choose the gentler hill. On the other hand, one may wish to minimize distance—or, if moving for the purpose of exercise,
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to maximize force input to burn calories. In either case, the steeper hill would be the better option.
Mechanical Advantage and Simple Machines
W E D G E S . The type of inclined plane discussed thus far is a ramp, but there are a number of much smaller varieties of inclined plane at work in the everyday world. A knife is an excellent example of one of the most common types, a wedge. Again, the mechanical advantage of a wedge is the ratio of length to height, which, in the knife, would be the depth of the blade compared to its cross-sectional width. Due to the ways in which wedges are used, however, friction plays a much greater role, therefore greatly reducing the theoretical mechanical advantage.
Other types of wedges may be used with a lever, as a form of fulcrum for raising objects. Or, a wedge may be placed under objects to stabilize them, as for instance, when a person puts a folded matchbook under the leg of a restaurant table to stop it from wobbling. Wedges also stop other objects from moving: a triangular piece of wood under a door will keep it from closing, and a more substantial wedge under the front wheels of a car will stop it from rolling forward. Variations of the wedge are everywhere. Consider all the types of cutting or chipping devices that exist: scissors, chisels, ice picks, axes, splitting wedges (used with a mallet to split a log down the center), saws, plows, electric razors, etc. Then there are devices that use a complex assembly of wedges working together. The part of a key used to open a lock is really just a row of wedges for moving the pins inside the lock to the proper position for opening the door. Similarly, each tooth in a zipper is a tiny wedge that fits tightly with the adjacent teeth. S C R E W S . As the wheel is, without a doubt, the greatest conceptual variation on the lever, so the screw may be identified as a particularly cunning adaptation of an inclined plane. The uses of screws today are many and obvious, but as with wheels and axles, these machines have more applications than are commonly recognized. Not only are there screws for holding things together, but there are screws such as those on vises, clamps, or monkey wrenches for applying force to objects.
A screw is an inclined plane in the shape of a helix, wrapped around an axis or cylinder. In order to determine its mechanical advantage, one must first find the pitch, which is the distance
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A
SCREW, LIKE THIS CORKSCREW USED TO OPEN A BOTTLE OF WINE, IS AN INCLINED PLANE IN THE SHAPE OF A
HELIX, WRAPPED AROUND AN AXIS OR CYLINDER. (Ecoscene/Corbis. Reproduced by permission.)
between adjacent threads. The other variable is lever arm, which with a screwdriver is the radius, or on a wrench, the length from the crescent or clamp to the area of applied force. Obviously, the lever arm is much greater for a wrench, which explains why a wrench is sometimes preferable to a screwdriver, when removing a highly resistant material screw or bolt. When one rotates a screw of a given pitch, the applied force describes a circle whose area may be calculated as 2πL, where L is the lever arm. This figure, when divided by the pitch, is the same as the ratio between the distance of force input to force output. Either number is equal to the mechanical advantage for a screw. As suggested earlier, that mechanical advantage is usually low, because force input (screwing in the screw) takes place in a much greater range of motion than force output (the screw working its way into the surface). But this is exactly what the screw is designed to do, and what it lacks in mechanical advantage, it more than makes up in its holding power.
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cal Archimedes screw, a device for lifting water. The invention consists of a metal pipe in a corkscrew shape, which draws water upward as it revolves. It proved particularly useful for lifting water that had seeped into the lower parts of a ship, and in many countries today, it remains in use as a simple pump for drawing water out of the ground. Some historians maintain that Archimedes did not invent the screw-type pump, but rather saw an example of it in Egypt. In any case, he clearly developed a practical version of the device, and it soon gained application throughout the ancient world. Archaeologists discovered a screw-driven olive press in the ruins of Pompeii, destroyed by the eruption of Mt. Vesuvius in A.D. 79, and Hero of Alexandria later mentioned the use of a screw-type machine in his Mechanica.
As with the lever and pulley, Archimedes did not invent the screw, but he did greatly improve human understanding of it. Specifically, he developed a mathematical formula for a simple spiral, and translated this into the highly practi-
Yet, Archimedes is the figure most widely associated with the development of this wondrous device. Hence, in 1837, when the SwedishAmerican engineer John Ericsson (1803-1899) demonstrated the use of a screw-driven ship’s propeller, he did so on a craft he named the Archimedes.
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From screws planted in wood to screws that drive ships at sea, the device is everywhere in modern life. Faucets, corkscrews, drills, and meat grinders are obvious examples. Though many types of jacks used for lifting an automobile or a house are levers, others are screw assemblies on which one rotates the handle along a horizontal axis. In fact, the jack is a particularly interesting device. Versions of the jack represent all three types of simple machine: lever, inclined plane, and hydraulic press.
The Hydraulic Press As noted earlier, the hydraulic press came into existence much, much later than the lever or inclined plane, and its birth can be seen within the context of a larger movement toward the use of water power, including steam. A little more than a quarter-century after Pascal created the theoretical framework for hydraulic power, his countryman Denis Papin (1647-1712) introduced the steam digester, a prototype for the pressure cooker. In 1687, Papin published a work describing a machine in which steam operated a piston—an early model for the steam engine. Papin’s concept, which was on the absolute cutting edge of technological development at that time, utilized not only steam power but also the very hydraulic concept that Pascal had identified a few decades earlier. Indeed, the assembly of pistons and cylinders that forms the central component of the internal-combustion engine reflects this hydraulic rule, discovered by Pascal in 1653. It was then that he formulated what is known as Pascal’s principle: that the external pressure applied on a fluid is transmitted uniformly throughout the entire body of that fluid. Inside a piston and cylinder assembly, one of the most basic varieties of hydraulic press, the pressure is equal to the ratio of force to the horizontal area of pressure. A simple hydraulic press of the variety that might be used to raise a car in an auto shop typically consists of two large cylinders side by side, connected at the bottom by a channel in which valves control flow. When one applies force over a given area of input—that is, by pressing down on one cylinder—this yields a uniform pressure that causes output in the second cylinder.
S C I E N C E O F E V E RY DAY T H I N G S
Once again, mechanical advantage is equal to the ratio of force output to force input, and for a hydraulic press, this can also be measured as the ratio of area output to area input. Just as there is an inverse relationship between lever arm and force in a lever, and between length and height in an inclined plane, so there is such a relationship between horizontal area and force in a hydraulic pump. Consequently, in order to increase force, one should minimize area.
Mechanical Advantage and Simple Machines
However, there is another factor to consider: height. The mechanical advantage of a hydraulic pump is equal to the vertical distance to which the input force is applied, divided by that of the output force. Hence, the greater the height of the input cylinder compared to the output cylinder, the greater the mechanical advantage. And since these three factors—height, area, and force— work together, it is possible to increase the lifting force and area by minimizing the height. Consider once again the auto-shop car jack. Typically, the input cylinder will be relatively tall and thin, and the output cylinder short and squat. Because the height of the input cylinder is large, the area of input will be relatively small, as will the force of input. But according to Pascal’s principle, whatever the force applied on the input, the pressure will be the same on the output. At the output end, where the car is raised, one needs a large amount of force and a relatively large lifting area. Therefore, height is minimized to increase force and area. If the output area is 10 times the size of the input area, an input force of 1 unit will produce an output force of 10 units—but in order to raise the weight by 1 unit of height, the input piston must move downward by 10 units. This type of car jack provides a basic model of the hydraulic press in operation, but, in fact, hydraulic technology has many more applications. A hydraulic pump, whether for pumping air into a tire or water from a basement, uses very much the same principle as the hydraulic jack. So too does the hydraulic ram, used in machines ranging from bulldozers to the hydraulic lifts used by firefighters and utility workers to reach great heights. In a hydraulic ram, however, the characteristics of the input and output cylinders are reversed from those of a car jack. The input cylinder, called the master cylinder, is short and squat, whereas the output cylinder—the slave
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Mechanical Advantage and Simple Machines
KEY TERMS A machine that
a crowbar, input would be the energy one
combines multiple levers to accomplish its
expends by pushing down on the bar.
task. An example is a piano or manual
Input force is often called applied force,
typewriter.
effort force, or simply effort.
COMPOUND LEVER:
CLASS I LEVER:
A lever in which the
One of the three basic varieties
of machine, a lever consists of a rigid bar
output force. Examples include a crowbar,
supported at one point, known as the ful-
a nail puller, and scissors.
crum.
CLASS II LEVER:
A lever in which the
output force is between the input force and the fulcrum. Class II levers, of which wheelbarrows and bottle openers are
On a lever, the distance
LEVER ARM:
from the input force or the output force to the fulcrum. A device that transmits or
examples, maximize output force at the
MACHINE:
expense of range of motion.
modifies force or torque for a specific pur-
CLASS III LEVER:
A lever in which
pose. The
the input force is between the output force
MECHANICAL
and the fulcrum. Class III levers, of which
ratio of force output to force input for a
a fishing rod is an example, maximize
machine.
range of motion at the expense of output force.
MOMENT ARM:
ADVANTAGE:
For an object experi-
encing torque, moment arm is the distance The ratio of actual
from the pivot or balance point to the vec-
mechanical advantage to theoretical
tor on which force is being applied.
mechanical advantage.
Moment arm is always perpendicular to
EFFICIENCY:
FRICTION:
The force that resists
motion when the surface of one object
the direction of force. OUTPUT:
The results achieved from the
comes into contact with the surface of
operation of a machine. In a Class I lever
another.
such as a crowbar, output is the moving of
FULCRUM:
The support point of a
lever. INERTIA:
a stone or other heavy load dislodged by the crowbar. Output force is often called
The tendency of an object in
the load or resistance force.
motion to remain in motion, and of an
TORQUE:
object at rest to remain at rest.
turning force; in scientific terms, it is
INPUT:
The effort supplied by the oper-
ator of a machine. In a Class I lever such as
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LEVER:
fulcrum is between the input force and
In general terms, torque is
the product of moment arm multiplied by force.
cylinder—is tall and thin. The reason for this change is that in objects using a hydraulic ram, height is more important than force output: they
are often raising people rather than cars. When the slave cylinder exerts pressure on the stabilizer ram above it (the bucket containing the firefight-
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er, for example), it rises through a much larger range of vertical motion than that of the fluid flowing from the master cylinder. As noted earlier, the pistons of a car engine are hydraulic pumps—specifically, reciprocating hydraulic pumps, so named because they all work together. In scientific terms, “fluid” can mean either a liquid or a gas such as air; hence, there is an entire subset of hydraulic machines that are pneumatic, or air-powered. Among these are power brakes in a car, pneumatic drills, and even hovercrafts. As with the other two varieties of simple machine, the hydraulic press is in evidence throughout virtually every nook and cranny of daily life. The pump in a toilet tank is a type of hydraulic press, as is the inner chamber of a pen. So too are aerosol cans, fire extinguishers, scuba tanks, water meters, and pressure gauges.
Bains, Rae. Simple Machines. Mahwah, N.J.: Troll Associates, 1985. Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Canizares, Susan. Simple Machines. New York: Scholastic, 1999. Haslam, Andrew and David Glover. Machines. Photography by Jon Barnes. Chicago: World Book, 1998. “Inventors Toolbox: The Elements of Machines” (Web site). (March 9, 2001). Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998. “Machines” (Web site). (March 9, 2001). “Motion, Energy, and Simple Machines” (Web site). (March 9, 2001). O’Brien, Robert, and the Editors of Life. Machines. New York: Time-Life Books, 1964.
WHERE TO LEARN MORE
“Simple Machines” (Web site). (March 9, 2001).
Archimedes (Web site). (March 9, 2001.)
Singer, Charles Joseph, et al., editors. A History of Technology (8 vols.) Oxford, England: Clarendon Press, 1954-84.
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ENERGY Energy
CONCEPT As with many concepts in physics, energy—along with the related ideas of work and power—has a meaning much more specific, and in some ways quite different, from its everyday connotation. According to the language of physics, a person who strains without success to pull a rock out of the ground has done no work, whereas a child playing on a playground produces a great deal of work. Energy, which may be defined as the ability of an object to do work, is neither created nor destroyed; it simply changes form, a concept that can be illustrated by the behavior of a bouncing ball.
HOW IT WORKS In fact, it might actually be more precise to say that energy is the ability of “a thing” or “something” to do work. Not only tangible objects (whether they be organic, mechanical, or electromagnetic) but also non-objects may possess energy. At the subatomic level, a particle with no mass may have energy. The same can be said of a magnetic force field. One cannot touch a force field; hence, it is not an object—but obviously, it exists. All one has to do to prove its existence is to place a natural magnet, such as an iron nail, within the magnetic field. Assuming the force field is strong enough, the nail will move through space toward it—and thus the force field will have performed work on the nail.
A person straining, and failing, to pull a rock from the ground has performed no work (in terms of physics) because nothing has been moved. On the other hand, a child on a playground performs considerable work: as she runs from the slide to the swing, for instance, she has moved her own weight (a variety of force) across a distance. She is even working when her movement is back-and-forth, as on the swing. This type of movement results in no net displacement, but as long as displacement has occurred at all, work has occurred. Similarly, when a man completes a full pushup, his body is in the same position—parallel to the floor, arms extended to support him—as he was before he began it; yet he has accomplished work. If, on the other hand, he at the end of his energy, his chest is on the floor, straining but failing, to complete just one more push-up, then he is not working. The fact that he feels as though he has worked may matter in a personal sense, but it does not in terms of physics.
Work may be defined in general terms as the exertion of force over a given distance. In order
CA L C U LAT I N G W O R K . Work can be defined more specifically as the product of force and distance, where those two vectors are exerted in the same direction. Suppose one were to drag a block of a certain weight across a given distance of floor. The amount of force one exerts parallel to the floor itself, multiplied by the distance, is equal to the amount of work exerted. On the other hand, if one pulls up on the block in a
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for work to be accomplished, there must be a displacement in space—or, in colloquial terms, something has to be moved from point A to point B. As noted earlier, this definition creates results that go against the common-sense definition of “work.”
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Energy
WHILE
THIS PLAYER DRIBBLES HIS BASKETBALL, THE BALL EXPERIENCES A COMPLEX ENERGY TRANSFER AS IT HITS
THE FLOOR AND BOUNCES BACK UP. (Photograph by David Katzenstein/Corbis. Reproduced by permission.)
position perpendicular to the floor, that force does not contribute toward the work of dragging the block across the floor, because it is not par allel to distance as defined in this particular situation.
force must be multiplied by cos 30°, which is equal to 0.866. Note that the cosine is less than 1; hence when multiplied by the total force exerted, it will yield a figure 13.4% smaller than the total force. In fact, the larger the angle, the smaller the cosine; thus for 90°, the value of cos = 0. On the other hand, for an angle of 0°, cos = 1. Thus, if total force is exerted parallel to the floor—that is, at a 0°-angle to it—then the component of force that counts toward total work is equal to the total force. From the standpoint of physics, this would be a highly work-intensive operation.
Similarly, if one exerts force on the block at an angle to the floor, only a portion of that force counts toward the net product of work—a portion that must be quantified in terms of trigonometry. The line of force parallel to the floor may be thought of as the base of a triangle, with a line perpendicular to the floor as its second side. Hence there is a 90°-angle, making it a right triangle with a hypotenuse. The hypotenuse is the line of force, which again is at an angle to the floor.
G RAV I T Y A N D O T H E R P E C U L I A R I T I E S O F W O R K . The above dis-
The component of force that counts toward the total work on the block is equal to the total force multiplied by the cosine of the angle. A cosine is the ratio between the leg adjacent to an acute (less than 90°) angle and the hypotenuse. The leg adjacent to the acute angle is, of course, the base of the triangle, which is parallel to the floor itself. Sizes of triangles may vary, but the ratio expressed by a cosine (abbreviated cos) does not. Hence, if one is pulling on the block by a rope that makes a 30°-angle to the floor, then
cussion relates entirely to work along a horizontal plane. On the vertical plane, by contrast, work is much simpler to calculate due to the presence of a constant downward force, which is, of course, gravity. The force of gravity accelerates objects at a rate of 32 ft (9.8 m)/sec2. The mass (m) of an object multiplied by the rate of gravitational acceleration (g) yields its weight, and the formula for work done against gravity is equal to weight multiplied by height (h) above some lower reference point: mgh.
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Energy
HYDROELECTRIC
DAMS, LIKE THE
SHASTA
DAM IN
CALIFORNIA,
SUPERBLY ILLUSTRATE THE PRINCIPLE OF ENERGY
CONVERSION. (Photograph by Charles E. Rotkin/Corbis. Reproduced by permission.)
Distance and force are both vectors—that is, quantities possessing both magnitude and direction. Yet work, though it is the product of these two vectors, is a scalar, meaning that only the magnitude of work (and not the direction over which it is exerted) is important. Hence mgh can refer either to the upward work one exerts against gravity (that is, by lifting an object to a certain height), or to the downward work that gravity performs on the object when it is dropped. The direction of h does not matter, and its value is purely relative, referring to the vertical distance between one point and another.
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the truth that work, in the sense in which it is applied by physicists, is quite different from “work” as it understood in the day-to-day world. There is a highly personal quality to the everyday meaning of the term, which is completely lacking from its physics definition.
The fact that gravity can “do work”—and the irrelevance of direction—further illustrates
If someone carried a heavy box up five flights of stairs, that person would quite naturally feel justified in saying “I’ve worked.” Certainly he or she would feel that the work expended was far greater than that of someone who had simply allowed the the elevator to carry the box up those five floors. Yet in terms of work done against gravity, the work done on the box by the elevator is exactly the same as that performed by the per-
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son carrying it upstairs. The identity of the “worker”—not to mention the sweat expended or not expended—is irrelevant from the standpoint of physics.
Energy
Measurement of Work and Power In the metric system, a newton (N) is the amount of force required to accelerate 1 kg of mass by 1 meter per second squared (m/s2). Work is measured by the joule (J), equal to 1 newton-meter (N • m). The British unit of force is the pound, and work is measured in foot-pounds, or the work done by a force of 1 lb over a distance of one foot. Power, the rate at which work is accomplished over time, is the same as work divided by time. It can also be calculated in terms of force multiplied by speed, much like the force-multiplied-by-distance formula for work. However, as with work, the force and speed must be in the same direction. Hence, the formula for power in these terms is F • cos θ • v, where F=force, v=speed, and cos θ is equal to the cosine of the angle θ (the Greek letter theta) between F and the direction of v. The metric-system measure of power is the watt, named after James Watt (1736-1819), the Scottish inventor who developed the first fully viable steam engine and thus helped inaugurate the Industrial Revolution. A watt is equal to 1 joule per second, but this is such a small unit that it is more typical to speak in terms of kilowatts, or units of 1,000 watts. Ironically, Watt himself—like most people in the British Isles and America—lived in a world that used the British system, in which the unit of power is the foot-pound per second. The latter, too, is very small, so for measuring the power of his steam engine, Watt suggested a unit based on something quite familiar to the people of his time: the power of a horse. One horsepower (hp) is equal to 550 foot-pounds per second.
IN THIS 1957 PHOTOGRAPH, ITALIAN OPERA SINGER LUIGI INFANTINO TRIES TO BREAK A WINE GLASS BY SINGING A HIGH “C” NOTE. CONTRARY TO POPULAR BELIEF, THE NOTE DOES NOT HAVE TO BE A PARTICULARLY HIGH ONE TO BREAK THE GLASS: RATHER, THE NOTE SHOULD BE ON THE SAME WAVELENGTH AS THE GLASS’S
OWN
VIBRATIONS.
WHEN
THIS
OCCURS,
SOUND ENERGY IS TRANSFERRED DIRECTLY TO THE GLASS, WHICH IS SHATTERED BY THIS SUDDEN NET INTAKE OF ENERGY. (Hulton-Deutsch Collection/Corbis. Repro-
duced by permission.)
created quite deliberately over a matter of just a few years following the French Revolution, which broke out in 1789. The metric system was adopted ten years later.
course, is horridly cumbersome compared to the metric system, and thus it long ago fell out of favor with the international scientific community. The British system is the product of loosely developed conventions that emerged over time: for instance, a foot was based on the length of the reigning king’s foot, and in time, this became standardized. By contrast, the metric system was
During the revolutionary era, French intellectuals believed that every aspect of existence could and should be treated in highly rational, scientific terms. Out of these ideas arose much folly—especially after the supposedly “rational” leaders of the revolution began chopping off people’s heads—but one of the more positive outcomes was the metric system. This system, based entirely on the number 10 and its exponents, made it easy to relate one figure to another: for instance, there are 100 centimeters in a meter and 1,000 meters in a kilometer. This is vastly more convenient than converting 12 inches to a foot, and 5,280 feet to a mile.
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S O RT I N G O U T M E T R I C A N D B R I T I S H U N I T S . The British system, of
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For this reason, scientists—even those from the Anglo-American world—use the metric system for measuring not only horizontal space, but volume, temperature, pressure, work, power, and so on. Within the scientific community, in fact, the metric system is known as SI, an abbreviation of the French Système International d’Unités— that is, “International System of Units.” Americans have shown little interest in adopting the SI system, yet where power is concerned, there is one exception. For measuring the power of a mechanical device, such as an automobile or even a garbage disposal, Americans use the British horsepower. However, for measuring electrical power, the SI kilowatt is used. When an electric utility performs a meter reading on a family’s power usage, it measures that usage in terms of electrical “work” performed for the family, and thus bills them by the kilowatt-hour.
Three Types of Energy KINETIC AND POTENTIAL ENE R GY F O R M U LA E . Earlier, energy was
defined as the ability of an object to accomplish work—a definition that by this point has acquired a great deal more meaning. There are three types of energy: kinetic energy, or the energy that something possesses by virtue of its motion; potential energy, the energy it possesses by virtue of its position; and rest energy, the energy it possesses by virtue of its mass. The formula for kinetic energy is KE = 1⁄2 mv2. In other words, for an object of mass m, kinetic energy is equal to half the mass multiplied by the square of its speed v. The actual derivation of this formula is a rather detailed process, involving reference to the second of the three laws of motion formulated by Sir Isaac Newton (1642-1727.) The second law states that F = ma, in other words, that force is equal to mass multiplied by acceleration. In order to understand kinetic energy, it is necessary, then, to understand the formula for uniform acceleration. The latter is vf2 = v02 + 2as, where vf2 is the final speed of the object, v02 its initial speed, a acceleration and s distance. By substituting values within these equations, one arrives at the formula of 1⁄2 mv2 for kinetic energy.
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within an object, one must perform an amount of work on it equal to Fs. Hence, kinetic energy also equals Fs, and thus the preceding paragraph simply provides a means for translating that into more specific terms. The potential energy (PE) formula is much simpler, but it also relates to a work formula given earlier: that of work done against gravity. Potential energy, in this instance, is simply a function of gravity and the distance h above some reference point. Hence, its formula is the same as that for work done against gravity, mgh or wh, where w stands for weight. (Note that this refers to potential energy in a gravitational field; potential energy may also exist in an electromagnetic field, in which case the formula would be different from the one presented here.) R E S T E N E R GY A N D I T S I N T R I G U I N G F O R M U LA . Finally, there is
rest energy, which, though it may not sound very exciting, is in fact the most intriguing—and the most complex—of the three. Ironically, the formula for rest energy is far, far more complex in derivation than that for potential or even kinetic energy, yet it is much more well-known within the popular culture. Indeed, E = mc2 is perhaps the most famous physics formula in the world—even more so than the much simpler F = ma. The formula for rest energy, as many people know, comes from the man whose Theory of Relativity invalidated certain specifics of the Newtonian framework: Albert Einstein (1879-1955). As for what the formula actually means, that will be discussed later.
REAL-LIFE A P P L I C AT I O N S Falling and Bouncing Balls
The above is simply another form of the general formula for work—since energy is, after all, the ability to perform work. In order to produce an amount of kinetic energy equal to 1⁄2 mv2
One of the best—and most frequently used— illustrations of potential and kinetic energy involves standing at the top of a building, holding a baseball over the side. Naturally, this is not an experiment to perform in real life. Due to its relatively small mass, a falling baseball does not have a great amount of kinetic energy, yet in the real world, a variety of other conditions (among them inertia, the tendency of an object to maintain its state of motion) conspire to make a hit on the head with a baseball potentially quite serious.
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If dropped from a great enough height, it could be fatal.
of another ball and another form of vertical motion.
When one holds the baseball over the side of the building, potential energy is at a peak, but once the ball is released, potential energy begins to decrease in favor of kinetic energy. The relationship between these, in fact, is inverse: as the value of one decreases, that of the other increases in exact proportion. The ball will only fall to the point where its potential energy becomes 0, the same amount of kinetic energy it possessed before it was dropped. At the same point, kinetic energy will have reached maximum value, and will be equal to the potential energy the ball possessed at the beginning. Thus the sum of kinetic energy and potential energy remains constant, reflecting the conservation of energy, a subject discussed below.
This time instead of a baseball, the ball should be one that bounces: any ball will do, from a basketball to a tennis ball to a superball. And rather than falling from a great height, this one is dropped through a range of motion ordinary for a human being bouncing a ball. It hits the floor and bounces back—during which time it experiences a complex energy transfer.
It is relatively easy to understand how the ball acquires kinetic energy in its fall, but potential energy is somewhat more challenging to comprehend. The ball does not really “possess” the potential energy: potential energy resides within an entire system comprised by the ball, the space through which it falls, and the Earth. There is thus no “magic” in the reciprocal relationship between potential and kinetic energy: both are part of a single system, which can be envisioned by means of an analogy. Imagine that one has a 20-dollar bill, then buys a pack of gum. Now one has, say, $19.20. The positive value of dollars has decreased by $0.80, but now one has increased “non-dollars” or “anti-dollars” by the same amount. After buying lunch, one might be down to $12.00, meaning that “anti-dollars” are now up to $8.00. The same will continue until the entire $20.00 has been spent. Obviously, there is nothing magical about this: the 20-dollar bill was a closed system, just like the one that included the ball and the ground. And just as potential energy decreased while kinetic energy increased, so “non-dollars” increased while dollars decreased.
Energy
As was the case with the baseball dropped from the building, the ball (or more specifically, the system involving the ball and the floor) possesses maximum potential energy prior to being released. Then, in the split-second before its impact on the floor, kinetic energy will be at a maximum while potential energy reaches zero. So far, this is no different than the baseball scenario discussed earlier. But note what happens when the ball actually hits the floor: it stops for an infinitesimal fraction of a moment. What has happened is that the impact on the floor (which in this example is assumed to be perfectly rigid) has dented the surface of the ball, and this saps the ball’s kinetic energy just at the moment when the energy had reached its maximum value. In accordance with the energy conservation law, that energy did not simply disappear: rather, it was transferred to the floor. Meanwhile, in the wake of its huge energy loss, the ball is motionless. An instant later, however, it reabsorbs kinetic energy from the floor, undents, and rebounds. As it flies upward, its kinetic energy begins to diminish, but potential energy increases with height. Assuming that the person who released it catches it at exactly the same height at which he or she let it go, then potential energy is at the level it was before the ball was dropped. WHEN A BALL LOSES ITS B O U N C E . The above, of course, takes little
B O U N C I N G B AC K . The example of the baseball illustrates one of the most fundamental laws in the universe, the conservation of energy: within a system isolated from all other outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place. An interesting example of this comes from the case
account of energy “loss”—that is, the transfer of energy from one body to another. In fact, a part of the ball’s kinetic energy will be lost to the floor because friction with the floor will lead to an energy transfer in the form of thermal, or heat, energy. The sound that the ball makes when it bounces also requires a slight energy loss; but friction—a force that resists motion when the surface of one object comes into contact with the surface of another—is the principal culprit where energy transfer is concerned.
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Of particular importance is the way the ball responds in that instant when it hits bottom and stops. Hard rubber balls are better suited for this purpose than soft ones, because the harder the rubber, the greater the tendency of the molecules to experience only elastic deformation. What this means is that the spacing between molecules changes, yet their overall position does not. If, however, the molecules change positions, this causes them to slide against one another, which produces friction and reduces the energy that goes into the bounce. Once the internal friction reaches a certain threshold, the ball is “dead”—that is, unable to bounce. The deader the ball is, the more its kinetic energy turns into heat upon impact with the floor, and the less energy remains for bouncing upward.
Varieties of Energy in Action The preceding illustration makes several references to the conversion of kinetic energy to thermal energy, but it should be stressed that there are only three fundamental varieties of energy: potential, kinetic, and rest. Though heat is often discussed as a form unto itself, this is done only because the topic of heat or thermal energy is complex: in fact, thermal energy is simply a result of the kinetic energy between molecules. To draw a parallel, most languages permit the use of only three basic subject-predicate constructions: first person (“I”), second person (“you”), and third person (“he/she/it.”) Yet within these are endless varieties such as singular and plural nouns or various temporal orientations of verbs: present (“I go”); present perfect (“I have gone”); simple past (“I went”); past perfect (“I had gone.”) There are even “moods,” such as the subjunctive or hypothetical, which permit the construction of complex thoughts such as “I would have gone.” Yet for all this variety in terms of sentence pattern—actually, a degree of variety much greater than for that of energy types—all subject-predicate constructions can still be identified as first, second, or third person.
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between two electromagnetically charged particles is analogous to the force of gravity. M E C H A N I CA L E N E R GY. One term
not listed among manifestations of energy is mechanical energy, which is something different altogether: the sum of potential and kinetic energy. A dropped or bouncing ball was used as a convenient illustration of interactions within a larger system of mechanical energy, but the example could just as easily have been a roller coaster, which, with its ups and downs, quite neatly illustrates the sliding scale of kinetic and potential energy. Likewise, the relationship of Earth to the Sun is one of potential and kinetic energy transfers: as with the baseball and Earth itself, the planet is pulled by gravitational force toward the larger body. When it is relatively far from the Sun, it possesses a higher degree of potential energy, whereas when closer, its kinetic energy is highest. Potential and kinetic energy can also be illustrated within the realm of electromagnetic, as opposed to gravitational, force: when a nail is some distance from a magnet, its potential energy is high, but as it moves toward the magnet, kinetic energy increases. E N E R GY C O N V E R S I O N I N A DA M . A dam provides a beautiful illustration
of energy conversion: not only from potential to kinetic, but from energy in which gravity provides the force component to energy based in electromagnetic force. A dam big enough to be used for generating hydroelectric power forms a vast steel-and-concrete curtain that holds back millions of tons of water from a river or other body. The water nearest the top—the “head” of the dam—thus has enormous potential energy.
One might thus describe thermal energy as a manifestation of energy, rather than as a discrete form. Other such manifestations include electromagnetic (sometimes divided into electrical and magnetic), sound, chemical, and nuclear. The principles governing most of these are similar: for instance, the positive or negative attraction
Hydroelectric power is created by allowing controlled streams of this water to flow downward, gathering kinetic energy that is then transferred to powering turbines. Dams in popular vacation spots often release a certain amount of water for recreational purposes during the day. This makes it possible for rafters, kayakers, and others downstream to enjoy a relatively fast-flowing river. (Or, to put it another way, a stream with high kinetic energy.) As the day goes on, however, the sluice-gates are closed once again to build up the “head.” Thus when night comes, and energy demand is relatively high as people retreat to their homes, vacation cabins, and hotels, the dam is ready to provide the power they need.
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O T H E R M A N I F E S TAT I O N S O F E N E R G Y. Thermal and electromagnetic
energy are much more readily recognizable manifestations of energy, yet sound and chemical energy are two forms that play a significant part as well. Sound, which is essentially nothing more than the series of pressure fluctuations within a medium such as air, possesses enormous energy: consider the example of a singer hitting a certain note and shattering a glass. Contrary to popular belief, the note does not have to be particularly high: rather, the note should be on the same wavelength as the glass’s own vibrations. When this occurs, sound energy is transferred directly to the glass, which is shattered by this sudden net intake of energy. Sound waves can be much more destructive than that: not only can the sound of very loud music cause permanent damage to the ear drums, but also, sound waves of certain frequencies and decibel levels can actually drill through steel. Indeed, sound is not just a by-product of an explosion; it is part of the destructive force. As for chemical energy, it is associated with the pull that binds together atoms within larger molecular structures. The formation of water molecules, for instance, depends on the chemical bond between hydrogen and oxygen atoms. The combustion of materials is another example of chemical energy in action. With both chemical and sound energy, however, it is easy to show how these simply reflect the larger structure of potential and kinetic energy discussed earlier. Hence sound, for instance, is potential energy when it emerges from a source, and becomes kinetic energy as it moves toward a receiver (for example, a human ear). Furthermore, the molecules in a combustible material contain enormous chemical potential energy, which becomes kinetic energy when released in a fire.
energy—to a much greater extent than thermal or chemical energy—involves not only kinetic and potential energy, but also the mysterious, extraordinarily powerful, form known as rest energy. Throughout this discussion, there has been little mention of rest energy; yet it is ever-present. Kinetic and potential energy rise and fall with respect to one another; but rest energy changes little. In the baseball illustration, for instance, the ball had the same rest energy at the top of the building as it did in flight—the same rest energy, in fact, that it had when sitting on the ground. And its rest energy is enormous. N U C L E A R WA R FA R E . This brings back the subject of the rest energy formula: E = mc2, famous because it made possible the creation of the atomic bomb. The latter, which fortunately has been detonated in warfare only twice in history, brought a swift end to World War II when the United States unleashed it against Japan in August 1945. From the beginning, it was clear that the atom bomb possessed staggering power, and that it would forever change the way nations conducted their affairs in war and peace.
Yet the atom bomb involved only nuclear fission, or the splitting of an atom, whereas the hydrogen bomb that appeared just a few years after the end of World War II used an even more powerful process, the nuclear fusion of atoms. Hence, the hydrogen bomb upped the ante to a much greater extent, and soon the two nuclear superpowers—the United States and the Soviet Union—possessed the power to destroy most of the life on Earth.
Nuclear energy is similar to chemical energy, though in this instance, it is based on the binding of particles within an atom and its nucleus. But it is also different from all other kinds of energy, because its force component is neither gravitational nor electromagnetic, but based on one of two other known varieties of force: strong nuclear and weak nuclear. Furthermore, nuclear
The next four decades were marked by a superpower struggle to control “the bomb” as it came to be known—meaning any and all nuclear weapons. Initially, the United States controlled all atomic secrets through its heavily guarded Manhattan Project, which created the bombs used against Japan. Soon, however, spies such as Julius and Ethel Rosenberg provided the Soviets with U.S. nuclear secrets, ensuring that the dictatorship of Josef Stalin would possess nuclear capabilities as well. (The Rosenbergs were executed for treason, and their alleged innocence became a celebrated cause among artists and intellectuals; however, Soviet documents released since the collapse of the Soviet empire make it clear that they were guilty as charged.)
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Energy
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Energy
KEY TERMS CONSERVATION OF ENERGY:
A
JOULE:
The SI measure of work. One
law of physics which holds that within a
joule (1 J) is equal to the work required
system isolated from all other outside fac-
to accelerate 1 kilogram of mass by 1
tors, the total amount of energy re-mains
meter per second squared (1 m/s2) over a
the same, though transformations of ener-
distance of 1 meter. Due to the small size
gy from one form to another take place.
of the joule, however, it is often replaced
COSINE:
For an acute (less than 90°)
in a right triangle, the cosine (abbreviated
by the kilowatt-hour, equal to 3.6 million (3.6 • 106) J.
cos) is the ratio between the adjacent leg
KINETIC ENERGY:
and the hypotenuse. Regardless of the size
an object possesses by virtue of its motion.
of the triangle, this figure is a constant for MATTER:
any particular angle.
The energy that
Physical substance that occu-
pies space, has mass, is composed of atoms
The ability of an object (or
(or in the case of subatomic particles, is
in some cases a non-object, such as a mag-
part of an atom), and is convertible into
netic force field) to accomplish work.
energy.
ENERGY:
FRICTION:
The force that resists
MECHANICAL ENERGY:
motion when the surface of one object
potential energy and kinetic energy within
comes into contact with the surface of
a system.
another. POTENTIAL ENERGY: HORSEPOWER:
The British unit of
power, equal to 550 foot-pounds per
position. POWER:
HYPOTENUSE:
In a right triangle, the
side opposite the right angle.
Both nations began building up missile arsenals. It was not, however, just a matter of the United States and the Soviet Union. By the 1970s, there were at least three other nations in the “nuclear club”: Britain, France, and China. There were also other countries on the verge of developing nuclear bombs, among them India and Israel. Furthermore, there was a great threat that a terrorist leader such as Libya’s Muammar alQaddafi would acquire nuclear weapons and do the unthinkable: actually use them.
The energy
that an object possesses by virtue of its
second.
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The sum of
The rate at which work is
accomplished over time, a figure rendered mathematically as work divided by time.
a sort of high-stakes chess game—to use a metaphor mentioned frequently during the 1970s. Soviet leaders and their American counterparts both recognized that it would be the end of the world if either unleashed their nuclear weapons; yet each was determined to be able to meet the other’s ever-escalating nuclear threat.
Though other nations acquired nuclear weapons, however, the scale of the two superpower arsenals dwarfed all others. And at the heart of the U.S.-Soviet nuclear competition was
United States President Ronald Reagan earned harsh criticism at home for his nuclear buildup and his hard line in negotiations with Soviet President Mikhail Gorbachev; but as a result of this one-upmanship, he put the Soviets into a position where they could no longer compete. As they put more and more money into nuclear weapons, they found themselves less and
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Energy
KEY TERMS
CONTINUED
The SI unit of power is the watt, while the
actions free from interference by outside
British unit is the foot-pound per second.
factors. An example is the baseball dropped
The latter, because it is small, is usually
from a height to illustrate potential energy
reckoned in terms of horsepower.
and kinetic energy the ball, the space
REST ENERGY:
The energy an object
possesses by virtue of its mass. RIGHT TRIANGLE:
A triangle that
includes a right (90°) angle. The other two
through which it falls, and the ground below together form a system. A quantity that possesses
VECTOR:
both magnitude and direction.
angles are, by definition, acute or less
WATT:
than 90°.
to 1 joule per second. Because this is such a
SCALAR:
A quantity that possesses
only magnitude, with no specific direction. SI:
small unit, scientists and engineers typically speak in terms of kilowatts, or units of 1,000 watts.
An abbreviation of the French
Système International d’Unités, which means “International System of Units.” This is the term within the scientific community for the entire metric system, as applied to a wide variety of quantities ranging from length, weight and volume to work and power, as well as electromagnetic units. SYSTEM:
The metric unit of power, equal
WORK:
The exertion of force over a
given distance. Work is the product of force and distance, where force and distance are exerted in the same direction. Hence the actual formula for work is F • cos θ • s, where F = force, s = distance, and cos θ is equal to the cosine of the angle θ (the Greek letter theta) between F and s. In the metric or SI system, work is measured by
In discussions of energy, the
term “system” refers to a closed set of inter-
less able to uphold their already weak economic system. This was precisely Reagan’s purpose in using American economic might to outspend the Soviets—or, in the case of the proposed multitrillion-dollar Strategic Defense Initiative (SDI or “Star Wars”)—threatening to outspend them. The Soviets expended much of their economic energy in competing with U.S. military strength, and this (along with a number of other complex factors), spelled the beginning of the end of the Communist empire.
the joule (J), and in the British system by the foot-pound.
war like it would ever happen again—but brought on the specter of global annihilation. It created a superpower struggle—yet it also ultimately helped bring about the end of Soviet totalitarianism, thus opening the way for a greater level of peace and economic and cultural exchange than the world has ever known. Yet nuclear arsenals still remain, and the nuclear threat is far from over.
historical brief is to illustrate the epoch-making significance of a single scientific formula: E = mc2. It ended World War II and ensured that no
So just what is this literally earth-shattering formula? E stands for rest energy, m for mass, and c for the speed of light, which is 186,000 mi (297,600 km) per second. Squared, this yields an almost unbelievably staggering number.
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E = m c 2 . The purpose of the preceding
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Hence, even an object of insignificant mass possesses an incredible amount of rest energy. The baseball, for instance, weighs only about 0.333 lb, which—on Earth, at least—converts to 0.15 kg. (The latter is a unit of mass, as opposed to weight.) Yet when factored into the rest energy equation, it yields about 3.75 billion kilowatthours—enough to provide an American home with enough electrical power to last it more than 156,000 years! How can a mere baseball possess such energy? It is not the baseball in and of itself, but its mass; thus every object with mass of any kind possesses rest energy. Often, mass energy can be released in very small quantities through purely thermal or chemical processes: hence, when a fire burns, an almost infinitesimal portion of the matter that went into making the fire is converted into energy. If a stick of dynamite that weighed 2.2 lb (1 kg) exploded, the portion of it that “disappeared” would be equal to 6 parts out of 100 billion; yet that portion would cause a blast of considerable proportions. As noted much earlier, the derivation of Einstein’s formula—and, more to the point, how he came to recognize the fundamental principles involved—is far beyond the scope of this essay. What is important is the fact, hypothesized by Einstein and confirmed in subsequent experiments, that matter is convertible to energy, a fact that becomes apparent when matter is accelerated to speeds close to that of light.
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energy. Instead, atomic energy—whether of the wartime or peacetime varieties (that is, in power plants)—involves the acceleration of mere atomic particles. Nor is any atom as good as another. Typically physicists use uranium and other extremely rare minerals, and often, they further process these minerals in highly specialized ways. It is the rarity and expense of those minerals, incidentally—not the difficulty of actually putting atomic principles to work—that has kept smaller nations from developing their own nuclear arsenals. WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Berger, Melvin. Sound, Heat and Light: Energy at Work. Illustrated by Anna DiVito. New York: Scholastic, 1992. Gardner, Robert. Energy Projects for Young Scientists. New York: F. Watts, 1987. “Kinetic and Potential Energy” Thinkquest (Web site). (March 12, 2001). Snedden, Robert. Energy. Des Plaines, IL: Heinemann, Library, 1999. Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996. “Work and Energy” (Web site). (March 12, 2001). World of Coasters (Web site). (March 12, 2001).
Physicists do not possess a means for propelling a baseball to a speed near that of light— or of controlling its behavior and capturing its
Zubrowski, Bernie. Raceways: Having Fun with Balls and Tracks. Illustrated by Roy Doty. New York: Morrow, 1985.
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S C I E N C E O F E V E RY DAY T H I N G S real-life Physics
THERMODYNAMICS GAS LAWS MOLECULAR DYNAMICS S T R U C T U R E O F M AT T E R THERMODYNAMICS H E AT T E M P E RAT U R E T H E R M A L E X PA N S I O N
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Gas Laws
CONCEPT Gases respond more dramatically to temperature and pressure than do the other three basic types of matter (liquids, solids and plasma). For gases, temperature and pressure are closely related to volume, and this allows us to predict their behavior under certain conditions. These predictions can explain mundane occurrences, such as the fact that an open can of soda will soon lose its fizz, but they also apply to more dramatic, lifeand-death situations.
HOW IT WORKS Ordinary air pressure at sea level is equal to 14.7 pounds per square inch, a quantity referred to as an atmosphere (atm). Because a pound is a unit of force and a kilogram a unit of mass, the metric equivalent is more complex in derivation. A newton (N), or 0.2248 pounds, is the metric unit of force, and a pascal (Pa)—1 newton per square meter—the unit of pressure. Hence, an atmosphere, expressed in metric terms, is 1.013 ⫻ 105 Pa.
Gases vs. Solids and Liquids: A Strikingly Different Response Regardless of the units you use, however, gases respond to changes in pressure and temperature in a remarkably different way than do solids or liquids. Using a small water sample, say, 0.2642 gal (1 l), an increase in pressure from 1-2 atm will decrease the volume of the water by less than 0.01%. A temperature increase from 32° to 212°F (0 to 100°C) will increase its volume by only 2% The response of a solid to these changes is even
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less dramatic; however, the reaction of air (a combination of oxygen, nitrogen, and other gases) to changes in pressure and temperature is radically different. For air, an equivalent temperature increase would result in a volume increase of 37%, and an equivalent pressure increase will decrease the volume by a whopping 50%. Air and other gases also have a boiling point below room temperature, whereas the boiling point for water is higher than room temperature and that of solids is much higher. The reason for this striking difference in response can be explained by comparing all three forms of matter in terms of their overall structure, and in terms of their molecular behavior. (Plasma, a gas-like state found, for instance, in stars and comets’ tails, does not exist on Earth, and therefore it will not be included in the comparisons that follow.)
Molecular Structure Determines Reaction Solids possess a definite volume and a definite shape, and are relatively noncompressible: for instance, if you apply extreme pressure to a steel plate, it will bend, but not much. Liquids have a definite volume, but no definite shape, and tend to be noncompressible. Gases, on the other hand, possess no definite volume or shape, and are compressible. At the molecular level, particles of solids tend to be definite in their arrangement and close in proximity—indeed, part of what makes a solid “solid,” in the everyday meaning of that term, is the fact that its constituent parts are basically immovable. Liquid molecules, too, are close in proximity, though random in arrangement. Gas
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molecules, too, are random in arrangement, but tend to be more widely spaced than liquid molecules. Solid particles are slow moving, and have a strong attraction to one another, whereas gas particles are fast-moving, and have little or no attraction. (Liquids are moderate in both regards.) Given these interesting characteristics of gases, it follows that a unique set of parameters— collectively known as the “gas laws”—are needed to describe and predict their behavior. Most of the gas laws were derived during the eighteenth and nineteenth centuries by scientists whose work is commemorated by the association of their names with the laws they discovered. These men include the English chemists Robert Boyle (1627-1691), John Dalton (1766-1844), and William Henry (1774-1836); the French physicists and chemists J. A. C. Charles (1746-1823) and Joseph Gay-Lussac (1778-1850), and the Italian physicist Amedeo Avogadro (1776-1856).
Boyle’s, Charles’s, and GayLussac’s Laws Boyle’s law holds that in isothermal conditions (that is, a situation in which temperature is kept constant), an inverse relationship exists between the volume and pressure of a gas. (An inverse relationship is a situation involving two variables, in which one of the two increases in direct proportion to the decrease in the other.) In this case, the greater the pressure, the less the volume and vice versa. Therefore the product of the volume multiplied by the pressure remains constant in all circumstances. Charles’s law also yields a constant, but in this case the temperature and volume are allowed to vary under isobarometric conditions—that is, a situation in which the pressure remains the same. As gas heats up, its volume increases, and when it cools down, its volume reduces accordingly. Hence, Charles established that the ratio of temperature to volume is constant.
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In Gay-Lussac’s law, a third parameter, volume, is treated as a constant, and the result is a constant ratio between the variables of pressure and temperature. According to Gay-Lussac’s law, the pressure of a gas is directly related to its absolute temperature. Absolute temperature refers to the Kelvin scale, established by William Thomson, Lord Kelvin (1824-1907). Drawing on Charles’s discovery that gas at 0°C (32°F) regularly contracted by about 1/273 of its volume for every Celsius degree drop in temperature, Thomson derived the value of absolute zero (-273.15°C or -459.67°F). Using the Kelvin scale of absolute temperature, Gay-Lussac found that at lower temperatures, the pressure of a gas is lower, while at higher temperatures its pressure is higher. Thus, the ratio of pressure to temperature is a constant.
Avogadro’s Law Gay-Lussac also discovered that the ratio in which gases combine to form compounds can be expressed in whole numbers: for instance, water is composed of one part oxygen and two parts hydrogen. In the language of modern science, this would be expressed as a relationship between molecules and atoms: one molecule of water contains one oxygen atom and two hydrogen atoms. In the early nineteenth century, however, scientists had yet to recognize a meaningful distinction between atoms and molecules. Avogadro was the first to achieve an understanding of the difference. Intrigued by the whole-number relationship discovered by Gay-Lussac, Avogadro reasoned that one liter of any gas must contain the same number of particles as a liter of another gas. He further maintained that gas consists of particles—which he called molecules—that in turn consist of one or more smaller particles.
By now a pattern should be emerging: both of the aforementioned laws treat one parameter (temperature in Boyle’s, pressure in Charles’s) as unvarying, while two other factors are treated as variables. Both in turn yield relationships between the two variables: in Boyle’s law, pressure and volume are inversely related, whereas in Charles’s law, temperature and volume are directly related.
In order to discuss the behavior of molecules, it was necessary to establish a large quantity as a basic unit, since molecules themselves are very small. For this purpose, Avogadro established the mole, a unit equal to 6.022137 ⫻ 1023 (more than 600 billion trillion) molecules. The term “mole” can be used in the same way we use the word “dozen.” Just as “a dozen” can refer to twelve cakes or twelve chickens, so “mole” always describes the same number of molecules.
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Just as one liter of water, or one liter of mercury, has a certain mass, a mole of any given substance has its own particular mass, expressed in grams. The mass of one mole of iron, for instance, will always be greater than that of one mole of oxygen. The ratio between them is exactly the same as the ratio of the mass of one iron atom to one oxygen atom. Thus the mole makes if possible to compare the mass of one element or one compound to that of another.
Gas Laws
Avogadro’s law describes the connection between gas volume and number of moles. According to Avogadro’s law, if the volume of gas is increased under isothermal and isobarometric conditions, the number of moles also increases. The ratio between volume and number of moles is therefore a constant.
The Ideal Gas Law Once again, it is easy to see how Avogadro’s law can be related to the laws discussed earlier, since they each involve two or more of the four parameters: temperature, pressure, volume, and quantity of molecules (that is, number of moles). In fact, all the laws so far described are brought together in what is known as the ideal gas law, sometimes called the combined gas law. The ideal gas law can be stated as a formula, pV = nRT, where p stands for pressure, V for volume, n for number of moles, and T for temperature. R is known as the universal gas constant, a figure equal to 0.0821 atm • liter/mole • K. (Like most terms in physics, this one is best expressed in metric rather than English units.) Given the equation pV = nRT and the fact that R is a constant, it is possible to find the value of any one variable—pressure, volume, number of moles, or temperature—as long as one knows the value of the other three. The ideal gas law also makes it possible to discern certain relations: thus if a gas is in a relatively cool state, the product of its pressure and volume is proportionately low; and if heated, its pressure and volume product increases correspondingly. Thus
V T1
p
1 1
=
V T2 ,
p
2 2
A
FIRE EXTINGUISHER CONTAINS A HIGH-PRESSURE MIX-
TURE OF WATER AND CARBON DIOXIDE THAT RUSHES OUT OF THE SIPHON TUBE, WHICH IS OPENED WHEN THE RELEASE VALVE IS DEPRESSED. (Photograph by Craig Lovell/
Corbis. Reproduced by permission.)
p2V2 the product of its final volume and final pressure, and T2 its final temperature.
Five Postulates Regarding the Behavior of Gases Five postulates can be applied to gases. These more or less restate the terms of the earlier discussion, in which gases were compared to solids and liquids; however, now those comparisons can be seen in light of the gas laws. First, the size of gas molecules is minuscule in comparison to the distance between them, making gas highly compressible. In other words, there is a relatively high proportion of empty space between gas molecules. Second, there is virtually no force attracting gas molecules to one another.
where p1V1 is the product of its initial pressure and its initial volume, T1 its initial temperature,
Third, though gas molecules move randomly, frequently colliding with one another, their net effect is to create uniform pressure.
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Gas Laws
A
HOT-AIR BALLOON FLOATS BECAUSE THE AIR INSIDE IT IS NOT AS DENSE THAN THE AIR OUTSIDE.
THE
WAY IN
WHICH THE DENSITY OF THE AIR IN THE BALLOON IS REDUCED REFLECTS THE GAS LAWS. (Duomo/Corbis. Reproduced by
permission.)
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Fourth, the elastic nature of the collisions results in no net loss of kinetic energy, the energy that an object possesses by virtue of its motion. If a stone is dropped from a height, it
rapidly builds kinetic energy, but upon hitting a nonelastic surface such as pavement, most of that kinetic energy is transferred to the pavement. In the case of two gas molecules colliding, however,
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they simply bounce off one another, only to collide with other molecules and so on, with no kinetic energy lost. Fifth, the kinetic energy of all gas molecules is directly proportional to the absolute temperature of the gas.
Laws of Partial Pressure Two gas laws describe partial pressure. Dalton’s law of partial pressure states that the total pressure of a gas is equal to the sum of its par tial pressures—that is, the pressure exerted by each component of the gas mixture. As noted earlier, air is composed mostly of nitrogen and oxygen. Along with these are small components carbon dioxide and gases collectively known as the rare or noble gases: argon, helium, krypton, neon, radon, and xenon. Hence, the total pressure of a given quantity of air is equal to the sum of the pressures exerted by each of these gases. Henry’s law states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the surface of the solution. This applies only to gases such as oxygen and hydrogen that do not react chemically to liquids. On the other hand, hydrochloric acid will ionize when introduced to water: one or more of its electrons will be removed, and its atoms will convert to ions, which are either positive or negative in charge.
REAL-LIFE A P P L I C AT I O N S Pressure Changes O P E N I N G A S O DA CA N . Inside a can or bottle of carbonated soda is carbon dioxide gas (CO2), most of which is dissolved in the drink itself. But some of it is in the space (sometimes referred to as “head space”) that makes up the difference between the volume of the soft drink and the volume of the container.
At the bottling plant, the soda manufacturer adds high-pressure carbon dioxide to the head space in order to ensure that more CO2 will be absorbed into the soda itself. This is in accordance with Henry’s law: the amount of gas (in this case CO2) dissolved in the liquid (soda) is directly proportional to the partial pressure of
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the gas above the surface of the solution—that is, the CO2 in the head space. The higher the pressure of the CO2 in the head space, the greater the amount of CO2 in the drink itself; and the greater the CO2 in the drink, the greater the “fizz” of the soda.
Gas Laws
Once the container is opened, the pressure in the head space drops dramatically. Once again, Henry’s law indicates that this drop in pressure will be reflected by a corresponding drop in the amount of CO2 dissolved in the soda. Over a period of time, the soda will release that gas, and will eventually go “flat.” F I R E E X T I N G U I S H E R S . A fire extinguisher consists of a long cylinder with an operating lever at the top. Inside the cylinder is a tube of carbon dioxide surrounded by a quantity of water, which creates pressure around the CO2 tube. A siphon tube runs vertically along the length of the extinguisher, with one opening near the bottom of the water. The other end opens in a chamber containing a spring mechanism attached to a release valve in the CO2 tube.
The water and the CO2 do not fill the entire cylinder: as with the soda can, there is “head space,” an area filled with air. When the operating lever is depressed, it activates the spring mechanism, which pierces the release valve at the top of the CO2 tube. When the valve opens, the CO2 spills out in the “head space,” exerting pressure on the water. This high-pressure mixture of water and carbon dioxide goes rushing out of the siphon tube, which was opened when the release valve was depressed. All of this happens, of course, in a fraction of a second—plenty of time to put out the fire. A E R O S O L CA N S . Aerosol cans are
similar in structure to fire extinguishers, though with one important difference. As with the fire extinguisher, an aerosol can includes a nozzle that depresses a spring mechanism, which in turn allows fluid to escape through a tube. But instead of a gas cartridge surrounded by water, most of the can’s interior is made up of the product (for instance, deodorant), mixed with a liquid propellant. The “head space” of the aerosol can is filled with highly pressurized propellant in gas form, and in accordance with Henry’s law, a corresponding proportion of this propellant is dissolved in the product itself. When the nozzle is depressed,
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the pressure of the propellant forces the product out through the nozzle. A propellant, as its name implies, propels the product itself through the spray nozzle when the latter is depressed. In the past, chlorofluorocarbons (CFCs)—manufactured compounds containing carbon, chlorine, and fluorine atoms— were the most widely used form of propellant. Concerns over the harmful effects of CFCs on the environment, however, has led to the development of alternative propellants, most notably hydrochlorofluorocarbons (HCFCs), CFC-like compounds that also contain hydrogen atoms.
When the Temperature Changes A number of interesting things, some of them unfortunate and some potentially lethal, occur when gases experience a change in temperature. In these instances, it is possible to see the gas laws—particularly Boyle’s and Charles’s— at work. There are a number of examples of the disastrous effects that result from an increase in the temperature of a product containing combustible gases, as with natural gas and petroleum-based products. In addition, the pressure on the gases in aerosol cans makes the cans highly explosive—so much so that discarded cans at a city dump may explode on a hot summer day. Yet there are other instances when heating a gas can produce positive effects. A hot-air balloon, for instance, floats because the air inside it is not as dense than the air outside. By itself, this fact does not depend on any of the gas laws, but rather reflects the concept of buoyancy. However, the way in which the density of the air in the balloon is reduced does indeed reflect the gas laws. According to Charles’s law, heating a gas will increase its volume. Also, as noted in the first and second propositions regarding the behavior of gases, gas molecules are highly nonattractive to one another, and therefore, there is a great deal of space between them. The increase in volume makes that space even greater, leading to a significant difference in density between the air in the balloon and the air outside. As a result, the balloon floats, or becomes buoyant.
188
were to put a bag of potato chips into a freezer, thinking this would preserve their flavor, he would be in for a disappointment. Much of what maintains the flavor of the chips is the pressurization of the bag, which ensures a consistent internal environment in which preservative chemicals, added during the manufacture of the chips, can keep them fresh. Placing the bag in the freezer causes a reduction in pressure, as per GayLussac’s law, and the bag ends up a limp version of its earlier self. Propane tanks and tires offer an example of the pitfalls that may occur by either allowing a gas to heat up or cool down by too much. Because most propane tanks are made according to strict regulations, they are generally safe, but it is not entirely inconceivable that an extremely hot summer day could cause a defective tank to burst. Certainly the laws of physics are there: an increase in temperature leads to an increase in pressure, in accordance with Gay-Lussac’s law, and could lead to an explosion. Because of the connection between heat and pressure, propane trucks on the highways during the summer are subjected to weight tests to ensure that they are not carrying too much of the gas. On the other hand, a drastic reduction in temperature could result in a loss in gas pressure. If a propane tank from Florida were transported by truck during the winter to northern Canada, the pressure would be dramatically reduced by the time it reached its destination.
Gas Reactions That Move and Stop a Car In operating a car, we experience two examples of gas laws in operation. One of these, common to everyone, is that which makes the car run: the combustion of gases in the engine. The other is, fortunately, a less frequent phenomenon—but it can and does save lives. This is the operation of an air bag, which, though it is partly related to laws of motion, depends also on the behaviors explained in Charles’s law.
Although heating a gas can be beneficial, cooling a gas is not always a wise idea. If someone
With regard to the engine, when the driver pushes down on the accelerator, this activates a throttle valve that sprays droplets of gasoline mixed with air into the engine. (Older vehicles used a carburetor to mix the gasoline and air, but most modern cars use fuel-injection, which sprays the air-gas combination without requiring an intermediate step.) The mixture goes into the
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Gas Laws
IN
CASE OF A CAR COLLISION, A SENSOR TRIGGERS THE AIR BAG TO INFLATE RAPIDLY WITH NITROGEN GAS.
BEFORE
YOUR BODY REACHES THE BAG, HOWEVER, IT HAS ALREADY BEGUN DEFLATING. (Illustration by Hans & Cassidy. The Gale
Group.)
cylinder, where the piston moves up, compressing the gas and air.
and air are what move the piston, which turns a crankshaft that causes the wheels to rotate.
While the mixture is still compressed (high pressure, high density), an electric spark plug produces a flash that ignites it. The heat from this controlled explosion increases the volume of air, which forces the piston down into the cylinder. This opens an outlet valve, causing the piston to rise and release exhaust gases.
So much for moving—what about stopping? Most modern cars are equipped with an airbag, which reacts to sudden impact by inflating. This protects the driver and front-seat passenger, who, even if they are wearing seatbelts, may otherwise be thrown against the steering wheel or dashboard..
As the piston moves back down again, an inlet valve opens, bringing another burst of gasoline-air mixture into the chamber. The piston, whose downward stroke closed the inlet valve, now shoots back up, compressing the gas and air to repeat the cycle. The reactions of the gasoline
But an airbag is much more complicated than it seems. In order for it to save lives, it must deploy within 40 milliseconds (0.04 seconds). Not only that, but it has to begin deflating before the body hits it. An airbag does not inflate if a car simply goes over a bump; it only operates in sit-
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Gas Laws
KEY TERMS Tem-
1691), which holds that for gases in
perature in relation to absolute zero
isothermal conditions, an inverse relation-
(-273.15°C or -459.67°F). Its unit is the
ship exists between the volume and pres-
Kelvin (K), named after William Thomson,
sure of a gas. This means that the greater
Lord Kelvin (1824-1907), who created the
the pressure, the less the volume and vice
scale. The Kelvin and Celsius scales are
versa, and therefore the product of pres-
directly related; hence, Celsius tempera-
sure multiplied by volume yields a constant
tures can be converted to Kelvins (for
figure.
ABSOLUTE TEMPERATURE:
which neither the word or symbol for “degree” are used) by adding 273.15.
LAW:
A
statement,
derived by French physicist and chemist
A statement,
J. A. C. Charles (1746-1823), which holds
derived by the Italian physicist Amedeo
that for gases in isobarometric conditions,
Avogadro (1776-1856), which holds that as
the ratio between the volume and temper-
the volume of gas increases under isother-
ature of a gas is constant. This means that
mal and isobarometric conditions, the
the greater the temperature, the greater the
number of molecules (expressed in terms
volume and vice versa.
AVOGADRO’S
LAW:
of mole number), increases as well. Thus the ratio of volume to mole number is a constant.
DALTON’S LAW OF PARTIAL PRESSURE:
A statement, derived by the
English chemist John Dalton (1766-1844), A statement, derived
which holds that the total pressure of a gas
by English chemist Robert Boyle (1627-
is equal to the sum of its partial pres-
BOYLE’S LAW:
uations when the vehicle experiences extreme deceleration. When this occurs, there is a rapid transfer of kinetic energy to rest energy, as with the earlier illustration of a stone hitting concrete. And indeed, if you were to smash against a fully inflated airbag, it would feel like hitting concrete—with all the expected results. The airbag’s sensor contains a steel ball attached to a permanent magnet or a stiff spring. The spring holds it in place through minor mishaps in which an airbag would not be warranted—for instance, if a car were simply to be “tapped” by another in a parking lot. But in a case of sudden deceleration, the magnet or spring releases the ball, sending it down a smooth bore. It flips a switch, turning on an electrical circuit. This in turn ignites a pellet of sodium azide, which fills the bag with nitrogen gas.
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CHARLES’S
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The events described in the above illustration take place within 40 milliseconds—less time than it takes for your body to come flying forward; and then the airbag has to begin deflating before the body reaches it. At this point, the highly pressurized nitrogen gas molecules begin escaping through vents. Thus as your body hits the bag, the deflation of the latter is moving it in the same direction that your body is going—only much, much more slowly. Two seconds after impact, which is an eternity in terms of the processes involved, the pressure inside the bag has returned to 1 atm. WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. “Chemistry Units: Gas Laws.” (Web site). (February 21, 2001).
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Gas Laws
KEY TERMS
CONTINUED
sures—that is, the pressure exerted by each
expressed as the formula pV = nRT, where
component of the gas mixture.
p stands for pressure, V for volume, n for
A statement,
number of moles, and T for temperature. R
derived by the French physicist and
is known as the universal gas constant, a
chemist Joseph Gay-Lussac (1778-1850),
figure equal to 0.0821 atm • liter/mole • K.
which holds that the pressure of a gas is
INVERSE RELATIONSHIP:
directly related to its absolute temperature.
tion involving two variables, in which one
Hence the ratio of pressure to absolute
of the two increases in direct proportion to
temperature is a constant.
the decrease in the other.
GAY-LUSSAC’S LAW:
HENRY’S LAW:
A statement, derived
IONIZATION:
A situa-
A reaction in which an
by the English chemist William Henry
atom or group of atoms loses one or more
(1774-836), which holds that the amount
electrons. The atoms are then converted to
of gas dissolved in a liquid is directly pro-
ions, which are either wholly positive or
portional to the partial pressure of the gas
negative in charge.
above the solution. This holds true only for gases, such as hydrogen and oxygen, that are capable of dissolving in water without undergoing ionization. IDEAL GAS LAW:
ISOTHERMAL:
Referring to a situa-
tion in which temperature is kept constant. ISOBAROMETRIC:
A proposition, also
uation in which pressure is kept constant.
known as the combined gas law, that draws
MOLE:
on all the gas laws. The ideal gas law can be
molecules.
Laws of Gases. New York: Arno Press, 1981. Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998.
Referring to a sit-
A unit equal to 6.022137 ⫻ 1023
“Tutorials—6.” (February 21, 2001).
Mebane, Robert C. and Thomas R. Rybolt. Air and Other Gases. Illustrations by Anni Matsick. New York: Twenty-First Century Books, 1995.
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MOLECUL AR DYNAMICS Molecular Dynamics
CONCEPT Physicists study matter and motion, or matter in motion. These forms of matter may be large, or they may be far too small to be seen by the most high-powered microscopes available. Such is the realm of molecular dynamics, the study and simulation of molecular motion. As its name suggests, molecular dynamics brings in aspects of dynamics, the study of why objects move as they do, as well as thermodynamics, the study of the relationships between heat, work, and energy. Existing at the borders between physics and chemistry, molecular dynamics provides understanding regarding the properties of matter— including phenomena such as the liquefaction of gases, in which one phase of matter is transformed into another.
HOW IT WORKS Molecules The physical world is made up of matter, physical substance that has mass; occupies space; is composed of atoms; and is, ultimately, convertible to energy. On Earth, three principal phases of matter exist, namely solid, liquid, and gas. The differences between these three are, on the surface at least, easily perceivable. Clearly, water is a liquid, just as ice is a solid and steam a gas. Yet, the ways in which various substances convert between phases are often complex, as are the interrelations between these phases. Ultimately, understanding of the phases depends on an awareness of what takes place at the molecular level.
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in the universe; atoms are composed of subatomic particles, including protons, neutrons, and electrons. These subatomic particles are discussed in the context of the structure of matter elsewhere in this volume, where they are examined largely with regard to their electromagnetic properties. In the present context, the concern is primarily with the properties of atomic and molecular particles, in terms of mechanics, the study of bodies in motion, and thermodynamics. An atom must, by definition, represent one and only one chemical element, of which 109 have been identified and named. It should be noted that the number of elements changes with continuing research, and that many of the elements, particularly those discovered relatively recently—as, for instance, meitnerium (No. 109), isolated in the 1990s—are hardly part of everyday experience. So, perhaps 100 would be a better approximation; in any case, consider the multitude of possible ways in which the elements can be combined.
An atom is the smallest particle of a chemical element. It is not, however, the smallest thing
Musicians have only seven tones at their disposal, and artists only seven colors—yet they manage to create a seemingly infinite variety of mutations in sound and sight, respectively. There are only 10 digits in the numerical system that has prevailed throughout the West since the late Middle Ages, yet it is possible to use that system to create such a range of numbers that all the books in all the libraries in the world could not contain them. This gives some idea of the range of combinations available using the hundredodd chemical elements nature has provided—in other words, the number of possible molecular combinations that exist in the universe.
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Molecular Dynamics
THIS
HUGE LIQUEFIED NATURAL GAS CONTAINER WILL BE INSTALLED ON A SHIP.
THE
VOLUME OF THE LIQUEFIED GAS
IS FAR LESS THAN IT WOULD BE IF THE GAS WERE IN A VAPORIZED STATE, THUS ENABLING EASE AND ECONOMY IN TRANSPORT. (Photograph by James L. Amos/Corbis. Reproduced by permission.)
THE
STRUCTURE
OF
MOLE-
A molecule is a group of atoms joined in a single structure. Often, these atoms come from different elements, in which case the molecule represents a particular chemical compound, such as water, carbon dioxide, sodium chloride (salt), and so on. On the other hand, a molecule may consist only of one type of atom: oxygen molecules, for instance, are formed by the joining of two oxygen atoms.
CULES.
As much as scientists understand about molecules and their structure, there is much that they do not know. Molecules of water are fairly easy to understand, because they have a simple, regular structure that does not change. A water molecule is composed of one oxygen atom joined by two hydrogen atoms, and since the oxygen atom is much larger than the two hydrogens, its shape can be compared to a basketball with two softballs attached. The scale of the molecule, of course, is so small as to boggle the mind: to borrow an illustration from American physicist Richard Feynman (1918-1988), if a basketball were blown up to the size of Earth, the molecules inside of it would not even be as large as an ordinary-sized basketball.
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As for the water molecule, scientists know a number of things about it: the distance between the two hydrogen atoms (measured in units called an angstrom), and even the angle at which they join the oxygen atom. In the case of salt, however, the molecular structure is not nearly as uniform as that of water: atoms join together, but not always in regular ways. And then there are compounds far more complex than water or salt, involving numerous elements that fit together in precise and complicated ways. But, once that discussion is opened, one has stepped from the realm of physics into that of chemistry, and that is not the intention here. Rather, the purpose of the foregoing and very cursory discussion of molecular structure is to point out that molecules are at the heart of all physical existence— and that the things we cannot see are every bit as complicated as those we can. T H E M O L E . Given the tiny—to use an understatement—size of molecules, how do scientists analyze their behavior? Today, physicists have at their disposal electron microscopes and other advanced forms of equipment that make it possible to observe activity at the atomic and molecular levels. The technology that makes this possible is beyond the scope of the present dis-
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Molecular Dynamics
HOW
SMALL ARE MOLECULES? IF THIS BASKETBALL WERE BLOWN UP TO THE SIZE OF
EARTH,
THE MOLECULES INSIDE
IT WOULD NOT BE AS BIG AS A REAL BASKETBALL. (Photograph by Dimitri Iundt/Corbis. Reproduced by permission.)
cussion. On the other hand, consider a much simpler question: how do physicists weigh molecules? Obviously “a bunch” of iron (an element known by the chemical symbol Fe) weighs more than “a bunch” of oxygen, but what exactly is “a bunch”? Italian physicist Amedeo Avogadro (1776-1856), the first scientist to clarify the distinction between atoms and molecules, created a unit that made it possible to compare the masses of various molecules. This is the mole, also known as “Avogadro’s number,” a unit equal to 6.022137 ⫻ 1023 (more than 600 billion trillion) molecules.
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Molecular Attraction and Motion Molecular dynamics can be understood primarily in terms of the principles of motion, identified by Sir Isaac Newton (1642-1727), principles that receive detailed discussion at several places in this volume. However, the attraction between particles at the atomic and molecular level cannot be explained by reference to gravitational force, also identified by Newton. For more than a century, gravity was the only type of force known to physicists, yet the pull of gravitation alone was too weak to account for the strong pull between atoms and molecules.
The term “mole” can be used in the same way that the word “dozen” is used. Just as “a dozen” can refer to twelve cakes or twelve chickens, so “mole” always describes the same number of molecules. A mole of any given substance has its own particular mass, expressed in grams. The mass of one mole of iron, for instance, will always be greater than that of one mole of oxygen. The ratio between them is exactly the same as the ratio of the mass of one iron atom to one oxygen atom. Thus, the mole makes it possible to compare the mass of one element or compound to that of another.
During the eighteenth century and early nineteenth centuries, however, physicists and other scientists became increasingly aware of another form of interaction at work in the world—one that could not be explained in gravitational terms. This was the force of electricity and magnetism, which Scottish physicist James Clerk Maxwell (1831-1879) suggested were different manifestations of a “new” kind of force, electromagnetism. All subatomic particles possess either a positive, negative, or neutral electrical charge. An atom usually has a neutral charge, meaning that it is composed of an equal number of protons (positive) and electrons (negative). In
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certain situations, however, it may lose one or more electrons and, thus, acquire a net charge, making it an ion. Positive and negative charges attract one another, much as the north and south poles of two different magnets attract. (In fact, magnetism is simply an aspect of electromagnetic force.) Not only do the positive and negative elements of an atom attract one another, but positive elements in atoms attract negative elements in other atoms, and vice versa. These interactions are much more complex than the preceding discussion suggests, of course; the important point is that a force other than gravitation draws matter together at the atomic and molecular levels. On the other hand, the interactions that are critical to the study of molecular dynamics are primarily mechanical, comprehensible from the standpoint of Newtonian dynamics. M O L E C U LA R B E H AV I O R A N D P H AS E S O F M AT T E R. All molecules are
in motion, and the rate of that motion is affected by the attraction between them. This attraction or repulsion can be though of like a spring connecting two molecules, an analogy that works best for solids, but in a limited way for liquids. Most molecular motion in liquids and gases is caused by collisions with other molecules; even in solids, momentum is transferred from one molecule to the next along the “springs,” but ultimately the motion is caused by collisions. Hence molecular collisions provide the mechanism by which heat is transferred between two bodies in contact. The rate at which molecules move in relation to one another determines phase of matter—that is, whether a particular item can be described as solid, liquid, or gas. The movement of molecules means that they possess kinetic energy, or the energy of movement, which is manifested as thermal energy and measured by temperature. Temperature is really nothing more than molecules in motion, relative to one another: the faster they move, the greater the kinetic energy, and the greater the temperature. When the molecules in a material move slowly in relation to one another, they tend to be close in proximity, and hence the force of attraction between them is strong. Such a material is called a solid. In molecules of liquid, by contrast, the rate of relative motion is higher, so the molecules tend to be a little more spread out, and
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therefore the force between them is weaker. A material substance whose molecules move at high speeds, and therefore exert little attraction toward one another, is known as a gas. All forms of matter possess a certain (very large) amount of energy due to their mass; thermal energy, however, is—like phase of matter—a function of the attractions between particles. Hence, solids generally have less energy than liquids, and liquids less energy than gases.
Molecular Dynamics
REAL-LIFE A P P L I C AT I O N S Kinetic Theories of Matter English chemist John Dalton (1766-1844) was the first to recognize that nature is composed of tiny particles. In putting forward his idea, Dalton adopted a concept from the Greek philosopher Democritus (c. 470-380 B.C.), who proposed that matter is made up of tiny units he called atomos, or “indivisible.” Dalton recognized that the structure of atoms in a particular element or compound is uniform, and maintained that compounds are made up of compound atoms: in other words, that water, for instance, is composed of “water atoms.” Soon after Dalton, however, Avogadro clarified the distinction between atoms and molecules. Neither Dalton nor Avogadro offered much in the way of a theory regarding atomic or molecular behavior; but another scientist had already introduced the idea that matter at the smallest levels is in a constant state of motion. This was Daniel Bernoulli (1700-1782), a Swiss mathematician and physicist whose studies of fluids—a term which encompasses both gases and liquids—provided a foundation for the field of fluid mechanics. (Today, Bernoulli’s principle, which relates the velocity and pressure of fluids, is applied in the field of aerodynamics, and explains what keeps an airplane aloft.) Bernoulli published his fluid mechanics studies in Hydrodynamica (1700-1782), a work in which he provided the basis for what came to be known as the kinetic theory of gases. B R O W N I A N M O T I O N . Because he came before Dalton and Avogadro, and, thus, did not have the benefit of their atomic and molecular theories, Bernoulli was not able to develop his kinetic theory beyond the seeds of an idea. The
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subsequent elaboration of kinetic theory, which is applied not only to gases but (with somewhat less effectiveness) to liquids and solids, in fact, resulted from an accidental discovery. In 1827, Scottish botanist Robert Brown (1773-1858) was studying pollen grains under a microscope, when he noticed that the grains underwent a curious zigzagging motion in the water. The pollen assumed the shape of a colloid, a pattern that occurs when particles of one substance are dispersed—but not dissolved—in another substance. Another example of a colloidal pattern is a puff of smoke. At first, Brown assumed that the motion had a biological explanation—that is, that it resulted from life processes within the pollen—but later, he discovered that even pollen from long-dead plants behaved in the same way. He never understood what he was witnessing. Nor did a number of other scientists, who began noticing other examples of what came to be known as Brownian motion: the constant but irregular zigzagging of colloidal particles, which can be seen clearly through a microscope.
In 1905, Albert Einstein (1879-1955) analyzed the behavior of particles subjected to Brownian motion. His work, and the confirmation of his results by French physicist Jean Baptiste Perrin (1870-1942), finally put an end to any remaining doubts concerning the molecular structure of matter. The kinetic explanation of molecular behavior, however, remains a theory.
M AX W E L L , B O LT Z M A N N , A N D T H E M AT U R I N G O F K I N E T I C T H E O RY. A generation after Brown’s time, kinetic
Maxwell’s and Boltzmann’s work helped explain characteristics of matter at the molecular level, but did so most successfully with regard to gases. Kinetic theory fits with a number of behaviors exhibited by gases: their tendency to fill any container by expanding to fit its interior, for instance, and their ability to be easily compressed.
theory came to maturity through the work of Maxwell and Austrian physicist Ludwig E. Boltzmann (1844-1906). Working independently, the two men developed a theory, later dubbed the Maxwell-Boltzmann theory of gases, which described the distribution of molecules in a gas. In 1859, Maxwell described the distribution of molecular velocities, work that became the foundation of statistical mechanics—the study of large systems—by examining the behavior of their smallest parts. A year later, in 1860, Maxwell published a paper in which he presented the kinetic theory of gases: the idea that a gas consists of numerous molecules, relatively far apart in space, which interact by colliding. These collisions, he proposed, are responsible for the production of thermal energy, because when the velocity of the molecules increases—as it does after collision— the temperature increases as well. Eight years later, in 1868, Boltzmann independently applied statistics to the kinetic theory, explaining the behavior of gas molecules by means of what would come to be known as statistical mechanics.
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Kinetic theory offered a convincing explanation of the processes involved in Brownian motion. According to the kinetic view, what Brown observed had nothing to do with the pollen particles; rather, the movement of those particles was simply the result of activity on the part of the water molecules. Pollen grains are many thousands of times larger than water molecules, but since there are so many molecules in even one drop of water, and their motion is so constant but apparently random, the water molecules are bound to move a pollen grain once every few thousand collisions.
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Kinetic Theory and Gases
This, in turn, concurs with the gas laws (discussed in a separate essay titled “Gas Laws”)—for instance, Boyle’s law, which maintains that pressure decreases as volume increases, and vice versa. Indeed, the ideal gas law, which shows an inverse relationship between pressure and volume, and a proportional relationship between temperature and the product of pressure and volume, is an expression of kinetic theory. T H E GAS LAW S I L LU S T RAT E D .
The operations of the gas laws are easy to visualize by means of kinetic theory, which portrays gas molecules as though they were millions upon billions of tiny balls colliding at random. Inside a cube-shaped container of gas, molecules are colliding with every possible surface, but the net effect of these collisions is the same as though the molecules were divided into thirds, each third colliding with opposite walls inside the cube.
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If the cube were doubled in size, the molecules bouncing back and forth between two sets of walls would have twice as far to travel between each collision. Their speed would not change, but the time between collisions would double, thus, cutting in half the amount of pressure they would exert on the walls. This is an illustration of Boyle’s law: increasing the volume by a factor of two leads to a decrease in pressure to half of its original value. On the other hand, if the size of the container were decreased, the molecules would have less distance to travel from collision to collision. This means they would be colliding with the walls more often, and, thus, would have a higher degree of energy—and, hence, a higher temperature. This illustrates another gas law, Charles’s law, which relates volume to temperature: as one of the two increases or decreases, so does the other. Thus, it can be said, in light of kinetic theory, that the average kinetic energy produced by the motions of all the molecules in a gas is proportional to the absolute temperature of the gas. GAS E S A N D A B S O LU T E T E M P E RAT U R E . The term “absolute tempera-
ture” refers to the Kelvin scale, established by William Thomson, Lord Kelvin (1824-1907). Drawing on Charles’s discovery that gas at 0°C (32°F) regularly contracts by about 1/273 of its volume for every Celsius degree drop in temperature, Thomson derived the value of absolute zero (-273.15°C or -459.67°F). The Kelvin and Celsius scales are directly related; hence, Celsius temperatures can be converted to Kelvins by adding 273.15. The Kelvin scale measures temperature in relation to absolute zero, or 0K. (Units in the Kelvin system, known as Kelvins, do not include the word or symbol for degree.) But what is absolute zero, other than a very cold temperature? Kinetic theory provides a useful definition: the temperature at which all molecular movement in a gas ceases. But this definition requires some qualification.
Changes of Phase Kinetic theory is more successful when applied to gases than to liquids and solids, because liquid and solid molecules do not interact nearly as frequently as gas particles do. Nonetheless, the proposition that the internal energy of any substance—gas, liquid, or solid—is at least partly related to the kinetic energies of its molecules helps explain much about the behavior of matter.
Molecular Dynamics
The thermal expansion of a solid, for instance, can be clearly explained in terms of kinetic theory. As discussed in the essay on elasticity, many solids are composed of crystals, regular shapes composed of molecules joined to one another, as though on springs. A spring that is pulled back, just before it is released, is an example of potential energy: the energy that an object possesses by virtue of its position. For a crystalline solid at room temperature, potential energy and spacing between molecules are relatively low. But as temperature increases and the solid expands, the space between molecules increases—as does the potential energy in the solid. An example of a liquid displaying kinetic behavior is water in the process of vaporization. The vaporization of water, of course, occurs in boiling, but water need not be anywhere near the boiling point to evaporate. In either case, the process is the same. Speeds of molecules in any substance are distributed along a curve, meaning that a certain number of molecules have speeds well below, or well above, the average. Those whose speeds are well above the average have enough energy to escape the surface, and once they depart, the average energy of the remaining liquid is less than before. As a result, evaporation leads to cooling. (In boiling, of course, the continued application of thermal energy to the entire water sample will cause more molecules to achieve greater energy, even as highly energized molecules leave the surface of the boiling water as steam.)
The Phase Diagram
First of all, the laws of thermodynamics show the impossibility of actually reaching absolute zero. Second, the vibration of atoms never completely ceases: rather, the vibration of the average atom is zero. Finally, one element— helium—does not freeze, even at temperatures near absolute zero. Only the application of pressure will push helium past the freezing point.
The vaporization of water is an example of a change of phase—the transition from one phase of matter to another. The properties of any substance, and the points at which it changes phase, are plotted on what is known as a phase diagram. The latter typically shows temperature along the x-axis, and pressure along the y-axis. It is also possible to construct a phase diagram that plots
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volume against temperature, or volume against pressure, and there are even three-dimensional phase diagrams that measure the relationship between all three—volume, pressure, and temperature. Here we will consider the simpler twodimensional diagram we have described. For simple substances such as water and carbon dioxide, the solid form of the substance appears at a relatively low temperature, and at pressures anywhere from zero upward. The line between solids and liquids, indicating the temperature at which a solid becomes a liquid at any pressure above a certain level, is called the fusion curve. Though it appears to be a line, it is indeed curved, reflecting the fact that at high pressures, a solid well below the normal freezing point for that substance may be melted to create a liquid. Liquids occupy the area of the phase diagram corresponding to relatively high temperatures and high pressures. Gases or vapors, on the other hand, can exist at very low temperatures, but only if the pressure is also low. Above the melting point for the substance, gases exist at higher pressures and higher temperatures. Thus, the line between liquids and gases often looks almost like a 45° angle. But it is not a straight line, as its name, the vaporization curve, indicates. The curve of vaporization reflects the fact that at relatively high temperatures and high pressures, a substance is more likely to be a gas than a liquid. C R I T I CA L P O I N T A N D S U B L I M AT I O N . There are several other interesting
phenomena mapped on a phase diagram. One is the critical point, which can be found at a place of very high temperature and pressure along the vaporization curve. At the critical point, high temperatures prevent a liquid from remaining a liquid, no matter how high the pressure. At the same time, the pressure causes gas beyond that point to become more and more dense, but due to the high temperatures, it does not condense into a liquid. Beyond the critical point, the substance cannot exist in anything other than the gaseous state. The temperature component of the critical point for water is 705.2°F (374°C)—at 218 atm, or 218 times ordinary atmospheric pressure. For helium, however, critical temperature is just a few degrees above absolute zero. This is why helium is rarely seen in forms other than a gas.
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There is also a certain temperature and pressure, called the triple point, at which some substances—water and carbon dioxide are examples—will be a liquid, solid, and gas all at once. Another interesting phenomenon is the sublimation curve, or the line between solid and gas. At certain very low temperatures and pressures, a substance may experience sublimation, meaning that a gas turns into a solid, or a solid into a gas, without passing through a liquid stage. A wellknown example of sublimation occurs when “dry ice,” which is made of carbon dioxide, vaporizes at temperatures above (-109.3°F [-78.5°C]). Carbon dioxide is exceptional, however, in that it experiences sublimation at relatively high pressures, such as those experienced in everyday life: for most substances, the sublimation point occurs at such a low pressure point that it is seldom witnessed outside of a laboratory.
Liquefaction of Gases One interesting and useful application of phase change is the liquefaction of gases, or the change of gas into liquid by the reduction in its molecular energy levels. There are two important properties at work in liquefaction: critical temperature and critical pressure. Critical temperature is that temperature above which no amount of pressure will cause a gas to liquefy. Critical pressure is the amount of pressure required to liquefy the gas at critical temperature. Gases are liquefied by one of three methods: (1) application of pressure at temperatures below critical; (2) causing the gas to do work against external force, thus, removing its energy and changing it to the liquid state; or (3) causing the gas to do work against some internal force. The second option can be explained in terms of the operation of a heat engine, as explored in the Thermodynamics essay. In a steam engine, an example of a heat engine, water is boiled, producing energy in the form of steam. The steam is introduced to a cylinder, in which it pushes on a piston to drive some type of machinery. In pushing against the piston, the steam loses energy, and as a result, changes from a gas back to a liquid. As for the use of internal forces to cool a gas, this can be done by forcing the vapor through a small nozzle or porous plug. Depending on the temperature and properties of the gas, such an
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Molecular Dynamics
KEY TERMS The temperature,
ABSOLUTE ZERO:
DYNAMICS:
The study of why objects
defined as 0K on the Kelvin scale, at which
move as they do. Dynamics is an element
the motion of molecules in a solid virtu-
of mechanics.
ally ceases. Absolute zero is equal to
FLUID:
-459.67°F (-273.15°C).
liquid, which tends to flow, and which con-
Any substance, whether gas or
The smallest particle of a chem-
forms to the shape of its container. Unlike
ical element. An atom can exist either
solids, fluids are typically uniform in
alone or in combination with other atoms
molecular structure: for instance, one mol-
in a molecule.
ecule of water is the same as another water
ATOM:
The constant
molecule.
but irregular zigzagging of colloidal parti-
FUSION
cles, which can be seen clearly through a
between solid and liquid for any given sub-
microscope. The phenomenon is named
stance, as plotted on a phase diagram.
BROWNIAN MOTION:
CURVE:
The boundary
after Scottish botanist Robert Brown
GAS:
(1773-1858), who first witnessed it but was
cules exert little or no attraction toward
not able to explain it. The behavior exhib-
one another, and, therefore, move at high
ited in Brownian motion provides evi-
speeds.
dence for the kinetic theory of matter. HEAT: CHANGE OF PHASE:
The transition
A phase of matter in which mole-
Internal thermal energy that
flows from one body of matter to another.
from one phase of matter to another. KELVIN
SCALE:
Established
by
A sub-
William Thomson, Lord Kelvin (1824-
stance made up of atoms of more than one
1907), the Kelvin scale measures tempera-
chemical element. These atoms are usually
ture in relation to absolute zero, or 0K.
joined in molecules.
(Units in the Kelvin system, known as
CHEMICAL
COMPOUND:
CHEMICAL ELEMENT:
A substance
made up of only one kind of atom.
Kelvins, do not include the word or symbol for degree.) The Kelvin and Celsius scales
A pattern that occurs when
are directly related; hence, Celsius temper-
particles of one substance are dispersed—
atures can be converted to Kelvins by
but not dissolved—in another substance. A
adding 273.15.
puff of smoke in the air is an example of a
KINETIC ENERGY:
colloid, whose behavior is typically charac-
an object possesses by virtue of its motion.
terized by Brownian motion.
KINETIC THEORY OF GASES:
COLLOID:
The energy that The
A coordinate, plot-
idea that a gas consists of numerous mole-
ted on a phase diagram, above which a sub-
cules, relatively far apart in space, which
stance cannot exist in anything other than
interact by colliding. These collisions are
the gaseous state. Located at a position of
responsible for the production of thermal
very high temperature and pressure, the
energy, because when the velocity of the
critical point marks the termination of the
molecules increases—as it does after colli-
vaporization curve.
sion—the temperature increases as well.
CRITICAL POINT:
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Molecular Dynamics
KEY TERMS
CONTINUED
The
MOLE: A unit equal to 6.022137 ⫻ 1023
application of the kinetic theory of gases to
(more than 600 billion trillion) molecules.
all forms of matter. Since particles of liq-
Since their size makes it impossible to
uids and solids move much more slowly
weigh molecules in relatively small quanti-
than do gas particles, kinetic theory is not
ties; hence, the mole, devised by Italian
as successful in this regard; however, the
physicist Amedeo Avogadro (1776-1856),
proposition that the internal energy of any
facilitates comparisons of mass between
substance is at least partly related to the
substances.
kinetic energies of its molecules helps
MOLECULAR DYNAMICS:
explain much about the behavior of
and simulation of molecular motion.
KINETIC THEORY OF MATTER:
matter. MOLECULE: LIQUID:
A phase of matter in which
molecules exert moderate attractions
A group of atoms, usual-
ly of more than one chemical element, joined in a structure.
toward one another, and, therefore, move PHASE DIAGRAM:
at moderate speeds.
A chart, plotted
for any particular substance, identifying
Physical substance that has
the particular phase of matter for that sub-
mass; occupies space; is composed of
stance at a given temperature and pressure
atoms; and is ultimately convertible to
level. A phase diagram usually shows tem-
energy. There are several phases of matter,
perature along the x-axis, and pressure
including solids, liquids, and gases.
along the y-axis.
MATTER:
MECHANICS:
The study of bodies in
motion.
HISTORICAL
PHASES OF MATTER:
The various
forms of material substance (matter),
operation may be enough to remove energy sufficient for liquefaction to take place. Sometimes, the process must be repeated before the gas fully condenses into a liquid. BACKGROUND.
Like the steam engine itself, the idea of gas liquefaction is a product of the early Industrial Age. One of the pioneering figures in the field was the brilliant English physicist Michael Faraday (1791-1867), who liquefied a number of highcritical temperature gases, such as carbon dioxide.
200
The study
uefy gases with much lower critical temperatures, among them oxygen, nitrogen, and carbon monoxide. By the end of the nineteenth century, physicists were able to liquefy the gases with the lowest critical temperatures. James Dewar of Scotland (1842-1923) liquefied hydrogen, whose critical temperature is -399.5°F (-239.7°C). Some time later, Dutch physicist Heike Kamerlingh Onnes (1853-1926) successfully liquefied the gas with the lowest critical temperature of them all: helium, which, as mentioned earlier, becomes a gas at almost unbelievably low temperatures. Its critical temperature is -449.9°F (-267.7°C), or just 5.3K.
Half a century after Faraday, French physicist Louis Paul Cailletet (1832-1913) and Swiss chemist Raoul Pierre Pictet (1846-1929) developed the nozzle and porous-plug methods of liquefaction. This, in turn, made it possible to liq-
A P P L I CAT I O N S O F GAS L I Q U E FAC T I O N . Liquefied natural gas (LNG)
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Molecular Dynamics
KEY TERMS
CONTINUED
which are defined primarily in terms of the
all factors and forces irrelevant to a discus-
behavior exhibited by their atomic or
sion of that system, is known as the envi-
molecular structures. On Earth, three prin-
ronment.
cipal phases of matter exist, namely solid, TEMPERATURE:
liquid, and gas.
A measure of the
average kinetic energy—or molecular POTENTIAL ENERGY:
The energy an
object possesses by virtue of its position. SOLID:
A phase of matter in which
molecules exert strong attractions toward
translational energy in a system. Differences in temperature determine the direction of internal energy flow between two systems when heat is being transferred.
one another, and, therefore, move slowly. THERMAL ENERGY: STATISTICAL MECHANICS:
A realm
of the physical sciences devoted to the study of large systems by examining the behavior of their smallest parts. SUBLIMATION CURVE:
Heat energy, a
form of kinetic energy produced by the movement of atomic or molecular particles. The greater the movement of these particles, the greater the thermal energy.
The bound-
ary between solid and gas for any given substance, as plotted on a phase diagram.
THERMODYNAMICS:
The study of
the relationships between heat, work, and energy.
SYSTEM:
In physics, the term “system” The bound-
usually refers to any set of physical interac-
VAPORIZATION CURVE:
tions isolated from the rest of the universe.
ary between liquid and gas for any given
Anything outside of the system, including
substance as plotted on a phase diagram.
and liquefied petroleum gas (LPG), the latter a mixture of by-products obtained from petroleum and natural gas, are among the examples of liquefied gas in daily use. In both cases, the volume of the liquefied gas is far less than it would be if the gas were in a vaporized state, thus enabling ease and economy in transport. Liquefied gases are used as heating fuel for motor homes, boats, and homes or cabins in remote areas. Other applications of liquefied gases include liquefied oxygen and hydrogen in rocket engines, and liquefied oxygen and petroleum used in welding. The properties of liquefied gases also figure heavily in the science of producing and studying low-temperature environments. In addition, liquefied helium is used in studying the behavior of matter at temperatures close to absolute zero.
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A “New” Form of Matter? Physicists at a Colorado laboratory in 1995 revealed a highly interesting aspect of atomic motion at temperatures approaching absolute zero. Some 70 years before, Einstein had predicted that, at extremely low temperatures, atoms would fuse to form one large “superatom.” This hypothesized structure was dubbed the BoseEinstein Condensate after Einstein and Satyendranath Bose (1894-1974), an Indian physicist whose statistical methods contributed to the development of quantum theory. Because of its unique atomic structure, the Bose-Einstein Condensate has been dubbed a “new” form of matter. It represents a quantum mechanical effect, relating to a cutting-edge area of physics devoted to studying the properties of
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subatomic particles and the interaction of matter with radiation. Thus it is not directly related to molecular dynamics; nonetheless, the Bose-Einstein Condensate is mentioned here as an example of the exciting work being performed at a level beyond that addressed by molecular dynamics. Its existence may lead to a greater understanding of quantum mechanics, and on an everyday level, the “superatom” may aid in the design of smaller, more powerful computer chips. WHERE TO LEARN MORE Cooper, Christopher. Matter. New York: DK Publishing, 1999.
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“The Kinetic Theory Page” (Web site). (April 15, 2001). Medoff, Sol and John Powers. The Student Chemist Explores Atoms and Molecules. Illustrated by Nancy Lou Gahan. New York: R. Rosen Press, 1977. “Molecular Dynamics” (Web site). (April 15, 2001). “Molecular Simulation Molecular Dynamics Page” (Web site). (April 15, 2001). Santrey, Laurence. Heat. Illustrated by Lloyd Birmingham. Mahwah, NJ: Troll Associates, 1985. Strasser, Ben. Molecules in Motion. Illustrated by Vern Jorgenson. Pasadena, CA: Franklin Publications, 1967.
“Kinetic Theory of Gases: A Brief Review” University of Virginia Department of Physics (Web site). (April 15, 2001).
Van, Jon. “U.S. Scientists Create a ‘Superatom.’” Chicago Tribune, July 14, 1995, p. 3.
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S T R U C T U R E O F M AT T E R
Structure of Matter
CONCEPT The physical realm is made up of matter. On Earth, matter appears in three clearly defined forms—solid, liquid, and gas—whose visible and perceptible structure is a function of behavior that takes place at the molecular level. Though these are often referred to as “states” of matter, it is also useful to think of them as phases of matter. This terminology serves as a reminder that any one substance can exist in any of the three phases. Water, for instance, can be ice, liquid, or steam; given the proper temperature and pressure, it may be solid, liquid, and gas all at once! But the three definite earthbound states of matter are not the sum total of the material world: in outer space a fourth phase, plasma, exists—and there may be still other varieties in the physical universe.
HOW IT WORKS Matter and Energy Matter can be defined as physical substance that has mass; occupies space; is composed of atoms; and is ultimately convertible to energy. A significant conversion of matter to energy, however, occurs only at speeds approaching that of the speed of light, a fact encompassed in the famous statement formulated by Albert Einstein (18791955), E = mc2. Einstein’s formula means that every item possesses a quantity of energy equal to its mass multiplied by the squared speed of light. Given the fact that light travels at 186,000 mi (297,600 km) per second, the quantities of energy avail-
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able from even a tiny object traveling at that speed are massive indeed. This is the basis for both nuclear power and nuclear weaponry, each of which uses some of the smallest particles in the known universe to produce results that are both amazing and terrifying. The forms of matter that most people experience in their everyday lives, of course, are traveling at speeds well below that of the speed of light. Even so, transfers between matter and energy take place, though on a much, much smaller scale. For instance, when a fire burns, only a tiny fraction of its mass is converted to energy. The rest is converted into forms of mass different from that of the wood used to make the fire. Much of it remains in place as ash, of course, but an enormous volume is released into the atmosphere as a gas so filled with energy that it generates not only heat but light. The actual mass converted into energy, however, is infinitesimal. C O N S E R V AT I O N A N D C O N V E R S I O N . The property of energy is, at all
times and at all places in the physical universe, conserved. In physics, “to conserve” something means “to result in no net loss of ” that particular component—in this case, energy. Energy is never destroyed: it simply changes form. Hence, the conservation of energy, a law of physics stating that within a system isolated from all other outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place. Whereas energy is perfectly conserved, matter is only approximately conserved, as shown with the example of the fire. Most of the matter from the wood did indeed turn into more mat-
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Structure of Matter
AN
ICEBERG FLOATS BECAUSE THE DENSITY OF ICE IS LOWER THAN WATER, WHILE ITS VOLUME IS GREATER, MAKING
THE ICEBERG BUOYANT. (Photograph by Ric Engenbright/Corbis. Reproduced by permission.)
The conservation of mass holds that total mass is constant, and is unaffected by factors such as position, velocity, or temperature, in any system that does not exchange any matter with its environment. This, however, is a qualified statement: at speeds well below c (the speed of light), it is essentially true, but for matter approaching c and thus, turning into energy, it is not.
Consider an item of matter moving at the speed of 100 mi (160 km)/sec. This is equal to 360,000 MPH (576,000 km/h) and in terms of the speeds to which humans are accustomed, it seems incredibly fast. After all, the fastest any human beings have ever traveled was about 25,000 MPH (40,000 km/h), in the case of the astronauts aboard Apollo 11 in May 1969, and the speed under discussion is more than 14 times greater. Yet 100 mi/sec is a snail’s pace compared to c: in fact, the proportional difference between an actual snail’s pace and the speed of a human
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ter—that is, vapor and ash. Yet, as also noted, a tiny quantity of matter—too small to be perceived by the senses—turned into energy.
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walking is not as great. Yet even at this leisurely gait, equal to 0.00054c, a portion of mass equal to 0.0001% (one-millionth of the total mass) converts to energy.
Matter at the Atomic Level
One of the most well-known molecular forms in the world is water, or H2O, composed of two hydrogen atoms and one oxygen atom. The arrangement is extremely precise and never varies: scientists know, for instance, that the two hydrogen atoms join the oxygen atom (which is much larger than the hydrogen atoms) at an angle of 105° 3’. Other molecules are much more complex than those of water—some of them much, much more complex, which is reflected in the sometimes unwieldy names required to identify their chemical components.
In his brilliant work Six Easy Pieces, American physicist Richard Feynman (1918-1988) asked his readers, “If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms—little articles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.” Feynman went on to offer a powerful series of illustrations concerning the size of atoms relative to more familiar objects: if an apple were magnified to the size of Earth, for instance, the atoms in it would each be about the size of a regular apple. Clearly atoms and other atomic particles are far too small to be glimpsed by even the most highly powered optical microscope. Yet, it is the behavior of particles at the atomic level that defines the shape of the entire physical world. Viewed from this perspective, it becomes easy to understand how and why matter is convertible to energy. Likewise, the interaction between atoms and other particles explains why some types of matter are solid, others liquid, and still others, gas. AT O M S A N D M O L E C U L E S . An atom is the smallest particle of a chemical element. It is not, however, the smallest particle in the universe; atoms are composed of subatomic particles, including protons, neutrons, and electrons. But at the subatomic level, it is meaningless to refer to, for instance, “an oxygen electron”: electrons are just electrons. An atom, then, is the fundamental unit of matter. Most of the substances people encounter in the world, however, are not pure elements, such as oxygen or iron; they are chemical compounds, in which atoms of more than one element join together to form molecules.
than 24 centuries ago, the Greek philosopher Democritus (c. 470-380 B.C.) proposed that matter is composed of tiny particles he called atomos, or “indivisible.” Democritus was not, however, describing matter in a concrete, scientific way: his “atoms” were idealized, philosophical constructs, not purely physical units. Yet, he came amazingly close to identifying the fundamental structure of physical reality— much closer than any number of erroneous theories (such as the “four elements” of earth, air, fire, and water) that prevailed until modern times. English chemist John Dalton (1766-1844) was the first to identify what Feynman later called the “atomic hypothesis”: that nature is composed of tiny particles. In putting forward his idea, Dalton adopted Democritus’s word “atom” to describe these basic units. Dalton recognized that the structure of atoms in a particular element or compound is uniform. He maintained that compounds are made up of compound atoms: in other words, that water, for instance, is a compound of “water atoms.” Water, however, is not an element, and thus, it was necessary to think of its atomic composition in a different way—in terms of molecules rather than atoms. Dalton’s contemporary Amedeo Avogadro (1776-1856), an Italian physicist, was the first scientist to clarify the distinction between atoms and molecules. T H E M O L E . Obviously, it is impractical to weigh a single molecule, or even several thousand; what was needed, then, was a number large enough to make possible practical comparisons of mass. Hence, the mole, a quantity equal to “Avogadro’s number.” The latter, named after Avogadro though not derived by him, is equal to 6.022137 x 1023 (more than 600 billion trillion) molecules.
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Structure of Matter
AT O M I C AND MOLECULAR T H E O RY. The idea of atoms is not new. More
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The term “mole” can be used in the same way that the word “dozen” is used. Just as “a dozen” can refer to twelve cakes or twelve chickens, so “mole” always describes the same number of molecules. A mole of any given substance has its own particular mass, expressed in grams. The mass of one mole of iron, for instance, will always be greater than that of one mole of oxygen. The ratio between them is exactly the same as the ratio of the mass of one iron atom to one oxygen atom. Thus, the mole makes it possible to compare the mass of one element or compound to that of another.
Jean Baptiste Perrin (1870-1942), finally put an end to any remaining doubts concerning the molecular structure of matter.
BROWNIAN MOTION AND KIN E T I C T H E O RY. Contemporary to both
Eventually, physicists identified protons and electrons, but the neutron, with no electrical charge, was harder to discover: it was not identified until 1932. After that point, scientists were convinced that just three types of subatomic particles existed. However, subsequent activity among physicists—particularly those in the field of quantum mechanics—led to the discovery of other elementary particles, such as the photon. However, in this discussion, the only subatomic particles whose behavior is reviewed are the proton, electron, and neutron.
Dalton and Avogadro was Scottish naturalist Robert Brown (1773-1858), who in 1827 stumbled upon a curious phenomenon. While studying pollen grains under a microscope, Brown noticed that the grains underwent a curious zigzagging motion in the water. At first, he assumed that the motion had a biological explanation—that is, it resulted from life processes within the pollen—but later he discovered that even pollen from long-dead plants behaved in the same way. Brown never understood what he was witnessing. Nor did a number of other scientists, who began noticing other examples of what came to be known as Brownian motion: the constant but irregular zigzagging of particles in a puff of smoke, for instance. Later, however, Scottish physicist James Clerk Maxwell (1831-1879) and others were able to explain it by what came to be known as the kinetic theory of matter. The kinetic theory, which is discussed in depth elsewhere in this book, is based on the idea that molecules are constantly in motion: hence, the water molecules were moving the pollen grains Brown observed. Pollen grains are many thousands of times as large as water molecules, but there are so many molecules in just one drop of water, and their motion is so constant but apparently random, that they are bound to move a pollen grain once every few thousand collisions.
Motion and Attraction in Atoms and Molecules At the molecular level, every item of matter in the world is in motion. This may be easy enough to imagine with regard to air or water, since both tend to flow. But what about a piece of paper, or a glass, or a rock? In fact, all molecules are in constant motion, and depending on the particular phase of matter, this motion may vary from a mere vibration to a high rate of speed. Molecular motion generates kinetic energy, or the energy of movement, which is manifested as heat or thermal energy. Indeed, heat is really nothing more than molecules in motion relative to one another: the faster they move, the greater the kinetic energy, and the greater the heat.
Maxwell died, published a series of papers in which he analyzed the behavior of particles subjected to Brownian motion. His work, and the confirmation of his results by French physicist
The movement of atoms and molecules is always in a straight line and at a constant velocity, unless acted upon by some outside force. In fact, the motion of atoms and molecules is constantly being interfered with by outside forces, because they are perpetually striking one another. These collisions cause changes in direction, and may lead to transfers of energy from one particle to another.
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G R O W T H I N U N D E R S TA N D I N G T H E AT O M . Einstein, who was born the year
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It may seem amazing that the molecular and atomic ideas were still open to question in the early twentieth century; however, the vast majority of what is known today concerning the atom emerged after World War I. At the end of the nineteenth century, scientists believed the atom to be indivisible, but growing evidence concerning electrical charges in atoms brought with it the awareness that there must be something smaller creating those charges.
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ELECTROMAGNETIC FORCE I N AT O M S . The behavior of molecules can-
not be explained in terms of gravitational force. This force, and the motions associated with it, were identified by Sir Isaac Newton (1642-1727), and Newton’s model of the universe seemed to answer most physical questions. Then in the late nineteenth century, Maxwell discovered a second kind of force, electromagnetism. (There are two other known varieties of force, strong and weak nuclear, which are exhibited at the subatomic level.) Electromagnetic force, rather than gravitation, explains the attraction between atoms. Several times up to this point, the subatomic particles have been mentioned but not explained in terms of their electrical charge, which is principal among their defining characteristics. Protons have a positive electrical charge, while neutrons exert no charge. These two types of particles, which make up the vast majority of the atom’s mass, are clustered at the center, or nucleus. Orbiting around this nucleus are electrons, much smaller particles which exert a negative charge. Chemical elements are identified by the number of protons they possess. Hydrogen, first element listed on the periodic table of elements, has one proton and is thus identified as 1; carbon, or element 6, has six protons, and so on. An atom usually has a neutral charge, meaning that it is composed of an equal number of protons or electrons. In certain situations, however, it may lose one or more electrons and thus acquire a net charge. Such an atom is called an ion. But electrical charge, like energy, is conserved, and the electrons are not “lost” when an atom becomes an ion: they simply go elsewhere. M O L E C U LA R B E H AV I O R A N D S TAT E S O F M AT T E R. Positive and neg-
ative charges interact at the molecular level in a way that can be compared to the behavior of poles in a pair of magnets. Just as two north poles or two south poles repel one another, so like charges—two positives, or two negatives—repel. Conversely, positive and negative charges exert an attractive force on one another similar to that of a north pole and south pole in contact. In discussing phases of matter, the attraction between molecules provides a key to distinguishing between states of matter. This is not to say one particular phase of matter is a particularly good conductor of electrical current, however.
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For instance, certain solids—particularly metals such as copper—are extremely good conductors. But wood is a solid, too, and conducts electrical current poorly.
Structure of Matter
The properties of various forms of matter, viewed from the larger electromagnetic picture, are a subject far beyond the scope of this essay. In any case, the electromagnetic properties of concern in the present instance are not the ones demonstrated at a macroscopic level—that is, in view of “the big picture.” Rather, the subject of the attractive force operating at the atomic or molecular levels has been introduced to show that certain types of material have a greater intermolecular attraction. As previously stated, all matter is in motion. The relative speed of that motion, however, is a function of the attraction between molecules, which in turn defines a material according to one of the phases of matter. When the molecules in a material exert a strong attraction toward one another, they move slowly, and the material is called a solid. Molecules of liquid, by contrast, exert a moderate attraction and move at moderate speeds. A material substance whose molecules exert little or no attraction, and therefore, move at high speeds, is known as a gas. These comparisons of molecular speed and attraction, obviously, are relative. Certainly, it is easy enough in most cases to distinguish between one phase of matter and another, but there are some instances in which they overlap. Examples of these will follow, but first it is necessary to discuss the phases of matter in the context of their behavior in everyday situations.
REAL-LIFE A P P L I C AT I O N S From Solid to Liquid The attractions between particles have a number of consequences in defining the phases of matter. The strong attractive forces in solids cause its particles to be positioned close together. This means that particles of solids resist attempts to compress them, or push them together. Because of their close proximity, solid particles are fixed in an orderly and definite pattern. As a result, a solid usually has a definite volume and shape. A crystal is a type of solid in which the constituent parts are arranged in a simple, definite
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geometric arrangement that is repeated in all directions. Metals, for instance, are crystalline solids. Other solids are said to be amorphous, meaning that they possess no definite shape. Amorphous solids—clay, for example—either possess very tiny crystals, or consist of several varieties of crystal mixed randomly. Still other solids, among them glass, do not contain crystals. V I B RAT I O N S A N D F R E E Z I N G .
Because of their strong attractions to one another, solid particles move slowly, but like all particles of matter, they do move. Whereas the particles in a liquid or gas move fast enough to be in relative motion with regard to one another, however, solid particles merely vibrate from a fixed position. This can be shown by the example of a singer hitting a certain note and shattering a glass. Contrary to popular belief, the note does not have to be particularly high: rather, the note should be on the same wavelength as the vibration of the glass. When this occurs, sound energy is transferred directly to the glass, which shatters because of the sudden net intake of energy. As noted earlier, the attraction and motion of particles in matter has a direct effect on heat and temperature. The cooler the solid, the slower and weaker the vibrations, and the closer the particles are to one another. Thus, most types of matter contract when freezing, and their density increases. Absolute zero, or 0K on the Kelvin scale of temperature—equal to -459.67°F (-273°C)— is the point at which vibration virtually stops. Note that the vibration virtually stops, but does not stop entirely. In any event, the lowest temperature actually achieved, at a Finnish nuclear laboratory in 1993, is 2.8 • 10-10K, or 0.00000000028K—still above absolute zero. U N U S UA L C H A RAC T E R I S T I CS O F I C E . The behavior of water at the freez-
ing/melting point is interesting and exceptional. Above 39.2°F (4°C) water, like most substances, expands when heated. But between 32°F (0°C) and that temperature, however, it actually contracts. And whereas most substances become much denser with lowered temperatures, the density of water reaches its maximum at 39.2°F. Below that point, it starts to decrease again. Not only does the density of ice begin decreasing just before freezing, but its volume increases. This is the reason ice floats: its weight is less than that of the water it has displaced, and
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therefore, it is buoyant. Additionally, the buoyant qualities of ice atop very cold water explain why the top of a lake may freeze, but lakes rarely freeze solid—even in the coldest of inhabited regions. Instead of freezing from the bottom up, as it would if ice were less buoyant than the water, the lake freezes from the top down. Furthermore, ice is a poorer conductor of heat than water, and, thus, little of the heat from the water below escapes. Therefore, the lake does not freeze completely—only a layer at the top—and this helps preserve animal and plant life in the body of water. On the other hand, the increased volume of frozen water is not always good for humans: when water in pipes freezes, it may increase in volume to the point where the pipe bursts. M E LT I N G . When heated, particles begin to vibrate more and more, and, therefore, move further apart. If a solid is heated enough, it loses its rigid structure and becomes a liquid. The temperature at which a solid turns into a liquid is called the melting point, and melting points are different for different substances. For the most part, however, solids composed of heavier particles require more energy—and, hence, higher temperatures—to induce the vibrations necessary for freezing. Nitrogen melts at -346°F (-210°C), ice at 32°F (0°C), and copper at 1,985°F (1,085°C). The melting point of a substance, incidentally, is the same as its freezing point: the difference is a matter of orientation—that is, whether the process is one of a solid melting to become a liquid, or of a liquid freezing to become a solid.
The energy required to change a solid to a liquid is called the heat of fusion. In melting, all the heat energy in a solid (energy that exists due to the motion of its particles) is used in breaking up the arrangement of crystals, called a lattice. This is why the water resulting from melted ice does not feel any warmer than when it was frozen: the thermal energy has been expended, with none left over for heating the water. Once all the ice is melted, however, the absorbed energy from the particles—now moving at much greater speeds than when the ice was in a solid state— causes the temperature to rise.
From Liquid to Gas The particles of a liquid, as compared to those of a solid, have more energy, more motion, and less
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attraction to one another. The attraction, however, is still fairly strong: thus, liquid particles are in close enough proximity that the liquid resists compression. On the other hand, their arrangement is loose enough that the particles tend to move around one another rather than merely vibrating in place, as solid particles do. A liquid is therefore not definite in shape. Both liquids and gases tend to flow, and to conform to the shape of their container; for this reason, they are together classified as fluids. Owing to the fact that the particles in a liquid are not as close in proximity as those of a solid, liquids tend to be less dense than solids. The liquid phase of substance is thus inclined to be larger in volume than its equivalent in solid form. Again, however, water is exceptional in this regard: liquid water actually takes up less space than an equal mass of frozen water. B O I L I N G . When a liquid experiences an
increase in temperature, its particles take on energy and begin to move faster and faster. They collide with one another, and at some point the particles nearest the surface of the liquid acquire enough energy to break away from their neighbors. It is at this point that the liquid becomes a gas or vapor. As heating continues, particles throughout the liquid begin to gain energy and move faster, but they do not immediately transform into gas. The reason is that the pressure of the liquid, combined with the pressure of the atmosphere above the liquid, tends to keep particles in place. Those particles below the surface, therefore, remain where they are until they acquire enough energy to rise to the surface. The heated particle moves upward, leaving behind it a hollow space—a bubble. A bubble is not an empty space: it contains smaller trapped particles, but its small weight relative to that of the liquid it disperses makes it buoyant. Therefore, a bubble floats to the top, releasing its trapped particles as gas or vapor. At that point, the liquid is said to be boiling. T H E E F F E C T O F AT M O S P H E R I C P R E SS U R E . As they rise, the particles
thus have to overcome atmospheric pressure, and this means that the boiling point for any liquid depends in part on the pressure of the surrounding air. This is why cooking instructions often vary with altitude: the greater the distance from
S C I E N C E O F E V E RY DAY T H I N G S
sea level, the less the air pressure, and the shorter the required cooking time.
Structure of Matter
Atop Mt. Everest, Earth’s highest peak at about 29,000 ft (8,839 m) above sea level, the pressure is approximately one-third normal atmospheric pressure. This means the air is onethird as dense as it is as sea level, which explains why mountain-climbers on Everest and other tall peaks must wear oxygen masks to stay alive. It also means that water boils at a much lower temperature on Everest than it does elsewhere. At sea level, the boiling point of water is 212°F (100°C), but at 29,000 ft it is reduced by one-quarter, to 158°F (70°C). Of course, no one lives on the top of Mt. Everest—but people do live in Denver, Colorado, where the altitude is 5,577 ft (1,700 m) and the boiling point of water is 203°F (95°C). Given the lower boiling point, one might assume that food would cook faster in Denver than in New York, Los Angeles, or some other city close to sea level. In fact, the opposite is true: because heated particles escape the water so much faster at high altitudes, they do not have time to acquire the energy needed to raise the temperature of the water. It is for this reason that a recipe may contain a statement such as “at altitudes above XX feet, add XX minutes to cooking time.” If lowered atmospheric pressure means a lowered boiling point, what happens in outer space, where there is no atmospheric pressure? Liquids boil at very, very low temperatures. This is one of the reasons why astronauts have to wear pressurized suits: if they did not, their blood would boil—even though space itself is incredibly cold. L I Q U I D T O GAS A N D B AC K AGA I N . Note that the process of a liquid
changing to a gas is similar to what occurs when a solid changes to a liquid: particles gain heat and therefore energy, begin to move faster, break free from one another, and pass a certain threshold into a new phase of matter. And just as the freezing and melting point for a given substance are the same temperature, the only difference being one of orientation, the boiling point of a liquid transforming into a gas is the same as the condensation point for a gas turning into a liquid. The behavior of water in boiling and condensation makes possible distillation, one of the principal methods for purifying seawater in various parts of the world. First, the water is boiled,
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then, it is allowed to cool and condense, thus forming water again. In the process, the water separates from the salt, leaving it behind in the form of brine. A similar separation takes place when salt water freezes: because salt, like most solids, has a much lower freezing point than water, very little of it remains joined to the water in ice. Instead, the salt takes the form of a briny slush. Having reached the gaseous state, a substance takes on characteristics quite different from those of a solid, and somewhat different from those of a liquid. Whereas liquid particles exert a moderate attraction to one another, particles in a gas exert little to no attraction. They are thus free to move, and to move quickly. The shape and arrangement of gas is therefore random and indefinite—and, more importantly, the motion of gas particles give it much greater kinetic energy than the other forms of matter found on Earth. GAS
AND
ITS
LAWS.
The constant, fast, and random motion of gas particles means that they are always colliding and thereby transferring kinetic energy back and forth without any net loss. These collisions also have the overall effect of producing uniform pressure in a gas. At the same time, the characteristics and behavior of gas particles indicate that they will tend not to remain in an open container. Therefore, in order to maintain any pressure on a gas—other than the normal atmospheric pressure exerted on the surface of the gas by the atmosphere (which, of course, is also a gas)—it is necessary to keep it in a closed container. There are a number of gas laws (examined in another essay in this book) describing the response of gases to changes in pressure, temperature, and volume. Among these is Boyle’s law, which holds that when the temperature of a gas is constant, there is an inverse relationship between volume and pressure: in other words, the greater the pressure, the less the volume, and vice versa. According to a second gas law, Charles’s law, for gases in conditions of constant pressure, the ratio between volume and temperature is constant—that is, the greater the temperature, the greater the volume, and vice versa.
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versa. Gay-Lussac’s law is combined, along with Boyle’s and Charles’s and other gas laws, in the ideal gas law, which makes it possible to find the value of any one variable—pressure, volume, number of moles, or temperature—for a gas, as long as one knows the value of the other three.
Other States of Matter P L A S M A . Principal among states of matter other than solid, liquid, and gas is plasma, which is similar to gas. (The term “plasma,” when referring to the state of matter, has nothing to do with the word as it is often used, in reference to blood plasma.) As with gas, plasma particles collide at high speeds—but in plasma, the speeds are even greater, and the kinetic energy levels even higher.
The speed and energy of these collisions is directly related to the underlying property that distinguishes plasma from gas. So violent are the collisions between plasma particles that electrons are knocked away from their atoms. As a result, plasma does not have the atomic structure typical of a gas; rather, it is composed of positive ions and electrons. Plasma particles are thus electrically charged, and, therefore, greatly influenced by electrical and magnetic fields. Formed at very high temperatures, plasma is found in stars and comets’ tails; furthermore, the reaction between plasma and atomic particles in the upper atmosphere is responsible for the aurora borealis or “northern lights.” Though not found on Earth, plasma—ubiquitous in other parts of the universe—may be the most plentiful among the four principal states of matter. Q UAS I - S TAT E S . Among the quasistates of matter discussed by physicists are several terms that describe the structure in which particles are joined, rather than the attraction and relative movement of those particles. “Crystalline,” “amorphous,” and “glassy” are all terms to describe what may be individual states of matter; so too is “colloidal.”
In addition, Gay-Lussac’s law shows that the pressure of a gas is directly related to its absolute temperature on the Kelvin scale: the higher the temperature, the higher the pressure, and vice
A colloid is a structure intermediate in size between a molecule and a visible particle, and it has a tendency to be dispersed in another medium—as smoke, for instance, is dispersed in air. Brownian motion describes the behavior of most colloidal particles. When one sees dust floating in a ray of sunshine through a window, the light reflects off colloids in the dust, which are driven
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back and forth by motion in the air otherwise imperceptible to the human senses. DA R K M AT T E R. The number of states
or phases of matter is clearly not fixed, and it is quite possible that more will be discovered in outer space, if not on Earth. One intriguing candidate is called dark matter, so described because it neither reflects nor emits light, and is therefore invisible. In fact, luminous or visible matter may very well make up only a small fraction of the mass in the universe, with the rest being taken up by dark matter. If dark matter is invisible, how do astronomers and physicists know it exists? By analyzing the gravitational force exerted on visible objects when there seems to be no visible object to account for that force. An example is the center of our galaxy, the Milky Way, which appears to be nothing more than a dark “halo.” In order to cause the entire galaxy to revolve around it in the same way that planets revolve around the Sun, the Milky Way must contain a staggering quantity of invisible mass. Dark matter may be the substance at the heart of a black hole, a collapsed star whose mass is so great that its gravitational field prevents light from escaping. It is possible, also, that dark matter is made up of neutrinos, subatomic particles thought to be massless. Perhaps, the theory goes, neutrinos actually possess tiny quantities of mass, and therefore in huge groups—a mole times a mole times a mole—they might possess appreciable mass. In addition, dark matter may be the deciding factor as to whether the universe is infinite. The more mass the universe possesses, the greater its overall gravity, and if the mass of the universe is above a certain point, it will eventually begin to contract. This, of course, would mean that it is finite; on the other hand, if the mass is below this threshold, it will continue to expand indefinitely. The known mass of the universe is nowhere near that threshold—but, because the nature of dark matter is still largely unknown, it is not possible yet to say what effect its mass may have on the total equation. A “ N E W ” F O R M O F M AT T E R ?
ed that, at extremely low temperatures, atoms would fuse to form one large “superatom.” This hypothesized structure was dubbed the BoseEinstein Condensate (BEC) after Einstein and Satyendranath Bose (1894-1974), an Indian physicist whose statistical methods contributed to the development of quantum theory.
Structure of Matter
Cooling about 2,000 atoms of the element rubidium to a temperature just 170 billionths of a degree Celsius above absolute zero, the physicists succeeded in creating an atom 100 micrometers across—still incredibly small, but vast in comparison to an ordinary atom. The superatom, which lasted for about 15 seconds, cooled down all the way to just 20 billionths of a degree above absolute zero. The Colorado physicists won the Nobel Prize in physics in 1997 for their work. In 1999, researchers in a lab at Harvard University also created a superatom of BEC, and used it to slow light to just 38 MPH (60.8 km/h)—about 0.02% of its ordinary speed. Dubbed a “new” form of matter, the BEC may lead to a greater understanding of quantum mechanics, and may aid in the design of smaller, more powerful computer chips.
States and Phases and In Between At places throughout this essay, references have been made variously to “phases” and “states” of matter. This is not intended to confuse, but rather to emphasize a particular point. Solids, liquids, and gases are referred to as “phases,” because substances on Earth—water, for instance—regularly move from one phase to another. This change, a function of temperature, is called (aptly enough) “change of phase.” There is absolutely nothing incorrect in referring to “states of matter.” But “phases of matter” is used in the present context as a means of emphasizing the fact that most substances, at the appropriate temperature and pressure, can be solid, liquid, or gas. In fact, a substance may even be solid, liquid, and gas.
An Analogy to Human Life
Physicists at the Joint Institute of Laboratory Astrophysics in Boulder, Colorado, in 1995 revealed a highly interesting aspect of atomic behavior at temperatures approaching absolute zero. Some 70 years before, Einstein had predict-
The phases of matter can be likened to the phases of a person’s life: infancy, babyhood, childhood, adolescence, adulthood, old age. The transition between these stages is indefinite, yet it is
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Structure of Matter
THE RESPONSE OF LIQUID CRYSTALS ERS. (AFP/Corbis. Reproduced by permission.)
TO LIGHT MAKES THEM USEFUL IN THE DISPLAYS USED ON LAPTOP COMPUT-
easy enough to say when a person is at a certain stage. At the transition point between adolescence and adulthood—say, at seventeen years old—a young person may say that she is an adult, but her parents may insist that she is still an adolescent or a child. And indeed, she might qualify as either. On the other hand, when she is thirty, it would be ridiculous to assert that she is anything other than an adult. At the same time, a person at a certain age may exhibit behaviors typically associated with another age. A child, for instance, may behave like an adult, or an adult like a baby. One interesting example of this is the relationship between age two and late adolescence. In both cases, the person is in the process of individualizing, developing an identity separate from that of his or her parents—yet clearly, there are also plenty of differences between a two-year-old and a seventeenyear-old.
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clearly is what it is: water at very low temperature and pressure, for instance, is indisputably ice— just as an average thirty-year-old is obviously an adult. As for the second observation, that a person at one stage in life may reflect characteristics of another stage, this too is reflected in the behavior of matter. L I Q U I D C RY S TA L S . A liquid crystal
is a substance that, over a specific range of temperature, displays properties both of a liquid and a solid. Below this temperature range, it is unquestionably a solid, and above this range it is just as obviously a liquid. In between, however, liquid crystals exhibit a strange solid-liquid behavior: like a liquid, their particles flow, but like a solid, their molecules maintain specific crystalline arrangements.
As with the transitional phases in human life, in the borderline pressure levels and temperatures for phases of matter it is sometimes difficult to say, for instance, if a substance is fully a liquid or fully a gas. On the other hand, at a certain temperature and pressure level, a substance
Long, wide, and placed alongside one another, liquid crystal molecules exhibit interesting properties in response to light waves. The speed of light through a liquid crystal actually varies, depending on whether the light is traveling along the short or long sides of the molecules. These differences in light speed may lead to a change in the direction of polarization, or the vibration of light waves.
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Structure of Matter
KEY TERMS ATOM:
The smallest particle of a chem-
Negatively charged parti-
ELECTRON:
ical element. An atom can exist either alone
cles in an atom. Electrons, which spin
or in combination with other atoms in a
around the nucleus of protons and neu-
molecule. Atoms are made up of protons,
trons, constitute a very small portion of the
neutrons, and electrons. In most cases, the
atom’s mass. In most atoms, the number of
electrical charges in atoms cancel out one
electrons and protons is the same, thus
another; but when an atom loses one or
canceling out one another. When an atom
more electrons, and thus has a net charge,
loses one or more electrons, however—
it becomes an ion.
thus becoming an ion—it acquires a net
CHEMICAL
COMPOUND:
A sub-
stance made up of atoms of more than one chemical element. These atoms are usually joined in molecules. CHEMICAL ELEMENT:
electrical charge. FRICTION:
The force that resists
motion when the surface of one object comes into contact with the surface of
A substance
another.
made up of only one kind of atom. CONSERVATION OF ENERGY:
A
law of physics which holds that within a system isolated from all other outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place. CONSERVATION OF MASS:
A phys-
Any substance, whether gas or
FLUID:
liquid, that tends to flow, and that conforms to the shape of its container. Unlike solids, fluids are typically uniform in molecular structure for instance, one molecule of water is the same as another water molecule. A phase of matter in which mole-
ical principle which states that total mass is
GAS:
constant, and is unaffected by factors such
cules exert little or no attraction toward
as position, velocity, or temperature, in any
one another, and therefore move at high
system that does not exchange any matter
speeds.
with its environment. Unlike the other
ION:
conservation laws, however, conservation
one or more electrons, and thus has a net
of mass is not universally applicable, but
electrical charge.
An atom that has lost or gained
applies only at speeds significant lower than that of light—186,000 mi (297,600 km) per second. Close to the speed of light, mass begins converting to energy. CONSERVE:
In physics, “to conserve”
LIQUID:
A phase of matter in which
molecules exert moderate attractions toward one another, and therefore move at moderate speeds. Physical substance that has
something means “to result in no net loss
MATTER:
of ” that particular component. It is possi-
mass; occupies space; is composed of
ble that within a given system, the compo-
atoms; and is ultimately (at speeds
nent may change form or position, but as
approaching that of light) convertible to
long as the net value of the component
energy. There are several phases of matter,
remains the same, it has been conserved.
including solids, liquids, and gases.
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Structure of Matter
KEY TERMS
CONTINUED
A unit equal to 6.022137 ⫻ 1023
does not exist on Earth, but is found, for
(more than 600 billion trillion) molecules.
instance, in stars and comets’ tails. Con-
Their size makes it impossible to weigh
taining neither atoms nor molecules, plas-
molecules in relatively small quantities;
ma is made up of electrons and positive
hence the mole facilitates comparisons of
ions.
MOLE:
mass between substances. MOLECULE:
A group of atoms, usual-
ly of more than one chemical element,
A positively charged particle
in an atom. Protons and neutrons, which together form the nucleus around which
joined in a structure. A subatomic particle that
NEUTRON:
PROTON:
has no electrical charge. Neutrons are
electrons orbit, have approximately the same mass—a mass that is many times
found at the nucleus of an atom, alongside
greater than that of an electron.
protons.
SOLID:
PHASES OF MATTER:
The various
forms of material substance (matter),
A phase of matter in which
molecules exert strong attractions toward one another, and therefore move slowly.
which are defined primarily in terms of the SYSTEM:
molecular structures. On Earth, three prin-
usually refers to any set of physical interac-
cipal phases of matter exist, namely solid,
tions isolated from the rest of the universe.
liquid, and gas. Other forms of matter
Anything outside of the system, including
include plasma.
all factors and forces irrelevant to a discus-
PLASMA:
One of the phases of matter,
closely related to gas. Plasma apparently
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In physics, the term “system”
behavior exhibited by their atomic or
sion of that system, is known as the environment.
mometer displays those colors, since people typically associate red with heat and blue with cold.
The cholesteric class of liquid crystals is so named because the spiral patterns of light through the crystal are similar to those which appear in cholesterols. Depending on the physical properties of a cholesteric liquid crystal, only certain colors may be reflected. The response of liquid crystals to light makes them useful in liquid crystal displays (LCDs) found on laptop computer screens, camcorder views, and in other applications.
T H E T R I P L E P O I N T. A liquid crystal exhibits aspects of both liquid and solid, and thus, at certain temperatures may be classified within the crystalline quasi-state of matter. On the other hand, the phenomenon known as the triple point shows how an ordinary substance, such as water or carbon dioxide, can actually be a liquid, solid, and vapor—all at once.
In some cholesteric liquid crystals, high temperatures lead to a reflection of shorter visible light waves, and lower temperatures to a display of longer visible waves. Liquid crystal thermometers thus show red when cool, and blue as they are warmed. This may seem a bit unusual to someone who does not understand why the ther-
Again, water—the basis of all life on Earth— is an unusual substance in many regards. For instance, most people associate water as a gas or vapor (that is, steam) with very high temperatures. Yet, at a level far below normal atmospheric pressure, water can be a vapor at temperatures as low as -4°F (-20 °C). (All of the pressure values
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in the discussion of water at or near the triple point are far below atmospheric norms: the pressure at which water would turn into a vapor at 4°F, for instance, is about 1/1000 normal atmospheric pressure.) As everyone knows, at relatively low temperatures, water is a solid—ice. But if the pressure of ice falls below a very low threshold, it will turn straight into a gas (a process known as sublimation) without passing through the liquid stage. On the other hand, by applying enough pressure, it is possible to melt ice, and thereby transform it from a solid to a liquid, at temperatures below its normal freezing point. The phases and changes of phase for a given substance at specific temperatures and pressure levels can be plotted on a graph called a phase diagram, which typically shows temperature on the x-axis and pressure on the y-axis. The phase diagram of water shows a line between the solid and liquid states that is almost, but not quite, exactly perpendicular to the x-axis: it slopes slightly upward to the left, reflecting the fact that solid ice turns into water with an increase of pressure. Whereas the line between solid and liquid water is more or less straight, the division between these two states and water vapor is curved. And where the solid-liquid line intersects the vaporization curve, there is a place called the triple point. Just below freezing, in conditions
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equivalent to about 0.7% of normal atmospheric pressure, water is a solid, liquid, and vapor all at once.
Structure of Matter
WHERE TO LEARN MORE Biel, Timothy L. Atom: Building Blocks of Matter. San Diego, CA: Lucent Books, 1990. Feynman, Richard. Six Easy Pieces: Essentials of Physics Explained by Its Most Brilliant Teacher. New introduction by Paul Davies. Cambridge, MA: Perseus Books, 1995. Hewitt, Sally. Solid, Liquid, or Gas? New York: Children’s Press, 1998. “High School Chemistry Table of Contents—Solids and Liquids” Homeworkhelp.com (Web site). (April 10, 2001). “Matter: Solids, Liquids, Gases.” Studyweb (Web site). (April 10, 2001). “The Molecular Circus” (Web site). (April 10, 2001). Paul, Richard. A Handbook to the Universe: Explorations of Matter, Energy, Space, and Time for Beginning Scientific Thinkers. Chicago: Chicago Review Press, 1993. “Phases of Matter” (Web site). (April 10, 2001). Royston, Angela. Solids, Liquids, and Gasses. Chicago: Heinemann Library, 2001. Wheeler, Jill C. The Stuff Life’s Made Of: A Book About Matter. Minneapolis, MN: Abdo & Daughters Publishing, 1996.
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THERMODYNAMICS Thermodynamics
CONCEPT Thermodynamics is the study of the relationships between heat, work, and energy. Though rooted in physics, it has a clear application to chemistry, biology, and other sciences: in a sense, physical life itself can be described as a continual thermodynamic cycle of transformations between heat and energy. But these transformations are never perfectly efficient, as the second law of thermodynamics shows. Nor is it possible to get “something for nothing,” as the first law of thermodynamics demonstrates: the work output of a system can never be greater than the net energy input. These laws disappointed hopeful industrialists of the early nineteenth century, many of whom believed it might be possible to create a perpetual motion machine. Yet the laws of thermodynamics did make possible such highly useful creations as the internal combustion engine and the refrigerator.
HOW IT WORKS Historical Context Machines were, by definition, the focal point of the Industrial Revolution, which began in England during the late eighteenth and early nineteenth centuries. One of the central preoccupations of both scientists and industrialists thus became the efficiency of those machines: the ratio of output to input. The more output that could be produced with a given input, the greater the production, and the greater the economic advantage to the industrialists and (presumably) society as a whole.
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At that time, scientists and captains of industry still believed in the possibility of a perpetual motion machine: a device that, upon receiving an initial input of energy, would continue to operate indefinitely without further input. As it emerged that work could be converted into heat, a form of energy, it began to seem possible that heat could be converted directly back into work, thus making possible the operation of a perfectly reversible perpetual motion machine. Unfortunately, the laws of thermodynamics dashed all those dreams. S N O W ’ S E X P LA N AT I O N . Some texts identify two laws of thermodynamics, while others add a third. For these laws, which will be discussed in detail below, British writer and scientist C. P. Snow (1905-1980) offered a witty, nontechnical explanation. In a 1959 lecture published as The Two Cultures and the Scientific Revolution, Snow compared the effort to transform heat into energy, and energy back into heat again, as a sort of game.
The first law of thermodynamics, in Snow’s version, teaches that the game is impossible to win. Because energy is conserved, and thus, its quantities throughout the universe are always the same, one cannot get “something for nothing” by extracting more energy than one put into a machine. The second law, as Snow explained it, offers an even more gloomy prognosis: not only is it impossible to win in the game of energy-work exchanges, one cannot so much as break even. Though energy is conserved, that does not mean the energy is conserved within the machine where it is used: mechanical systems tend toward increasing disorder, and therefore, it is impossi-
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Thermodynamics
A
WOMAN WITH A SUNBURNED NOSE.
SUNBURNS
ARE CAUSED BY THE
SUN’S
ULTRAVIOLET RAYS. (Photograph by Lester
V. Bergman/Corbis. Reproduced by permission.)
ble for the machine even to return to the original level of energy. The third law, discovered in 1905, seems to offer a possibility of escape from the conditions imposed in the second law: at the temperature of absolute zero, this tendency toward breakdown drops to a level of zero as well. But the third law only proves that absolute zero cannot be attained: hence, Snow’s third observation, that it is impossible to step outside the boundaries of this unwinnable heat-energy transformation game.
Work and Energy Work and energy, discussed at length elsewhere in this volume, are closely related. Work is the exertion of force over a given distance to displace or move an object. It is thus the product of force and distance exerted in the same direction. Energy is the ability to accomplish work.
which is the sum of potential energy—the energy that an object has due to its position—and kinetic energy, or the energy an object possesses by virtue of its motion. M E C H A N I CA L E N E R GY. Kinetic energy relates to heat more clearly than does potential energy, discussed below; however, it is hard to discuss the one without the other. To use a simple example—one involving mechanical energy in a gravitational field—when a stone is held over the edge of a cliff, it has potential energy. Its potential energy is equal to its weight (mass times the acceleration due to gravity) multiplied by its height above the bottom of the canyon below. Once it is dropped, it acquires kinetic energy, which is the same as one-half its mass multiplied by the square of its velocity.
There are many manifestations of energy, including one of principal concern in the present context: thermal or heat energy. Other manifestations include electromagnetic (sometimes divided into electrical and magnetic), sound, chemical, and nuclear energy. All these, however, can be described in terms of mechanical energy,
Just before it hits bottom, the stone’s kinetic energy will be at a maximum, and its potential energy will be at a minimum. At no point can the value of its kinetic energy exceed the value of the potential energy it possessed before it fell: the mechanical energy, or the sum of kinetic and potential energy, will always be the same, though the relative values of kinetic and potential energy may change.
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C O N S E R VAT I O N
OF
E N E R GY.
What mechanical energy does the stone possess after it comes to rest at the bottom of the canyon? In terms of the system of the stone dropping from the cliffside to the bottom, none. Or, to put it another way, the stone has just as much mechanical energy as it did at the very beginning. Before it was picked up and held over the side of the cliff, thus giving it potential energy, it was presumably sitting on the ground away from the edge of the cliff. Therefore, it lacked potential energy, inasmuch as it could not be “dropped” from the ground. If the stone’s mechanical energy—at least in relation to the system of height between the cliff and the bottom—has dropped to zero, where did it go? A number of places. When it hit, the stone transferred energy to the ground, manifested as heat. It also made a sound when it landed, and this also used up some of its energy. The stone itself lost energy, but the total energy in the universe was unaffected: the energy simply left the stone and went to other places. This is an example of the conservation of energy, which is closely tied to the first law of thermodynamics. But does the stone possess any energy at the bottom of the canyon? Absolutely. For one thing, its mass gives it an energy, known as mass or rest energy, that dwarfs the mechanical energy in the system of the stone dropping off the cliff. (Mass energy is the other major form of energy, aside from kinetic and potential, but at speeds well below that of light, it is released in quantities that are virtually negligible.) The stone may have electromagnetic potential energy as well; and of course, if someone picks it up again, it will have gravitational potential energy. Most important to the present discussion, however, is its internal kinetic energy, the result of vibration among the molecules inside the stone.
Heat and Temperature Thermal energy, or the energy of heat, is really a form of kinetic energy between particles at the atomic or molecular level: the greater the movement of these particles, the greater the thermal energy. Heat itself is internal thermal energy that flows from one body of matter to another. It is not the same as the energy contained in a system—that is, the internal thermal energy of the
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system. Rather than being “energy-in-residence,” heat is “energy-in-transit.” This may be a little hard to comprehend, but it can be explained in terms of the stone-and-cliff kinetic energy illustration used above. Just as a system can have no kinetic energy unless something is moving within it, heat exists only when energy is being transferred. In the above illustration of mechanical energy, when the stone was sitting on the ground at the top of the cliff, it was analogous to a particle of internal energy in body A. When, at the end, it was again on the ground—only this time at the bottom of the canyon—it was the same as a particle of internal energy that has transferred to body B. In between, however, as it was falling from one to the other, it was equivalent to a unit of heat. T E M P E RAT U R E . In everyday life, people think they know what temperature is: a measure of heat and cold. This is wrong for two reasons: first, as discussed below, there is no such thing as “cold”—only an absence of heat. So, then, is temperature a measure of heat? Wrong again.
Imagine two objects, one of mass M and the other with a mass twice as great, or 2M. Both have a certain temperature, and the question is, how much heat will be required to raise their temperature by equal amounts? The answer is that the object of mass 2M requires twice as much heat to raise its temperature the same amount. Therefore, temperature cannot possibly be a measure of heat. What temperature does indicate is the direction of internal energy flow between bodies, and the average molecular kinetic energy in transit between those bodies. More simply, though a bit less precisely, it can be defined as a measure of heat differences. (As for the means by which a thermometer indicates temperature, that is beyond the parameters of the subject at hand; it is discussed elsewhere in this volume, in the context of thermal expansion.) MEASURING T E M P E R AT U R E A N D H E AT. Temperature, of course, can be
measured either by the Fahrenheit or Centigrade scales familiar in everyday life. Another temperature scale of relevance to the present discussion is the Kelvin scale, established by William Thomson, Lord Kelvin (1824-1907). Drawing on the discovery made by French physicist and chemist J. A. C. Charles (1746-
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1823), that gas at 0°C (32°F) regularly contracts by about 1/273 of its volume for every Celsius degree drop in temperature, Thomson derived the value of absolute zero (discussed below) as -273.15°C (-459.67°F). The Kelvin and Celsius scales are thus directly related: Celsius temperatures can be converted to Kelvins (for which neither the word nor the symbol for “degree” are used) by adding 273.15. M E AS U R I N G H E AT A N D H E AT CA PAC I T Y. Heat, on the other hand, is meas-
ured not by degrees (discussed along with the thermometer in the context of thermal expansion), but by the same units as work. Since energy is the ability to perform work, heat or work units are also units of energy. The principal unit of energy in the SI or metric system is the joule (J), equal to 1 newton-meter (N • m), and the primary unit in the British or English system is the foot-pound (ft • lb). One foot-pound is equal to 1.356 J, and 1 joule is equal to 0.7376 ft • lb. Two other units are frequently used for heat as well. In the British system, there is the Btu, or British thermal unit, equal to 778 ft • lb. or 1,054 J. Btus are often used in reference, for instance, to the capacity of an air conditioner. An SI unit that is also used in the United States—where British measures typically still prevail—is the kilocalorie. This is equal to the heat that must be added to or removed from 1 kilogram of water to change its temperature by 1°C. As its name suggests, a kilocalorie is 1,000 calories. A calorie is the heat required to change the temperature in 1 gram of water by 1°C—but the dietary Calorie (capital C), with which most people are familiar is the same as the kilocalorie. A kilocalorie is identical to the heat capacity for one kilogram of water. Heat capacity (sometimes called specific heat capacity or specific heat) is the amount of heat that must be added to, or removed from, a unit of mass for a given substance to change its temperature by 1°C. this is measured in units of J/kg • °C (joules per kilogram-degree Centigrade), though for the sake of convenience it is typically rendered in terms of kilojoules (1,000 joules): kJ/kg • °c. Expressed thus, the specific heat of water 4.185—which is fitting, since a kilocalorie is equal to 4.185 kJ. Water is unique in many aspects, with regard to specific heat, in that it requires far more heat to raise the temperature of water than that of mercury or iron.
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REAL-LIFE A P P L I C AT I O N S
Thermodynamics
Hot and “Cold” Earlier, it was stated that there is no such thing as “cold”—a statement hard to believe for someone who happens to be in Buffalo, New York, or International Falls, Minnesota, during a February blizzard. Certainly, cold is real as a sensory experience, but in physical terms, cold is not a “thing”—it is simply the absence of heat. People will say, for instance, that they put an ice cube in a cup of coffee to cool it, but in terms of physics, this description is backward: what actually happens is that heat flows from the coffee to the ice, thus raising its temperature. The resulting temperature is somewhere between that of the ice cube and the coffee, but one cannot obtain the value simply by averaging the two temperatures at the beginning of the transfer. For one thing, the volume of the water in the ice cube is presumably less than that of the water in the coffee, not to mention the fact that their differing chemical properties may have some minor effect on the interaction. Most important, however, is the fact that the coffee did not simply merge with the ice: in transferring heat to the ice cube, the molecules in the coffee expended some of their internal kinetic energy, losing further heat in the process. C O O L I N G M AC H I N E S . Even cooling machines, such as refrigerators and air conditioners, actually use heat, simply reversing the usual process by which particles are heated. The refrigerator pulls heat from its inner compartment—the area where food and other perishables are stored—and transfers it to the region outside. This is why the back of a refrigerator is warm.
Inside the refrigerator is an evaporator, into which heat from the refrigerated compartment flows. The evaporator contains a refrigerant—a gas, such as ammonia or Freon 12, that readily liquifies. This gas is released into a pipe from the evaporator at a low pressure, and as a result, it evaporates, a process that cools it. The pipe takes the refrigerant to the compressor, which pumps it into the condenser at a high pressure. Located at the back of the refrigerator, the condenser is a long series of pipes in which pressure turns the gas into liquid. As it moves through the condens-
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er, the gas heats, and this heat is released into the air around the refrigerator. An air conditioner works in a similar manner. Hot air from the room flows into the evaporator, and a compressor circulates refrigerant from the evaporator to a condenser. Behind the evaporator is a fan, which draws in hot air from the room, and another fan pushes heat from the condenser to the outside. As with a refrigerator, the back of an air conditioner is hot because it is moving heat from the area to be cooled. Thus, cooling machines do not defy the principles of heat discussed above; nor do they defy the laws of thermodynamics that will be discussed at the conclusion of this essay. In accordance with the second law, in order to move heat in the reverse of its usual direction, external energy is required. Thus, a refrigerator takes in energy from a electric power supply (that is, the outlet it is plugged into), and extracts heat. Nonetheless, it manages to do so efficiently, removing two or three times as much heat from its inner compartment as the amount of energy required to run the refrigerator.
Transfers of Heat It is appropriate now to discuss how heat is transferred. One must remember, again, that in order for heat to be transferred from one point to another, there must be a difference of temperature between those two points. If an object or system has a uniform level of internal thermal energy—no matter how “hot” it may be in ordinary terms—no heat transfer is taking place. Heat is transferred by one of three methods: conduction, which involves successive molecular collisions; convection, which requires the motion of hot fluid from one place to another; or radiation, which involves electromagnetic waves and requires no physical medium for the transfer. Conduction takes place best in solids and particularly in metals, whose molecules are packed in relatively close proximity. Thus, when one end of an iron rod is heated, eventually the other end will acquire heat due to conduction. Molecules of liquid or nonmetallic solids vary in their ability to conduct heat, but gas—due to the loose attractions between its molecules—is a poor conductor. CONDUCTION.
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shoulder, passing a secret down the line. In this case, however, the “secret” is kinetic thermal energy. And just as the original phrasing of the secret will almost inevitably become garbled by the time it gets to the tenth or hundredth person, some energy is lost in the transfer from molecule to molecule. Thus, if one end of the iron rod is sitting in a fire and one end is surrounded by air at room temperature, it is unlikely that the end in the air will ever get as hot as the end in the fire. Incidentally, the qualities that make metallic solids good conductors of heat also make them good conductors of electricity. In the first instance, kinetic energy is being passed from molecule to molecule, whereas in an electrical field, electrons—freed from the atoms of which they are normally a part—are able to move along the line of molecules. Because plastic is much less conductive than metal, an electrician will use a screwdriver with a plastic handle. Similarly, a metal pan typically has a handle of wood or plastic. C O N V E C T I O N . There is a term, “convection oven,” that is actually a redundancy: all ovens heat through convection, the principal means of transferring heat through a fluid. In physics, “fluid” refers both to liquids and gases— anything that tends to flow. Instead of simply moving heat, as in conduction, convection involves the movement of heated material—that is, fluid. When air is heated, it displaces cold (that is, unheated) air in its path, setting up a convection current.
Convection takes place naturally, as for instance when hot air rises from the land on a warm day. This heated air has a lower density than that of the less heated air in the atmosphere above it, and, therefore, is buoyant. As it rises, however, it loses energy and cools. This cooled air, now more dense than the air around it, sinks again, creating a repeating cycle. The preceding example illustrates natural convection; the heat of an oven, on the other hand, is an example of forced convection—a situation in which some sort of pump or mechanism moves heated fluid. So, too, is the cooling work of a refrigerator, though the refrigerator moves heat in the opposite direction.
When conduction takes place, it is as though a long line of people are standing shoulder to
Forced convection can also take place within a natural system. The human heart is a pump, and blood carries excess heat generated by the body to the skin. The heat passes through the
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skin by means of conduction, and at the surface of the skin, it is removed from the body in a number of ways, primarily by the cooling evaporation of moisture—that is, perspiration.
Thermodynamics
RA D I AT I O N . If the Sun is hot—hot enough to severely burn the skin of a person who spends too much time exposed to its rays—then why is it cold in the upper atmosphere? After all, the upper atmosphere is closer to the Sun. And why is it colder still in the empty space above the atmosphere, which is still closer to the Sun? The reason is that in outer space there is no medium for convection, and in the upper atmosphere, where the air molecules are very far apart, there is hardly any medium. How, then, does heat come to the Earth from the Sun? By radiation, which is radically different from conduction or convection. The other two involve ordinary thermal energy, but radiation involves electromagnetic energy.
A great deal of “stuff ” travels through the electromagnetic spectrum, discussed in another essay in this book: radio waves, microwaves for television and radar, infrared light, visible light, x rays, gamma rays. Though the relatively narrow band of visible-light wavelengths is the only part of the spectrum of which people are aware in everyday life, other parts—particularly the infrared and ultraviolet bands—are involved in the heat one feels from the Sun. (Ultraviolet rays, in fact, cause sunburns.) Heat by means of radiation is not as “otherworldly” as it might seem: in fact, one does not have to point to the Sun for examples of it. Any time an object glows as a result of heat—as for example, in the case of firelight—that is an example of radiation. Some radiation is emitted in the form of visible light, but the heat component is in infrared rays. This also occurs in an incandescent light bulb. In an incandescent bulb, incidentally, much of the energy is lost to the heat of infrared rays, and the efficiency of a fluorescent bulb lies in the fact that it converts what would otherwise be heat into usable light.
The Laws of Thermodynamics Having explored the behavior of heat, both at the molecular level and at levels more easily perceived by the senses, it is possible to discuss the laws of thermodynamics alluded to throughout this essay. These laws illustrate the relationships between heat and energy examined earlier, and
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BENJAMIN THOMPSON, COUNT RUMFORD. (Illustration by H. Humphrey. UPI/Corbis-Bettmann. Reproduced by permission.)
show, for instance, why a refrigerator or air conditioner must have an external source of energy to move heat in a direction opposite to its normal flow. The story of how these laws came to be discovered is a saga unto itself, involving the contributions of numerous men in various places over a period of more than a century. In 1791, Swiss physicist Pierre Prevost (1751-1839) put forth his theory of exchanges, stating correctly that all bodies radiate heat. Hence, as noted earlier, there is no such thing as “cold”: when one holds snow in one’s hand, cold does not flow from the snow into the hand; rather, heat flows from the hand to the snow. Seven years later, an American-British physicist named Benjamin Thompson, Count Rumford (1753) was boring a cannon with a blunt drill when he noticed that this action generated a great deal of heat. This led him to question the prevailing wisdom, which maintained that heat was a fluid form of matter; instead, Thompson began to suspect that heat must arise from some form of motion. C A R N O T ’ S E N G I N E . The next major contribution came from the French physicist and engineer Sadi Carnot (1796-1832).
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Though he published only one scientific work, Reflections on the Motive Power of Fire (1824), this treatise caused a great stir in the European scientific community. In it, Carnot made the first attempt at a scientific definition of work, describing it as “weight lifted through a height.” Even more important was his proposal for a highly efficient steam engine. A steam engine, like a modern-day internal combustion engine, is an example of a larger class of machine called heat engine. A heat engine absorbs heat at a high temperature, performs mechanical work, and, as a result, gives off heat a lower temperature. (The reason why that temperature must be lower is established in the second law of thermodynamics.) For its era, the steam engine was what the computer is today: representing the cutting edge in technology, it was the central preoccupation of those interested in finding new ways to accomplish old tasks. Carnot, too, was fascinated by the steam engine, and was determined to help overcome its disgraceful inefficiency: in operation, a steam engine typically lost as much as 95% of its heat energy. In his Reflections, Carnot proposed that the maximum efficiency of any heat engine was equal to (TH-TL)/TH, where TH is the highest operating temperature of the machine, and TL the lowest. In order to maximize this value, TL has to be absolute zero, which is impossible to reach, as was later illustrated by the third law of thermodynamics. In attempting to devise a law for a perfectly efficient machine, Carnot inadvertently proved that such a machine is impossible. Yet his work influenced improvements in steam engine design, leading to levels of up to 80% efficiency. In addition, Carnot’s studies influenced Kelvin— who actually coined the term “thermodynamics”—and others. T H E F I R S T LAW O F T H E R M O D Y N A M I C S . During the 1840s, Julius
Robert Mayer (1814-1878), a German physicist, published several papers in which he expounded the principles known today as the conservation of energy and the first law of thermodynamics. As discussed earlier, the conservation of energy shows that within a system isolated from all outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place.
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The first law of thermodynamics states this fact in a somewhat different manner. As with the other laws, there is no definitive phrasing; instead, there are various versions, all of which say the same thing. One way to express the law is as follows: Because the amount of energy in a system remains constant, it is impossible to perform work that results in an energy output greater than the energy input. For a heat engine, this means that the work output of the engine, combined with its change in internal energy, is equal to its heat input. Most heat engines, however, operate in a cycle, so there is no net change in internal energy. Earlier, it was stated that a refrigerator extracts two or three times as much heat from its inner compartment as the amount of energy required to run it. On the surface, this seems to contradict the first law: isn’t the refrigerator putting out more energy than it received? But the heat it extracts is only part of the picture, and not the most important part from the perspective of the first law. A regular heat engine, such as a steam or internal-combustion engine, pulls heat from a high-temperature reservoir to a low-temperature reservoir, and, in the process, work is accomplished. Thus, the hot steam from the high-temperature reservoir makes possible the accomplishment of work, and when the energy is extracted from the steam, it condenses in the low-temperature reservoir as relatively cool water. A refrigerator, on the other hand, reverses this process, taking heat from a low-temperature reservoir (the evaporator inside the cooling compartment) and pumping it to a high-temperature reservoir outside the refrigerator. Instead of producing a work output, as a steam engine does, it requires a work input—the energy supplied via the wall outlet. Of course, a refrigerator does produce an “output,” by cooling the food inside, but the work it performs in doing so is equal to the energy supplied for that purpose. T H E S E C O N D LAW O F T H E R M O D Y N A M I C S . Just a few years after
Mayer’s exposition of the first law, another German physicist, Rudolph Julius Emanuel Clausius (1822-1888) published an early version of the second law of thermodynamics. In an 1850 paper, Clausius stated that “Heat cannot, of itself, pass from a colder to a hotter body.” He refined
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this 15 years later, introducing the concept of entropy—the tendency of natural systems toward breakdown, and specifically, the tendency for the energy in a system to be dissipated.
inevitably break down and die, or cease to function, someday.
The second law of thermodynamics begins from the fact that the natural flow of heat is always from a high-temperature reservoir to a low-temperature reservoir. As a result, no engine can be constructed that simply takes heat from a source and performs an equivalent amount of work: some of the heat will always be lost. In other words, it is impossible to build a perfectly efficient engine.
directly to the third law of thermodynamics, formulated by German chemist Hermann Walter Nernst (1864-1941) in 1905. The third law states that at the temperature of absolute zero, entropy also approaches zero. From this statement, Nernst deduced that absolute zero is therefore impossible to reach.
Though its relation to the first law is obvious, inasmuch as it further defines the limitations of machine output, the second law of thermodynamics is not derived from the first. Elsewhere in this volume, the first law of thermodynamics—stated as the conservation of energy law—is discussed in depth, and, in that context, it is in fact necessary to explain how the behavior of machines in the real world does not contradict the conservation law.
Thermodynamics
T H E T H I R D LAW O F T H E R M O DY N A M I CS . The subject of entropy leads
All matter is in motion at the molecular level, which helps define the three major phases of matter found on Earth. At one extreme is a gas, whose molecules exert little attraction toward one another, and are therefore in constant motion at a high rate of speed. At the other end of the phase continuum (with liquids somewhere in the middle) are solids. Because they are close together, solid particles move very little, and instead of moving in relation to one another, they merely vibrate in place. But they do move.
Even though they mean the same thing, the first law of thermodynamics and the conservation of energy law are expressed in different ways. The first law of thermodynamics states that “the glass is half empty,” whereas the conservation of energy law shows that “the glass is half full.” The thermodynamics law emphasizes the bad news: that one can never get more energy out of a machine than the energy put into it. Thus, all hopes of a perpetual motion machine were dashed. The conservation of energy, on the other hand, stresses the good news: that energy is never lost.
Absolute zero, or 0K on the Kelvin scale of temperature, is the point at which all molecular motion stops entirely—or at least, it virtually stops. (In fact, absolute zero is defined as the temperature at which the motion of the average atom or molecule is zero.) As stated earlier, Carnot’s engine achieves perfect efficiency if its lowest temperature is the same as absolute zero; but the second law of thermodynamics shows that a perfectly efficient machine is impossible. This means that absolute zero is an unreachable extreme, rather like matter exceeding the speed of light, also an impossibility.
In this context, the second law of thermodynamics delivers another dose of bad news: though it is true that energy is never lost, the energy available for work output will never be as great as the energy put into a system. A car engine, for instance, cannot transform all of its energy input into usable horsepower; some of the energy will be used up in the form of heat and sound. Though energy is conserved, usable energy is not. Indeed, the concept of entropy goes far beyond machines as people normally understand them. Entropy explains why it is easier to break something than to build it—and why, for each person, the machine called the human body will
This does not mean that scientists do not attempt to come as close as possible to absolute zero, and indeed they have come very close. In 1993, physicists at the Helsinki University of Technology Low Temperature Laboratory in Finland used a nuclear demagnetization device to achieve a temperature of 2.8 • 10-10 K, or 0.00000000028K. This means that a fragment equal to only 28 parts in 100 billion separated this temperature from absolute zero—but it was still above 0K. Such extreme low-temperature research has a number of applications, most notably with superconductors, materials that exhibit virtually no resistance to electrical current at very low temperatures.
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Thermodynamics
KEY TERMS The temperature,
either a gas or a liquid, and convection is
defined as 0K on the Kelvin scale, at which
the principal means of heat transfer, for
the motion of molecules in a solid virtual-
instance, in air and water.
ly ceases. The third law of thermodynamics
ENERGY:
establishes the impossibility of actually
work.
ABSOLUTE ZERO:
reaching absolute zero.
The ability to accomplish
ENTROPY:
The tendency of natural
A
systems toward breakdown, and specifical-
measure of energy or heat in the British
ly, the tendency for the energy in a system
system, often used in reference to the
to be dissipated. Entropy is closely related
capacity of an air conditioner. A Btu is
to the second law of thermodynamics.
BTU (BRITISH THERMAL UNIT):
equal to 778 foot-pounds, or 1,054 joules. FIRST LAW OF THERMODYNAMICS: CALORIE:
A measure of heat or energy
in the SI or metric system, equal to the heat that must be added to or removed from 1 gram of water to change its temperature by 33.8°F (1°C). The dietary Calorie (capital C) with which most people are familiar is the same as the kilocalorie. CONDUCTION:
The transfer of heat
by successive molecular collisions. Conduction is the principal means of heat transfer in solids, particularly metals. CONSERVATION OF ENERGY:
A
law of physics which holds that within a system isolated from all other outside factors, the total amount of energy remains the same, though transformations of ener-
a system remains constant, and therefore it is impossible to perform work that results in an energy output greater than the energy input. This is the same as the conservation of energy. FOOT-POUND:
The principal unit of
energy—and thus of heat—in the British or English system. The metric or SI unit is the joule. A foot-pound (ft • lb) is equal to 1.356 J. HEAT:
Internal thermal energy that
flows from one body of matter to another. Heat is transferred by three methods conduction, convection, and radiation. The amount of heat
gy from one form to another take place.
HEAT CAPACITY:
The first law of thermodynamics is the
that must be added to, or removed from, a
same as the conservation of energy.
unit of mass of a given substance to change
In physics, “to conserve”
its temperature by 33.8°F (1°C). Heat
something means “to result in no net loss
capacity is sometimes called specific heat
of ” that particular component. It is possi-
capacity or specific heat. A kilocalorie is
ble that within a given system, the compo-
the heat capacity of 1 gram of water.
nent may change form or position, but as
HEAT
long as the net value of the component
absorbs heat at a high temperature, per-
remains the same, it has been conserved.
forms mechanical work, and as a result
CONSERVE:
CONVECTION:
224
A law which states the amount of energy in
The transfer of heat
ENGINE:
A machine that
gives off heat at a lower temperature. The energy that
through the motion of hot fluid from one
KINETIC ENERGY:
place to another. In physics, a “fluid” can be
an object possesses by virtue of its motion.
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Thermodynamics
KEY TERMS
CONTINUED
The principal unit of energy—
therefore it is impossible to build a perfect-
and thus of heat—in the SI or metric sys-
ly efficient engine. This is a result of the
tem, corresponding to 1 newton-meter (N
fact that the natural flow of heat is always
• m). A joule (J) is equal to 0.7376 foot-
from a high-temperature reservoir to a
pounds.
low-temperature
JOULE:
fact
by
expressed in the concept of entropy. The
William Thomson, Lord Kelvin (1824-
second law is sometimes referred to as “the
1907), the Kelvin scale measures tempera-
law of entropy.”
ture in relation to absolute zero, or 0K.
SYSTEM:
(Units in the Kelvin system, known as
usually refers to any set of physical interac-
Kelvins, do not include the word or symbol
tions isolated from the rest of the universe.
for degree.) The Kelvin and Celsius scales
Anything outside of the system, including
are directly related; hence Celsius tempera-
all factors and forces irrelevant to a discus-
KELVIN
SCALE:
Established
reservoir—a
tures can be converted to Kelvins by adding 273.15.
In physics, the term “system”
sion of that system, is known as the environment.
KILOCALORIE:
A measure of heat or
energy in the SI or metric system, equal to the heat that must be added to or removed from 1 kilogram of water to change its temperature by 33.8°F (1°C). As its name suggests, a kilocalorie is 1,000 calories. The dietary Calorie (capital C) with which most people are familiar is the same as the
TEMPERATURE:
The direction of
internal energy flow between bodies when heat is being transferred. Temperature measures the average molecular kinetic energy in transit between those bodies. THERMAL ENERGY:
Heat energy, a
form of kinetic energy produced by the movement of atomic or molecular parti-
kilocalorie. MECHANICAL ENERGY:
The sum of
potential energy and kinetic energy in a
cles. The greater the movement of these particles, the greater the thermal energy. THERMODYNAMICS:
given system. POTENTIAL ENERGY:
The energy
that an object possesses due to its position.
The study of
the relationships between heat, work, and energy.
The transfer of heat by
THIRD LAW OF THERMODYNAMICS:
means of electromagnetic waves, which
A law of thermodynamics which states that
require no physical medium (e.g., water or
at the temperature of absolute zero,
air) for the transfer. Earth receives the Sun’s
entropy also approaches zero. Zero entropy
heat by means of radiation.
would contradict the second law of ther-
SECOND LAW OF THERMODYNAM-
modynamics, meaning that absolute zero is
RADIATION:
ICS:
A law of thermodynamics which
therefore impossible to reach. The exertion of force over a
states that no engine can be constructed
WORK:
that simply takes heat from a source and
given distance to displace or move an
performs an equivalent amount of work.
object. Work is thus the product of force
Some of the heat will always be lost, and
and distance exerted in the same direction.
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WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Brown, Warren. Alternative Sources of Energy. Introduction by Russell E. Train. New York: Chelsea House, 1994. Encyclopedia of Thermodynamics (Web site). (April 12, 2001).
226
Fleisher, Paul. Matter and Energy: Principles of Matter and Thermodynamics. Minneapolis, MN: Lerner Publications, 2002. Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998. Moran, Jeffrey B. How Do We Know the Laws of Thermodynamics? New York: Rosen Publishing Group, 2001. Santrey, Laurence. Heat. Illustrated by Lloyd Birmingham. Mahwah, N.J.: Troll Associates, 1985. Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.
Entropy and the Second Law of Thermodynamics (Web site). (April 12, 2001).
“Temperature and Thermodynamics” PhysLINK.com (Web site). (April 12, 2001).
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Heat
CONCEPT Heat is a form of energy—specifically, the energy that flows between two bodies because of differences in temperature. Therefore, the scientific definition of heat is different from, and more precise than, the everyday meaning. Physicists working in the area of thermodynamics study heat from a number of perspectives, including specific heat, or the amount of energy required to change the temperature of a substance, and calorimetry, the measurement of changes in heat as a result of physical or chemical changes. Thermodynamics helps us to understand such phenomena as the operation of engines and the gradual breakdown of complexity in physical systems—a phenomenon known as entropy.
HOW IT WORKS Heat, Work, and Energy Thermodynamics is the study of the relationships between heat, work, and energy. Work is the exertion of force over a given distance to displace or move an object, and is, thus, the product of force and distance exerted in the same direction. Energy, the ability to accomplish work, appears in numerous manifestations—including thermal energy, or the energy associated with heat.
H E AT
return to its original position, it begins gaining kinetic energy and losing potential energy. All manifestations of energy appear in both kinetic and potential forms, somewhat like the way football teams are organized to play both offense or defense. Just as a football team takes an offensive role when it has the ball, and a defensive role when the other team has it, a physical system typically undergoes regular transformations between kinetic and potential energy, and may have more of one or the other, depending on what is taking place in the system.
What Heat Is and Is Not Thermal energy is actually a form of kinetic energy generated by the movement of particles at the atomic or molecular level: the greater the movement of these particles, the greater the thermal energy. Heat is internal thermal energy that flows from one body of matter to another—or, more specifically, from a system at a higher temperature to one at a lower temperature. Thus, temperature, like heat, requires a scientific definition quite different from its common meaning: temperature measures the average molecular kinetic energy of a system, and governs the direction of internal energy flow between them.
Thermal and other types of energy, including electromagnetic, sound, chemical, and nuclear energy, can be described in terms of two extremes: kinetic energy, or the energy associated with movement, and potential energy, or the energy associated with position. If a spring is pulled back to its maximum point of tension, its potential energy is also at a maximum; once it is released and begins springing through the air to
Two systems at the same temperature are said to be in a state of thermal equilibrium. When this occurs, there is no exchange of heat. Though in common usage, “heat” is an expression of relative warmth or coldness, in physical terms, heat exists only in transfer between two systems. What people really mean by “heat” is the internal energy of a system—energy that is a property of that system rather than a property of transferred internal energy.
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means, convection. In fact, there are three methods heat is transferred: conduction, involving successive molecular collisions and the transfer of heat between two bodies in contact; convection, which requires the motion of fluid from one place to another; or radiation, which takes place through electromagnetic waves and requires no physical medium, such as water or air, for the transfer.
Heat
C O N D U C T I O N . Solids, particularly metals, whose molecules are packed relatively close together, are the best materials for conduction. Molecules of liquid or non-metallic solids vary in their ability to conduct heat, but gas is a poor conductor, because of the loose attractions between its molecules.
IF YOU HOLD A WHITE AND HER
SNOWBALL IN YOUR HAND, AS
VANNA
SON ARE DOING IN THIS PICTURE, HEAT
WILL MOVE FROM YOUR HAND TO THE SNOWBALL.
YOUR
HAND EXPERIENCES THIS AS A SENSATION OF COLDNESS. (Reuters NewMedia Inc./Corbis. Reproduced by permission.)
N O S U C H T H I N G AS “ C O L D . ”
Though the term “cold” has plenty of meaning in the everyday world, in physics terminology, it does not. Cold and heat are analogous to darkness and light: again, darkness means something in our daily experience, but in physical terms, darkness is simply the absence of light. To speak of cold or darkness as entities unto themselves is rather like saying, after spending 20 dollars, “I have 20 non-dollars in my pocket.” If you grasp a snowball in your hand, of course, your hand gets cold. The human mind perceives this as a transfer of cold from the snowball, but, in fact, exactly the opposite happens: heat moves from your hand to the snow, and if enough heat enters the snowball, it will melt. At the same time, the departure of heat from your hand results in a loss of internal energy near the surface of your hand, which you experience as a sensation of coldness.
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228
The qualities that make metallic solids good conductors of heat, as a matter of fact, also make them good conductors of electricity. In the conduction of heat, kinetic energy is passed from molecule to molecule, like a long line of people standing shoulder to shoulder, passing a secret. (And, just as the original phrasing of the secret becomes garbled, some kinetic energy is inevitably lost in the series of transfers.) As for electrical conduction, which takes place in a field of electric potential, electrons are freed from their atoms; as a result, they are able to move along the line of molecules. Because plastic is much less conductive than metal, an electrician uses a screwdriver with a plastic handle; similarly, a metal cooking pan typically has a wooden or plastic handle. C O N V E C T I O N . Wherever fluids are involved—and in physics, “fluid” refers both to liquids and gases—convection is a common form of heat transfer. Convection involves the movement of heated material—whether it is air, water, or some other fluid.
Convection is of two types: natural convection and forced convection, in which a pump or other mechanism moves the heated fluid. When heated air rises, this is an example of natural convection. Hot air has a lower density than that of the cooler air in the atmosphere above it, and, therefore, is buoyant; as it rises, however, it loses energy and cools. This cooled air, now denser than the air around it, sinks again, creating a repeating cycle that generates wind.
In holding the snowball, heat passes from the surface of the hand by one means, conduction, then passes through the snowball by another
Examples of forced convection include some types of ovens and even a refrigerator or air conditioner. These two machines both move warm
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air from an interior to an exterior place. Thus, the refrigerator pulls hot air from the compartment and expels it to the surrounding room, while an air conditioner pulls heat from a building and releases it to the outside.
Heat
But forced convection does not necessarily involve humanmade machines: the human heart is a pump, and blood carries excess heat generated by the body to the skin. The heat passes through the skin by means of conduction, and at the surface of the skin, it is removed from the body in a number of ways, primarily by the cooling evaporation of perspiration. RA D I AT I O N . Outer space, of course, is
cold, yet the Sun’s rays warm the Earth, an apparent paradox. Because there is no atmosphere in space, convection is impossible. In fact, heat from the Sun is not dependant on any fluid medium for its transfer: it comes to Earth by means of radiation. This is a form of heat transfer significantly different from the other two, because it involves electromagnetic energy, instead of ordinary thermal energy generated by the action of molecules. Heat from the Sun comes through a relatively narrow area of the light spectrum, including infrared, visible light, and ultraviolet rays. Every form of matter emits electromagnetic waves, though their presence may not be readily perceived. Thus, when a metal rod is heated, it experiences conduction, but part of its heat is radiated, manifested by its glow—visible light. Even when the heat in an object is not visible, however, it may be radiating electromagnetic energy, for instance, in the form of infrared light. And, of course, different types of matter radiate better than others: in general, the better an object is at receiving radiation, the better it is at emitting it.
A
REFRIGERATOR IS A TYPE OF REVERSE HEAT ENGINE
THAT USES A COMPRESSOR, LIKE THE ONE SHOWN AT THE
BACK
OF
THIS
REFRIGERATOR,
TO
COOL
THE
REFRIGERATOR’S INTERIOR. (Ecoscene/Corbis. Reproduced by
permission.)
Abbreviated “J,” a joule is equal to 1 newtonmeter (N • m). The newton is the SI unit of force, and since work is equal to force multiplied by distance, measures of work can also be separated into these components. For instance, the British measure of work brings together a unit of distance, the foot, and a unit of force, the pound. A foot-pound (ft • lb) is equal to 1.356 J, and 1 joule is equal to 0.7376 ft • lb.
The principal unit of work or energy in the metric system (known within the scientific community as SI, or the SI system) is the joule.
In the British system, Btu, or British thermal unit, is another measure of energy used for machines such as air conditioners. One Btu is equal to 778 ft • lb or 1,054 J. The kilocalorie in addition to the joule, is an important SI measure of heat. The amount of energy required to change the temperature of 1 gram of water by 1°C is called a calorie, and a kilocalorie is equal to 1,000 calories. Somewhat confusing is the fact that the dietary Calorie (capital C), with which most people are familiar, is not the same as a calorie (lowercase C)—rather, a dietary Calorie is the equivalent of a kilocalorie.
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Measuring Heat The measurement of temperature by degrees in the Fahrenheit or Celsius scales is a part of everyday life, but measurements of heat are not as familiar to the average person. Because heat is a form of energy, and energy is the ability to perform work, heat is, therefore, measured by the same units as work.
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REAL-LIFE A P P L I C AT I O N S Specific Heat Specific heat is the amount of heat that must be added to, or removed from, a unit of mass for a given substance to change its temperature by 1°C. Thus, a kilocalorie, because it measures the amount of heat necessary to effect that change precisely for a kilogram of water, is identical to the specific heat for that particular substance in that particular unit of mass. The higher the specific heat, the more resistant the substance is to changes in temperature. Many metals, in fact, have a low specific heat, making them easy to heat up and cool down. This contributes to the tendency of metals to expand when heated (a phenomenon also discussed in the Thermal Expansion essay), and, thus, to their malleability. M E AS U R I N G A N D CA L C U LAT I N G S P E C I F I C H E AT. The specific heat
of any object is a function of its mass, its composition, and the desired change in temperature. The values of the initial and final temperature are not important—only the difference between them, which is the temperature change. The components of specific heat are related to one another in the formula Q = mcδT. Here Q is the quantity of heat, measured in joules, which must be added. The mass of the object is designated by m, and the specific heat of the particular substance in question is represented with c. The Greek letter delta (δ) designates change, and δT stands for “change in temperature.” Specific heat is measured in units of J/kg • °C (joules per kilogram-degree Centigrade), though for the sake of convenience, this is usually rendered in terms of kilojoules (kJ), or 1,000 joules—that is, kJ/kg • °C. The specific heat of water is easily derived from the value of a kilocalorie: it is 4.185, the same number of joules required to equal a kilocalorie.
By the mid-1800s, a number of thinkers had come to the realization that—contrary to prevailing theories of the day—heat was a form of energy, not a type of material substance. Among these were American-British physicist Benjamin Thompson, Count Rumford (1753-1814) and English chemist James Joule (1818-1889)—for whom, of course, the joule is named. Calorimetry as a scientific field of study actually had its beginnings with the work of French chemist Pierre-Eugene Marcelin Berthelot (1827-1907). During the mid-1860s, Berthelot became intrigued with the idea of measuring heat, and by 1880, he had constructed the first real calorimeter. CALORIMETERS. Essential to calorimetry is the calorimeter, which can be any device for accurately measuring the temperature of a substance before and after a change occurs. A calorimeter can be as simple as a styrofoam cup. Its quality as an insulator, which makes styrofoam ideal for holding in the warmth of coffee and protecting the hand from scalding as well, also makes styrofoam an excellent material for calorimetric testing. With a styrofoam calorimeter, the temperature of the substance inside the cup is measured, a reaction is allowed to take place, and afterward, the temperature is measured a second time.
The measurement of heat gain or loss as a result of physical or chemical change is called calorimetry (pronounced kal-IM-uh-tree). Like the word “calorie,” the term is derived from a Latin root meaning “heat.”
The most common type of calorimeter used is the bomb calorimeter, designed to measure the heat of combustion. Typically, a bomb calorimeter consists of a large container filled with water, into which is placed a smaller container, the combustion crucible. The crucible is made of metal, having thick walls with an opening through which oxygen can be introduced. In addition, the combustion crucible is designed to be connected to a source of electricity.
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The foundations of calorimetry go back to the mid-nineteenth century, but the field owes much to scientists’ work that took place over a period of about 75 years prior to that time. In 1780, French chemist Antoine Lavoisier (17431794) and French astronomer and mathematician Pierre Simon Laplace (1749-1827) had used a rudimentary ice calorimeter for measuring the heats in formations of compounds. Around the same time, Scottish chemist Joseph Black (17281799) became the first scientist to make a clear distinction between heat and temperature.
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In conducting a calorimetric test using a bomb calorimeter, the substance or object to be studied is placed inside the combustion crucible and ignited. The resulting reaction usually occurs so quickly that it resembles the explosion of a bomb—hence, the name “bomb calorimeter.” Once the “bomb” goes off, the resulting transfer of heat creates a temperature change in the water, which can be readily gauged with a thermometer.
tion engine, a steam engine burns its fuel outside the engine. That fuel may be simply firewood, which is used to heat water and create steam. The thermal energy of the steam is then used to power a piston moving inside a cylinder, thus, converting thermal energy to mechanical energy for purposes such as moving a train.
To study heat changes at temperatures higher than the boiling point of water (212°F or 100°C), physicists use substances with higher boiling points. For experiments involving extremely large temperature ranges, an aneroid (without liquid) calorimeter may be used. In this case, the lining of the combustion crucible must be of a metal, such as copper, with a high coefficient or factor of thermal conductivity.
science and technology, the historical roots of the steam engine can be traced to the Greeks, who— just as they did with ideas such as the atom or the Sun-centered model of the universe—thought about it, but failed to develop it. The great inventor Hero of Alexandria (c. 65-125) actually created several steam-powered devices, but he perceived these as mere novelties, hardly worthy of scientific attention. Though Europeans adopted water power, as, for instance, in waterwheels, during the late ancient and medieval periods, further progress in steam power did not occur for some 1,500 years.
Heat Engines The bomb calorimeter that Berthelot designed in 1880 measured the caloric value of fuels, and was applied to determining the thermal efficiency of a heat engine. A heat engine is a machine that absorbs heat at a high temperature, performs mechanical work, and as a result, gives off heat at a lower temperature. The desire to create efficient heat engines spurred scientists to a greater understanding of thermodynamics, and this resulted in the laws of thermodynamics, discussed at the conclusion of this essay. Their efforts were intimately connected with one of the greatest heat engines ever created, a machine that literally powered the industrialized world during the nineteenth century: the steam engine. HOW A STEAM ENGINE WORKS.
Like all heat engines (except reverse heat engines such as the refrigerator, discussed below), a steam engine pulls heat from a high-temperature reservoir to a low-temperature reservoir, and in the process, work is accomplished. The hot steam from the high-temperature reservoir makes possible the accomplishment of work, and when the energy is extracted from the steam, the steam condenses in the low-temperature reservoir, becoming relatively cool water.
Heat
E V O LU T I O N O F S T E A M P O W E R. As with a number of advanced concepts in
Following the work of French physicist Denis Papin (1647-1712), who invented the pressure cooker and conducted the first experiments with the use of steam to move a piston, English engineer Thomas Savery (c. 1650-1715) built the first steam engine. Savery had abandoned the use of the piston in his machine, but another English engineer, Thomas Newcomen (1663-1729), reintroduced the piston for his own steam-engine design. Then in 1763, a young Scottish engineer named James Watt (1736-1819) was repairing a Newcomen engine and became convinced he could build a more efficient model. His steam engine, introduced in 1769, kept the heating and cooling processes separate, eliminating the need for the engine to pause in order to reheat. These and other innovations that followed—including the introduction of a high-pressure steam engine by English inventor Richard Trevithick (17711833)—transformed the world. CA R N O T P R O V I D E S T H E O R E T I CA L U N D E R S TA N D I N G . The men
A steam engine is an external-combustion engine, as opposed to the internal-combustion engine that took its place at the forefront of industrial technology at the beginning of the twentieth century. Unlike an internal-combus-
who developed the steam engine were mostly practical-minded figures who wanted only to build a better machine; they were not particularly concerned with the theoretical explanation for its workings. Then in 1824, a French physicist and engineer by the name of Sadi Carnot (17961832) published his sole work, the highly influ-
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ential Reflections on the Motive Power of Fire (1824), in which he discussed heat engines scientifically. In Reflections, Carnot offered the first definition of work in terms of physics, describing it as “weight lifted through a height.” Analyzing Watt’s steam engine, he also conducted groundbreaking studies in the nascent science of thermodynamics. Every heat engine, he explained, has a theoretical limit of efficiency related to the temperature difference in the engine: the greater the difference between the lowest and highest temperature, the more efficient the engine. Carnot’s work influenced the development of more efficient steam engines, and also had an impact on the studies of other physicists investigating the relationship between work, heat, and energy. Among these was William Thomson, Lord Kelvin (1824-1907). In addition to coining the term “thermodynamics,” Kelvin developed the Kelvin scale of absolute temperature and established the value of absolute zero, equal to -273.15°C or -459.67°F. According to Carnot’s theory, maximum effectiveness was achieved by a machine that could reach absolute zero. However, later developments in the understanding of thermodynamics, as discussed below, proved that both maximum efficiency and absolute zero are impossible to attain. R E V E R S E H E AT E N G I N E S . It is easy to understand that a steam engine is a heat engine: after all, it produces heat. But how is it that a refrigerator, an air conditioner, and other cooling machines are also heat engines? Moreover, given the fact that cold is the absence of heat and heat is energy, one might ask how a refrigerator or air conditioner can possibly use energy to produce cold, which is the same as the absence of energy. In fact, cooling machines simply reverse the usual process by which heat engines operate, and for this reason, they are called “reverse heat engines.” Furthermore, they use energy to extract heat.
A steam engine takes heat from a high-temperature reservoir—the place where the water is turned into steam—and uses that energy to produce work. In the process, energy is lost and the heat moves to a low-temperature reservoir, where it condenses to form relatively cool water. A refrigerator, on the other hand, pulls heat from a low-temperature reservoir called the evaporator,
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into which flows heat from the refrigerated compartment—the place where food and other perishables are kept. The coolant from the evaporator take this heat to the condenser, a high-temperature reservoir at the back of the refrigerator, and in the process it becomes a gas. Heat is released into the surrounding air; this is why the back of a refrigerator is hot. Instead of producing a work output, as a steam engine does, a refrigerator requires a work input—the energy supplied via the wall outlet. The principles of thermodynamics show that heat always flows from a high-temperature to a low-temperature reservoir, and reverse heat engines do not defy these laws. Rather, they require an external power source in order to effect the transfer of heat from a low-temperature reservoir, through the gases in the evaporator, to a high-temperature reservoir.
The Laws of Thermodynamics T H E F I R S T LAW O F T H E R M O DY N A M I CS . There are three laws of ther-
modynamics, which provide parameters as to the operation of thermal systems in general, and heat engines in particular. The history behind the derivation of these laws is discussed in the essay on Thermodynamics; here, the laws themselves will be examined in brief form. The physical law known as conservation of energy shows that within a system isolated from all outside factors, the total amount of energy remains the same, though transformations of energy from one form to another take place. The first law of thermodynamics states the same fact in a somewhat different manner. According to the first law of thermodynamics, because the amount of energy in a system remains constant, it is impossible to perform work that results in an energy output greater than the energy input. Thus, it could be said that the conservation of energy law shows that “the glass is half full”: energy is never lost. On the hand, the first law of thermodynamics shows that “the glass is half empty”: no machine can ever produce more energy than was put into it. Hence, a perpetual motion machine is impossible, because in order to keep a machine running continually, there must be a continual input of energy. T H E S E C O N D LAW O F T H E R M O DY N A M I CS . The second law of ther-
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Heat
KEY TERMS The temperature,
either a gas or a liquid, and convection is
defined as 0K on the Kelvin scale, at which
the principal means of heat transfer, for
the motion of molecules in a solid virtual-
instance, in air and water.
ly ceases. The third law of thermodynamics
ENERGY:
establishes the impossibility of actually
work.
ABSOLUTE ZERO:
The ability to accomplish
reaching absolute zero. ENTROPY: BTU (BRITISH THERMAL UNIT):
A
measure of energy or heat in the British system, often used in reference to the capacity of an air conditioner. A Btu is
The tendency of natural
systems toward breakdown, and specifically, the tendency for the energy in a system to be dissipated. Entropy is closely related to the second law of thermodynamics.
equal to 778 foot-pounds, or 1,054 joules. CALORIE:
A measure of heat or energy
in the SI or metric system, equal to the heat that must be added to or removed from 1 gram of water to change its temperature by 1°C. The dietary Calorie (capital C) with which most people are familiar is the same as the kilocalorie. CALORIMETRY:
The measurement of
heat gain or loss as a result of physical or chemical change. CONDUCTION:
The transfer of heat
by successive molecular collisions. Con-
FIRST LAW OF THERMODYNAMICS:
A law stating that the amount of energy in a system remains constant, and therefore, it is impossible to perform work that results in an energy, output greater than the energy input. This is the same as the conservation of energy. FOOT-POUND:
The principal unit of
energy—and, thus, of heat—in the British or English system. The metric or SI unit is the joule. A foot-pound (ft • lb) is equal to 1.356 J. Internal thermal energy that
duction is the principal means of heat
HEAT:
transfer in solids, particularly metals.
flows from one body of matter to another.
CONSERVATION OF ENERGY:
A
law of physics stating that within a system
Heat is transferred by three methods conduction, convection, and radiation. A machine that
isolated from all other outside factors, the
HEAT
total amount of energy remains the same,
absorbs heat at a high temperature, per-
though transformations of energy from
forms mechanical work, and, as a result,
one form to another take place. The first
gives off heat at a lower temperature.
law of thermodynamics is the same as the
JOULE:
conservation of energy.
and, thus, of heat—in the SI or metric sys-
ENGINE:
The principal unit of energy—
The transfer of heat
tem, corresponding to 1 newton-meter
through the motion of hot fluid from one
(N • m). A joule (J) is equal to 0.7376 foot-
place to another. In physics, a “fluid” can be
pounds.
CONVECTION:
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Heat
KEY TERMS KELVIN
SCALE:
Established
by
William Thomson, Lord Kelvin (18241907), the Kelvin scale measures tempera-
CONTINUED
POTENTIAL ENERGY:
The energy
that an object possesses due to its position. RADIATION:
The transfer of heat by
ture in relation to absolute zero, or 0K.
means of electromagnetic waves, which
(Units in the Kelvin system, known as
require no physical medium (for example,
Kelvins, do not include the word or symbol
water or air) for the transfer. Earth receives
for degree.) The Kelvin and Celsius scales
the Sun’s heat by means of radiation.
are directly related; hence, Celsius temperatures can be converted to Kelvins by adding 273.15.
ICS:
A law of thermodynamics stating
that no engine can be constructed that A measure of heat or
simply takes heat from a source and per-
energy in the SI or metric system, equal to
forms an equivalent amount of work.
the heat that must be added to or removed
Some of the heat will always be lost, and,
from 1 kilogram of water to change its
therefore, it is impossible to build a
KILOCALORIE:
temperature by 1°C. As its name suggests, a kilocalorie is 1,000 calories. The dietary Calorie (capital C) with which most people are familiar, is the same as the kilocalorie. KINETIC ENERGY:
The energy that
an object possesses by virtue of its motion.
modynamics begins from the fact that the natural flow of heat is always from a high-temperature to a low-temperature reservoir. As a result, no engine can be constructed that simply takes heat from a source and performs an equivalent amount of work: some of the heat will always be lost. In other words, it is impossible to build a perfectly efficient engine. In effect, the second law of thermodynamics compounds the “bad news” delivered by the first law with some even worse news: though it is true that energy is never lost, the energy available for work output will never be as great as the energy put into a system. Linked to the second law is the concept of entropy, the tendency of natural systems toward breakdown, and specifically, the tendency for the energy in a system to be dissipated. “Dissipated” in this context means that the highand low-temperature reservoirs approach equal
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VOLUME 2: REAL-LIFE PHYSICS
perfectly efficient engine. This is a result of the fact that the natural flow of heat is always from a high-temperature reservoir to a low-temperature reservoir—a fact expressed in the concept of entropy. The second law is sometimes referred to as “the law of entropy.”
temperatures, and as this occurs, entropy increases. T H E T H I R D LAW O F T H E R M O DY N A M I CS . Entropy also plays a part in the
third law of thermodynamics, which states that at the temperature of absolute zero, entropy also approaches zero. This might seem to counteract the “worse news” of the second law, but in fact, what the third law shows is that absolute zero is impossible to reach. As stated earlier, Carnot’s engine would achieve perfect efficiency if its lowest temperature were the same as absolute zero; but the second law of thermodynamics shows that a perfectly efficient machine is impossible. Relativity theory (which first appeared in 1905, the same year as the third law of thermodynamics) showed that matter can never exceed the speed of light. In the same way, the collective effect of the second and third laws is to prove that absolute
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Heat
KEY TERMS SPECIFIC HEAT:
The amount of heat
that must be added to, or removed from, a unit of mass of a given substance to change its temperature by 1°C. A kilocalorie is the specific heat of 1 gram of water. SYSTEM:
In physics, the term “system”
usually refers to any set of physical interac-
CONTINUED
cles. The greater the movement of these particles, the greater the thermal energy. THERMAL EQUILIBRIUM:
The state
that exists when two systems have the same temperature. As a result, there is no exchange of heat between them. THERMODYNAMICS:
The study of
tions isolated from the rest of the universe.
the relationships between heat, work, and
Anything outside of the system, including
energy.
all factors and forces irrelevant to a discussion of that system, is known as the environment.
THIRD LAW OF THERMODYNAMICS:
A law of thermodynamics which states that at the temperature of absolute zero,
The direction of
entropy also approaches zero. Zero entropy
internal energy flow between two systems
would contradict the second law of ther-
when heat is being transferred. Tempera-
modynamics, meaning that absolute zero
ture measures the average molecular kinet-
is, therefore, impossible to reach.
TEMPERATURE:
ic energy in transit between those systems. WORK:
The exertion of force over a
Heat energy, a
given distance to displace or move an
form of kinetic energy produced by the
object. Work is, thus, the product of force
movement of atomic or molecular parti-
and distance exerted in the same direction.
THERMAL ENERGY:
zero—the temperature at which molecular motion in all forms of matter theoretically ceases—can never be reached. WHERE TO LEARN MORE Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991. Bonnet, Robert L and Dan Keen. Science Fair Projects: Physics. Illustrated by Frances Zweifel. New York: Sterling, 1999. Encyclopedia of Thermodynamics (Web site). (April 12, 2001). Friedhoffer, Robert. Physics Lab in the Home. Illustrated by Joe Hosking. New York: Franklin Watts, 1997.
S C I E N C E O F E V E RY DAY T H I N G S
Manning, Mick and Brita Granström. Science School. New York: Kingfisher, 1998. Macaulay, David. The New Way Things Work. Boston: Houghton Mifflin, 1998. Moran, Jeffrey B. How Do We Know the Laws of Thermodynamics? New York: Rosen Publishing Group, 2001. Santrey, Laurence. Heat. Illustrated by Lloyd Birmingham. Mahwah, NJ: Troll Associates, 1985. Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996. “Temperature and Thermodynamics” PhysLINK.com (Web site). (April 12, 2001).
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T E M P E R AT U R E Temperature
CONCEPT Temperature is one of those aspects of the everyday world that seems rather abstract when viewed from the standpoint of physics. In scientific terms, it is not simply a measure of hot and cold, but an indicator of molecular motion and energy flow. Thermometers measure temperature by a number of means, including the expansion that takes place in a medium such as mercury or alcohol. These measuring devices are gauged in several different ways, with scales based on the freezing and boiling points of water—as well as, in the case of the absolute temperature scale, the point at which all molecular motion virtually ceases.
HOW IT WORKS Heat Energy appears in many forms, including thermal energy, or the energy associated with heat. Heat is internal thermal energy that flows from one body of matter to another—or, more specifically, from a system at a higher temperature to one at a lower temperature.
236
H E AT:
E N E R GY
IN
T RA N S I T.
Thus, heat cannot be said to exist unless there is one system in contact with another system of differing temperature. This can be illustrated by way of the old philosophical question: “If a tree falls in the woods when there is no one to hear it, does it make a sound?” From a physicist’s point of view, of course, sound waves are emitted whether or not there is an ear to receive their vibrations; but, consider this same scenario in terms of heat. First, replace the falling tree with a hypothetical object possessing a certain amount of internal energy; then replace sound waves with heat. In this case, if this object is not in contact with something else that has a different temperature, it “does not make a sound”—in other words, it transfers no internal energy, and, thus, there is no heat from the standpoint of physics. This could even be true of two incredibly “hot” objects placed next to one another inside a vacuum—an area devoid of matter, including air. If both have the same temperature, there is no heat, only two objects with high levels of internal energy. Note that a vacuum was specified: assuming there was air around them, and that the air was of a lower temperature, both objects would then be transferring heat to the air.
Two systems at the same temperature are said to be in a state of thermal equilibrium. When this occurs, there is no exchange of heat. Though people ordinarily speak of “heat” as an expression of relative warmth or coldness, in physical terms, heat only exists in transfer between two systems. It is never something inherently part of a system; thus, unless there is a transfer of internal energy, there is no heat, scientifically speaking.
energy in transfer, from whence does this energy originate? From the movement of molecules. Every type of matter is composed of molecules, and those molecules are in motion relative to one another. The greater the amount of relative motion between molecules, the greater the kinetic energy, or the energy of movement, which is manifested as thermal energy. Thus, “heat”—to
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R E LAT I V E M O T I O N B E T W E E N M O L E C U L E S . If heat is internal thermal
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use the everyday term for what physicists describe as thermal energy—is really nothing more than the result of relative molecular motion. Thus, thermal energy is sometimes identified as molecular translational energy.
Temperature
Note that the molecules are in relative motion, meaning that if one were “standing” on a molecule, one would see the other molecules moving. This is not the same as movement on the part of a large object composed of molecules; in this case, molecules themselves are not directly involved in relative motion. Put another way, the movement of Earth through space is an entirely different type of movement from the relative motion of objects on Earth—people, animals, natural forms such as clouds, manmade forms of transportation, and so forth. In this example, Earth is analogous to a “large” item of matter, such as a baseball, a stream of water, or a cloud of gas. The smaller objects on Earth are analogous to molecules, and, in both cases, the motion of the larger object has little direct impact on the motion of smaller objects. Hence, as discussed in the Frame of Reference essay, it is impossible to perceive with one’s senses the fact that Earth is actually hurling through space at incredible speeds. MOLECULAR MOTION AND P H A S E S O F M AT T E R. The relative
motion of molecules determines phase of matter—that is, whether something is a solid, liquid, or gas. When molecules move quickly in relation to one another, they exert a small electromagnetic attraction toward one another, and the larger material of which they are a part is called a gas. A liquid, on the other hand, is a type of matter in which molecules move at moderate speeds in relation to one another, and therefore exert a moderate intermolecular attraction. The kinetic theory of gases relates molecular motion to energy in gaseous substances. It does not work as well in relation to liquids and solids; nonetheless, it is safe to say that—generally speaking—a gas has more energy than a liquid, and a liquid more energy than a solid. In a solid, the molecules undergo very little relative motion: instead of bumping into each other, like gas molecules and (to a lesser extent) liquid molecules, solid molecules merely vibrate in place.
S C I E N C E O F E V E RY DAY T H I N G S
WILLIAM THOMSON, (BETTER
KNOWN AS
LORD KELVIN) KELVIN
ESTABLISHED WHAT IS NOW KNOWN AS THE SCALE.
Understanding Temperature As with heat, temperature requires a scientific definition quite different from its common meaning. Temperature may be defined as a measure of the average molecular translational energy in a system—that is, in any material body. Because it is an average, the mass or other characteristics of the body do not matter. A large quantity of one substance, because it has more molecules, possesses more thermal energy than a smaller quantity of that same substance. Since it has more thermal energy, it transfers more heat to any body or system with which it is in contact. Yet, assuming that the substance is exactly the same, the temperature, as a measure of average energy, will be the same as well. Temperature determines the direction of internal energy flow between two systems when heat is being transferred. This can be illustrated through an experience familiar to everyone: having one’s temperature taken with a thermometer. If one has a fever, one’s mouth will be warmer than the thermometer, and therefore heat will be transferred to the thermometer from the mouth until the two objects have the same temperature.
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Temperature
A
THERMOMETER WORKS BY MEASURING THE LEVEL OF
THERMAL
EXPANSION
EXPERIENCED
WITHIN THE THERMOMETER.
MERCURY
BY
A
MATERIAL
HAS BEEN A COM-
MON THERMOMETER MATERIAL SINCE THE
1700S. (Pho-
tograph by Michael Prince/Corbis. Reproduced by permission.)
At that point of thermal equilibrium, a temperature reading can be taken from the thermometer. T E M P E R AT U R E AND H E AT F LO W. The principles of thermodynamics—
the study of the relationships between heat, work, and energy, show that heat always flows from an area of higher temperature to an area of lower temperature. The opposite simply cannot happen, because coldness, though it is very real in terms of sensory experience, is not an independent phenomenon. There is not, strictly speaking, such a thing as “cold”—only the absence of heat, which produces the sensation of coldness.
238
The boiling water warms the tub of cool water, and due to the high ratio of cool water to boiling water in the bathtub, the boiling water expends all its energy raising the temperature in the bathtub as a whole. The greater the ratio of very hot water to cool water, on the other hand, the warmer the bathtub will be in the end. But even after the bath water is heated, it will continue to lose heat, assuming the air in the room is not warmer than the water in the tub. If the water in the tub is warmer than the air, it immediately begins transferring thermal energy to the lowtemperature air until their temperatures are equalized. As for the coffee and the ice cube, what happens is quite different from, indeed, opposite to, the common understanding of the process. In other words, the ice does not “cool down” the coffee: the coffee warms up the ice and presumably melts it. Once again, however, it expends at least some of its thermal energy in doing so, and as a result, the coffee becomes cooler than it was. If the coffee is placed inside a freezer, there is a large temperature difference between it and the surrounding environment—so much so that if it is left for hours, the once-hot coffee will freeze. But again, the freezer does not cool down the coffee; the molecules in the coffee respond to the temperature difference by working to warm up the freezer. In this case, they have to “work overtime,” and since the freezer has a constant supply of electrical energy, the heated molecules of the coffee continue to expend themselves in a futile effort to warm the freezer. Eventually, the coffee loses so much energy that it is frozen solid; meanwhile, the heat from the coffee has been transferred outside the freezer to the atmosphere in the surrounding room. T H E R M A L E X PA N S I O N A N D E Q U I L I B R I U M . Temperature is related to
One might pour a kettle of boiling water into a cold bathtub to heat it up; or put an ice cube in a hot cup of coffee “to cool it down.” These seem like two very different events, but from the standpoint of thermodynamics, they are exactly the same. In both cases, a body of high temperature is placed in contact with a body of low temperature, and in both cases, heat passes from the high-temperature body to the low-temperature one.
the concept of thermal equilibrium, and has an effect on thermal expansion. As discussed below, as well as within the context of thermal expansion, a thermometer provides a gauge of temperature by measuring the level of thermal expansion experienced by a material (for example, mercury) within the thermometer. In the examples used earlier—the thermometer in the mouth, the hot water in the cool bathtub, and the ice cube in the cup of coffee— the systems in question eventually reach thermal equilibrium. This is rather like averaging their temperatures, though, in fact, the equation
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involved is more complicated than a simple arithmetic average. In the case of an ordinary mercury thermometer, the need to achieve thermal equilibrium explains why one cannot get an instantaneous temperature reading: first, the mouth transfers heat to the thermometer, and once both mouth and thermometer reach the same temperature, they are in thermal equilibrium. At that point, it is possible to gauge the temperature of the mouth by reading the thermometer.
REAL-LIFE A P P L I C AT I O N S Development of the Thermometer A thermometer can be defined scientifically as a device that gauges temperature by measuring a temperature-dependent property, such as the expansion of a liquid in a sealed tube. As with many aspects of scientific or technological knowledge, the idea of the thermometer appeared in ancient times, but was never developed. Again, like so many other intellectual phenomena, it lay dormant during the medieval period, only to be resurrected at the beginning of the modern era. The Greco-Roman physician Galen (c. 129216) was among the first thinkers to envision a scale for measuring temperature. Of course, what he conceived of as “temperature” was closer to the everyday meaning of that term, not its more precise scientific definition: the ideas of molecular motion, heat, and temperature discussed in this essay emerged only in the period beginning about 1750. In any case, Galen proposed that equal amounts of boiling water and ice be combined to establish a “neutral” temperature, with four units of warmth above it and four degrees of cold below. T H E T H E R M O S C O P E . The great physicist Galileo Galilei (1564-1642) is sometimes credited with creating the first practical temperature measuring device, called a thermoscope. Certainly Galileo—whether or not he was the first—did build a thermoscope, which consisted of a long glass tube planted in a container of liquid. Prior to inserting the tube into the liquid—which was usually colored water, though Galileo’s thermoscope used wine—as much air as
S C I E N C E O F E V E RY DAY T H I N G S
possible was removed from the tube. This created a vacuum, and as a result of pressure differences between the liquid and the interior of the thermoscope tube, some of the liquid went into the tube.
Temperature
But the liquid was not the thermometric medium—that is, the substance whose temperature-dependent property changes the thermoscope measured. (Mercury, for instance, is the thermometric medium in most thermometers today.) Instead, the air was the medium whose changes the thermoscope measured: when it was warm, the air expanded, pushing down on the liquid; and when the air cooled, it contracted, allowing the liquid to rise. It is interesting to note the similarity in design between the thermoscope and the barometer, a device for measuring atmospheric pressure invented by Italian physicist Evangelista Torricelli (1608-1647) around the same time. Neither were sealed, but by the mid-seventeenth century, scientists had begun using sealed tubes containing liquid instead of air. These were the first true thermometers. E A R LY T H E R M O M E T E R S . Ferdinand II, Grand Duke of Tuscany (1610-1670), is credited with developing the first thermometer in 1641. Ferdinand’s thermometer used alcohol sealed in glass, which was marked with a temperature scale containing 50 units. It did not, however, designate a value for zero.
English physicist Robert Hooke (1635-1703) created a thermometer using alcohol dyed red. Hooke’s scale was divided into units equal to about 1/500 of the volume of the thermometric medium, and for the zero point, he chose the temperature at which water freezes. Thus, Hooke established a standard still used today; likewise, his thermometer itself set a standard. Built in 1664, it remained in use by the Royal Society— the foremost organization for the advancement of science in England during the early modern period—until 1709. Olaus Roemer (1644-1710), a Danish astronomer, introduced another important standard. In 1702, he built a thermometer based not on one but two fixed points, which he designated as the temperature of snow or crushed ice, and the boiling point of water. As with Hooke’s use of the freezing point, Roemer’s idea of the freezing and boiling points of water as the two parameters
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for temperature measurements has remained in use ever since.
Temperature Scales FA H R E N H E I T. Not only did he devel-
op the Fahrenheit scale, oldest of the temperature scales still used in Western nations today, but German physicist Daniel Fahrenheit (1686-1736) also built the first thermometer to contain mercury as a thermometric medium. Alcohol has a low boiling point, whereas mercury remains fluid at a wide range of temperatures. In addition, it expands and contracts at a very constant rate, and tends not to stick to glass. Furthermore, its silvery color makes a mercury thermometer easy to read. Fahrenheit also conceived the idea of using “degrees” to measure temperature in his thermometer, which he introduced in 1714. It is no mistake that the same word refers to portions of a circle, or that exactly 180 degrees—half the number in a circle—separate the freezing and boiling points for water on Fahrenheit’s thermometer. Ancient astronomers attempting to denote movement in the skies used a circle with 360 degrees as a close approximation of the ratio between days and years. The number 360 is also useful for computations, because it has a large quantity of divisors, as does 180—a total of 16 whole-number divisors other than 1 and itself. Though it might seem obvious that 0 should denote the freezing point and 180 the boiling point on Fahrenheit’s scale, such an idea was far from obvious in the early eighteenth century. Fahrenheit considered the idea not only of a 0to-180 scale, but also of a 180-to-360 scale. In the end, he chose neither—or rather, he chose not to equate the freezing point of water with zero on his scale. For zero, he chose the coldest possible temperature he could create in his laboratory, using what he described as “a mixture of sal ammoniac or sea salt, ice, and water.” Salt lowers the melting point of ice (which is why it is used in the northern United States to melt snow and ice from the streets on cold winter days), and, thus, the mixture of salt and ice produced an extremely cold liquid water whose temperature he equated to zero.
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French naturalist and physicist named Rene Antoine Ferchault de Reaumur (1683-1757) presented a scale for which 0° represented the freezing point of water and 80° the boiling point. Although the Reaumur scale never caught on to the same extent as Fahrenheit’s, it did include one valuable addition: the specification that temperature values be determined at standard sea-level atmospheric pressure. C E L S I U S . With its 32-degree freezing point and its 212-degree boiling point, the Fahrenheit system is rather ungainly, lacking the neat orderliness of a decimal or base-10 scale. The latter quality became particularly important when, 10 years after the French Revolution of 1789, France adopted the metric system for measuring length, mass, and other physical phenomena. The metric system eventually spread to virtually the entire world, with the exception of English-speaking countries, where the more cumbersome British system still prevails. But even in the United States and Great Britain, scientists use the metric system. The metric temperature measure is the Celsius scale, created in 1742 by Swedish astronomer Anders Celsius (17011744).
Like Fahrenheit, Celsius chose the freezing and boiling points of water as his two reference points, but he determined to set them 100, rather than 180, degrees apart. Interestingly, he planned to equate 0° with the boiling point, and 100° with the freezing point—proving that even the most apparently obvious aspects of a temperature scale were once open to question. Only in 1750 did fellow Swedish physicist Martin Strömer change the orientation of the Celsius scale. Celsius’s scale was based not simply on the boiling and freezing points of water, but, specifically, those points at normal sea-level atmospheric pressure. The latter, itself a unit of measure known as an atmosphere (atm), is equal to 14.7 lb/in2, or 101,325 pascals in the metric system. A Celsius degree is equal to 1/100 of the difference between the freezing and boiling temperatures of water at 1 atm.
With Fahrenheit’s scale, the ordinary freezing point of water was established at 32°, and the boiling point exactly 180° above it, at 212°. Just a few years after he introduced his scale, in 1730, a
The Celsius scale is sometimes called the centigrade scale, because it is divided into 100 degrees, cent being a Latin root meaning “hundred.” By international convention, its values were refined in 1948, when the scale was redefined in terms of temperature change for an ideal gas, as well as the triple point of water. (Triple
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point is the temperature and pressure at which a substance is at once a solid, liquid, and vapor.) As a result of these refinements, the boiling point of water on the Celsius scale is actually 99.975°. This represents a difference equal to about 1 part in 4,000—hardly significant in daily life, though a significant change from the standpoint of the precise measurements made in scientific laboratories. K E LV I N . In about 1787, French physicist
and chemist J. A. C. Charles (1746-1823) made an interesting discovery: that at 0°C, the volume of gas at constant pressure drops by 1/273 for every Celsius degree drop in temperature. This seemed to suggest that the gas would simply disappear if cooled to -273°C, which, of course, made no sense. In any case, the gas would most likely become first a liquid, and then a solid, long before it reached that temperature. The man who solved the quandary raised by Charles’s discovery was born a year after Charles—who also formulated Charles’s law— died. He was William Thomson, Lord Kelvin (1824-1907), and in 1848, he put forward the suggestion that it was molecular translational energy, and not volume, that would become zero at -273°C. He went on to establish what came to be known as the Kelvin scale. Sometimes known as the absolute temperature scale, the Kelvin scale is based not on the freezing point of water, but on absolute zero— the temperature at which molecular motion comes to a virtual stop. This is -273.15°C (-459.67°F), which in the Kelvin scale is designated as 0K. (Kelvin measures do not use the term or symbol for “degree.”) Though scientists normally use metric or SI measures, they prefer the Kelvin scale to Celsius, because the absolute temperature scale is directly related to average molecular translational energy. Thus, if the Kelvin temperature of an object is doubled, this means that its average molecular translational energy has doubled as well. The same cannot be said if the temperature were doubled from, say, 10°C to 20°C, or from 40°C to 80°F, since neither the Celsius nor the Fahrenheit scale is based on absolute zero. C O N V E R S I O N S . The Kelvin scale is, however, closely related to the Celsius scale, in that a difference of 1 degree measures the same amount of temperature in both. Therefore, Celsius temperatures can be converted to Kelvins by
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adding 273.15. There is also an absolute temperature scale that uses Fahrenheit degrees. This is the Rankine scale, created by Scottish engineer William Rankine (1820-1872), but it is seldom used today: scientists and others who desire absolute temperature measures prefer the precision and simplicity of the Celsius-based Kelvin scale.
Temperature
Conversion between Celsius and Fahrenheit figures is a bit more challenging. To convert a temperature from Celsius to Fahrenheit, multiply by 9/5 and add 32. It is important to perform the steps in that order, because reversing them will produce a wrong answer. Thus, 100°C multiplied by 9/5 or 1.8 equals 180, which, when added to 32 equals 212°F. Obviously, this is correct, since 100°C and 212°F each represent the boiling point of water. But, if one adds 32 to 100°, then multiplies it by 9/5, the result is 237.6°F—an incorrect answer. For converting Fahrenheit temperatures to Celsius, there are also two steps, involving multiplication and subtraction, but the order is reversed. Here, the subtraction step is performed before the multiplication step: thus, 32 is subtracted from the Fahrenheit temperature, then the result is multiplied by 5/9. Beginning with 212°F, if 32 is subtracted, this equals 180. Multiplied by 5/9, the result is 100°C—the correct answer. One reason the conversion formulae use fractions instead of decimal fractions (what most people simply call “decimals”) is that 5/9 is a repeating decimal fraction (0.55555....) Furthermore, the symmetry of 5/9 and 9/5 makes memorization easy. One way to remember the formula is that Fahrenheit is multiplied by a fraction— since 5/9 is a real fraction, whereas 9/5 is actually a whole number plus a fraction.
Thermometers As discussed earlier, with regard to the early history of the thermometer, it is important that the glass tube be kept sealed; otherwise, atmospheric pressure contributes to inaccurate readings, because it influences the movement of the thermometric medium. Also important is the choice of the thermometric medium itself. Water quickly proved unreliable, due to its unusual properties: it does not expand uniformly with a rise in temperature, or contract uniformly with a lowered temperature. Rather, it
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Temperature
KEY TERMS The temperature,
The Fahrenheit scale establishes the freez-
defined as 0K on the Kelvin scale, at which
ing and boiling points of water at 32° and
the motion of molecules in a solid virtual-
212° respectively. To convert a temperature
ly ceases.
from the Fahrenheit to the Celsius scale,
ABSOLUTE ZERO:
A scale of tempera-
subtract 32 and multiply by 5/9. Most Eng-
ture, sometimes known as the centigrade
lish-speaking countries use the Fahrenheit
scale, created in 1742 by Swedish
scale.
CELSIUS SCALE:
astronomer Anders Celsius (1701-1744). The Celsius scale establishes the freezing
HEAT:
Internal thermal energy that
flows from one body of matter to another.
and boiling points of water at 0° and 100°, respectively. To convert a temperature from the Celsius to the Fahrenheit scale, multiply by 9/5 and add 32. The Celsius scale is
SCALE:
Established
by
William Thomson, Lord Kelvin (18241907), the Kelvin scale measures tempera-
part of the metric system used by most
ture in relation to absolute zero, or 0K.
non-English speaking countries today.
(Units in the Kelvin system, known as
Though the worldwide scientific commu-
Kelvins, do not include the word or symbol
nity uses the metric or SI system for most
for degree.) The Kelvin and Celsius scales
measurements, scientists prefer the related
are directly related; hence, Celsius temper-
Kelvin scale.
atures can be converted to Kelvins by
FAHRENHEIT SCALE:
The oldest of
the temperature scales still used in Western
adding 273.15. The Kelvin scale is used almost exclusively by scientists. The energy that
nations today, created in 1714 by German
KINETIC ENERGY:
physicist Daniel Fahrenheit (1686-1736).
an object possesses by virtue of its motion.
reaches its maximum density at 39.2°F (4°C), and is less dense both above and below that temperature. Therefore, alcohol, which responds in a much more uniform fashion to changes in temperature, took its place. MERCURY
THERMOMETERS.
Alcohol is still used in thermometers today, but the preferred thermometric medium is mercury. As noted earlier, its advantages include a much higher boiling point, a tendency not to stick to glass, and a silvery color that makes its levels easy to gauge visually. Like alcohol, mercury expands at a uniform rate with an increase in temperature: hence, the higher the temperature, the higher the mercury stands in the thermometer.
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KELVIN
for a calibrated scale, usually in such a way as to allow easy conversions between Fahrenheit and Celsius. A thermometer is calibrated by measuring the difference in height between mercury at the freezing point of water, and mercury at the boiling point of water. The interval between these two points is then divided into equal increments—180, as we have seen, for the Fahrenheit scale, and 100 for the Celsius scale. ELECTRIC
THERMOMETERS.
In a typical mercury thermometer, mercury is placed in a long, narrow sealed tube called a capillary. The capillary is inscribed with figures
Faster temperature measures can be obtained by thermometers using electricity. All matter displays a certain resistance to electrical current, a resistance that changes with temperature. Therefore, a resistance thermometer uses a fine wire wrapped around an insulator, and when a change in temperature occurs, the resistance in the wire changes as well. This makes possible much quick-
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Temperature
KEY TERMS MOLECULAR TRANSLATIONAL EN-
CONTINUED
THERMAL EQUILIBRIUM:
The state
The kinetic energy in a system
that exists when two systems have the same
produced by the movement of molecules
temperature. As a result, there is no
in relation to one another.
exchange of heat between them.
ERGY:
SYSTEM:
In physics, the term “system”
THERMODYNAMICS:
The study of
usually refers to any set of physical interac-
the relationships between heat, work, and
tions, or any material body, isolated from
energy.
the rest of the universe. Anything outside of the system, including all factors and forces irrelevant to a discussion of that system, is known as the environment.
THERMOMETRIC MEDIUM:
A sub-
stance whose properties change with temperature. A mercury or alcohol thermometer measures such changes.
TEMPERATURE:
A measure of the
average kinetic energy—or molecular translational energy in a system. Differences in temperature determine the direction of internal energy flow between two systems when heat is being transferred. THERMAL ENERGY:
Heat energy, a
THERMOMETER:
A device that gauges
temperature by measuring a temperaturedependent property, such as the expansion of a liquid in a sealed tube, or resistance to electric current. TRIPLE POINT:
The temperature and
form of kinetic energy produced by the
pressure at which a substance is at once a
movement of atomic or molecular parti-
solid, liquid, and vapor.
cles. The greater the movement of these
VACUUM:
particles, the greater the thermal energy.
matter, including air.
er temperature readings than those offered by a thermometer containing a traditional thermometric medium. Resistance thermometers are highly reliable, but expensive, and are used primarily for very precise measurements. More practical for everyday use is a thermistor, which also uses the principle of electric resistance, but is much simpler and less expensive. Thermistors are used for providing measurements of the internal temperature of food, for instance, and for measuring human body temperature.
Space entirely devoid of
stant temperature, and a measurement junction. The measurement junction is applied to the item whose temperature is to be measured, and any temperature difference between it and the reference junction registers as a voltage change, which is measured with a meter connected to the system. OTHER TYPES OF THERMOMET E R. A pyrometer also uses electromagnetic
Another electric temperature-measurement device is a thermocouple. When wires of two different materials are connected, this creates a small level of voltage that varies as a function of temperature. A typical thermocouple uses two junctions: a reference junction, kept at some con-
properties, but of a very different kind. Rather than responding to changes in current or voltage, the pyrometer is a gauge that responds to visible and infrared radiation. Temperature and color are closely related: thus, it is no accident that greens, blues, and purples, at one end of the visible light spectrum, are associated with coolness, while reds, oranges, and yellows at the other end are associated with heat. As with the thermocou-
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ple, a pyrometer has both a reference element and a measurement element, which compares light readings between the reference filament and the object whose temperature is being measured. Still other thermometers, such as those in an oven that tell the user its internal temperature, are based on the expansion of metals with heat. In fact, there are a wide variety of thermometers, each suited to a specific purpose. A pyrometer, for instance, is good for measuring the temperature of an object that the thermometer itself does not touch.
WHERE TO LEARN MORE About Temperature (Web site). (April 18, 2001).
244
Gardner, Robert. Science Projects About Methods of Measuring. Berkeley Heights, N.J.: Enslow Publishers, 2000. Maestro, Betsy and Giulio Maestro. Temperature and You. New York: Macmillan/McGraw-Hill School Publishing, 1990. Megaconverter (Web site). (April 18, 2001). NPL: National Physics Laboratory: Thermal Stuff: Beginners’ Guides (Web site). (April 18, 2001). Royston, Angela. Hot and Cold. Chicago: Heinemann Library, 2001. Santrey, Laurence. Heat. Illustrated by Lloyd Birmingham. Mahwah, N.J.: Troll Associates, 1985. Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.
About Temperature Sensors (Web site). (April 18, 2001).
Walpole, Brenda. Temperature. Illustrated by Chris Fairclough and Dennis Tinkler. Milwaukee, WI: Gareth Stevens Publishing, 1995.
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T H E R M A L E X PA N S I O N Thermal Expansion
CONCEPT Most materials are subject to thermal expansion: a tendency to expand when heated, and to contract when cooled. For this reason, bridges are built with metal expansion joints, so that they can expand and contract without causing faults in the overall structure of the bridge. Other machines and structures likewise have built-in protection against the hazards of thermal expansion. But thermal expansion can also be advantageous, making possible the workings of thermometers and thermostats.
HOW IT WORKS Molecular Translational Energy In scientific terms, heat is internal energy that flows from a system of relatively high temperature to one at a relatively low temperature. The internal energy itself, identified as thermal energy, is what people commonly mean when they say “heat.” A form of kinetic energy due to the movement of molecules, thermal energy is sometimes called molecular translational energy. Temperature is defined as a measure of the average molecular translational energy in a system, and the greater the temperature change for most materials, as we shall see, the greater the amount of thermal expansion. Thus, all these aspects of “heat”—heat itself (in the scientific sense), as well as thermal energy, temperature, and thermal expansion—are ultimately affected by the motion of molecules in relation to one another.
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MOLECULAR MOTION AND N E W T O N I A N P H Y S I CS . In general, the
kinetic energy created by molecular motion can be understood within the framework of classical physics—that is, the paradigm associated with Sir Isaac Newton (1642-1727) and his laws of motion. Newton was the first to understand the physical force known as gravity, and he explained the behavior of objects within the context of gravitational force. Among the concepts essential to an understanding of Newtonian physics are the mass of an object, its rate of motion (whether in terms of velocity or acceleration), and the distance between objects. These, in turn, are all components central to an understanding of how molecules in relative motion generate thermal energy. The greater the momentum of an object— that is, the product of its mass multiplied by its rate of velocity—the greater the impact it has on another object with which it collides. The greater, also, is its kinetic energy, which is equal to one-half its mass multiplied by the square of its velocity. The mass of a molecule, of course, is very small, yet if all the molecules within an object are in relative motion—many of them colliding and, thus, transferring kinetic energy— this is bound to lead to a relatively large amount of thermal energy on the part of the larger object. M O L E C U LA R AT T RAC T I O N A N D P H AS E S O F M AT T E R. Yet, precisely
because molecular mass is so small, gravitational force alone cannot explain the attraction between molecules. That attraction instead must be understood in terms of a second type of force—electromagnetism—discovered by Scottish physicist James Clerk Maxwell (1831-1879). The details of electromagnetic force are not
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Thermal Expansion
BECAUSE
STEEL HAS A RELATIVELY HIGH COEFFICIENT OF THERMAL EXPANSION, STANDARD RAILROAD TRACKS ARE
CONSTRUCTED SO THAT THEY CAN SAFELY EXPAND ON A HOT DAY WITHOUT DERAILING THE TRAINS TRAVELING OVER THEM. (Milepost 92 1/2/Corbis. Reproduced by permission.)
important here; it is necessary only to know that all molecules possess some component of electrical charge. Since like charges repel and opposite charges attract, there is constant electromagnetic interaction between molecules, and this produces differing degrees of attraction. The greater the relative motion between molecules, generally speaking, the less their attraction toward one another. Indeed, these two aspects of a material—relative attraction and motion at the molecular level—determine whether that material can be classified as a solid, liquid, or gas. When molecules move slowly in relation to one another, they exert a strong attraction, and the material of which they are a
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part is usually classified as a solid. Molecules of liquid, on the other hand, move at moderate speeds, and therefore exert a moderate attraction. When molecules move at high speeds, they exert little or no attraction, and the material is known as a gas.
Predicting Thermal Expansion COEFFICIENT OF LINEAR EXPA N S I O N . A coefficient is a number that
serves as a measure for some characteristic or property. It may also be a factor against which other values are multiplied to provide a desired result. For any type of material, it is possible to
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Thermal Expansion
A
MAN ICE FISHING IN
MONTANA. BECAUSE
OF THE UNIQUE THERMAL EXPANSION PROPERTIES OF WATER, ICE FORMS
AT THE TOP OF A LAKE RATHER THAN THE BOTTOM, THUS ALLOWING MARINE LIFE TO CONTINUE LIVING BELOW ITS SURFACE DURING THE WINTER. (Corbis. Reproduced by permission.)
calculate the degree to which that material will expand or contract when exposed to changes in temperature. This is known, in general terms, as its coefficient of expansion, though, in fact, there are two varieties of expansion coefficient. The coefficient of linear expansion is a constant that governs the degree to which the length of a solid will change as a result of an alteration in temperature For any given substance, the coefficient of linear expansion is typically a number expressed in terms of 10-5/°C. In other words, the value of a particular solid’s linear expansion coefficient is multiplied by 0.00001 per °C. (The °C in the denominator, shown in the equation below, simply “drops out” when the coefficient of
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linear expansion is multiplied by the change in temperature.) For quartz, the coefficient of linear expansion is 0.05. By contrast, iron, with a coefficient of 1.2, is 24 times more likely to expand or contract as a result of changes in temperature. (Steel has the same value as iron.) The coefficient for aluminum is 2.4, twice that of iron or steel. This means that an equal temperature change will produce twice as much change in the length of a bar of aluminum as for a bar of iron. Lead is among the most expansive solid materials, with a coefficient equal to 3.0. C A L C U L AT I N G LINEAR EXPA N S I O N . The linear expansion of a given
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solid can be calculated according to the formula δL = aLO∆T. The Greek letter delta (d) means “a change in”; hence, the first figure represents change in length, while the last figure in the equation stands for change in temperature. The letter a is the coefficient of linear expansion, and LO is the original length. Suppose a bar of lead 5 meters long experiences a temperature change of 10°C; what will its change in length be? To answer this, a (3.0 • 10-5/°C) must be multiplied by LO (5 m) and δT (10°C). The answer should be 150 & 10-5 m, or 1.5 mm. Note that this is simply a change in length related to a change in temperature: if the temperature is raised, the length will increase, and if the temperature is lowered by 10°C, the length will decrease by 1.5 mm. V O LU M E E X PA N S I O N . Obviously,
linear equations can only be applied to solids. Liquids and gases, classified together as fluids, conform to the shape of their container; hence, the “length” of any given fluid sample is the same as that of the solid that contains it. Fluids are, however, subject to volume expansion—that is, a change in volume as a result of a change in temperature. To calculate change in volume, the formula is very much the same as for change in length; only a few particulars are different. In the formula δV = bVOδT, the last term, again, means change in temperature, while δV means change in volume and VO is the original volume. The letter b refers to the coefficient of volume expansion. The latter is expressed in terms of 10-4/°C, or 0.0001 per °C. Glass has a very low coefficient of volume expansion, 0.2, and that of Pyrex glass is extremely low—only 0.09. For this reason, items made of Pyrex are ideally suited for cooking. Significantly higher is the coefficient of volume expansion for glycerin, an oily substance associated with soap, which expands proportionally to a factor of 5.1. Even higher is ethyl alcohol, with a volume expansion coefficient of 7.5.
REAL-LIFE A P P L I C AT I O N S
The behavior of gasoline pumped on a hot day provides an example of liquid thermal expansion in response to an increase in temperature. When it comes from its underground tank at the gas station, the gasoline is relatively cool, but it will warm when sitting in the tank of an already warm car. If the car’s tank is filled and the vehicle left to sit in the sun—in other words, if the car is not driven after the tank is filled—the gasoline might very well expand in volume faster than the fuel tank, overflowing onto the pavement. E N G I N E C O O LA N T. Another example of thermal expansion on the part of a liquid can be found inside the car’s radiator. If the radiator is “topped off ” with coolant on a cold day, an increase in temperature could very well cause the coolant to expand until it overflows. In the past, this produced a problem for car owners, because car engines released the excess volume of coolant onto the ground, requiring periodic replacement of the fluid.
Later-model cars, however, have an overflow container to collect fluid released as a result of volume expansion. As the engine cools down again, the container returns the excess fluid to the radiator, thus, “recycling” it. This means that newer cars are much less prone to overheating as older cars. Combined with improvements in radiator fluid mixtures, which act as antifreeze in cold weather and coolant in hot, the “recycling” process has led to a significant decrease in breakdowns related to thermal expansion. WAT E R. One good reason not to use pure water in one’s radiator is that water has a far higher coefficient of volume expansion than a typical engine coolant. This can be particularly hazardous in cold weather, because frozen water in a radiator could expand enough to crack the engine block.
Most liquids follow a fairly predictable pattern of gradual volume increase, as a response to an
In general, water—whose volume expansion coefficient in the liquid state is 2.1, and 0.5 in the solid state—exhibits a number of interesting characteristics where thermal expansion is concerned. If water is reduced from its boiling point—212°F (100°C) to 39.2°F (4°C) it will
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increase in temperature, and volume decrease, in response to a decrease in temperature. Indeed, the coefficient of volume expansion for a liquid generally tends to be higher than for a solid, and—with one notable exception discussed below— a liquid will contract when frozen.
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steadily contract, like any other substance responding to a drop in temperature. Normally, however, a substance continues to become denser as it turns from liquid to solid; but this does not occur with water. At 32.9°F, water reaches it maximum density, meaning that its volume, for a given unit of mass, is at a minimum. Below that temperature, it “should” (if it were like most types of matter) continue to decrease in volume per unit of mass, but, in fact, it steadily begins to expand. Thus, it is less dense, with a greater volume per unit of mass, when it reaches the freezing point. It is for this reason that when pipes freeze in winter, they often burst—explaining why a radiator filled with water could be a serious problem in very cold weather. In addition, this unusual behavior with regard to thermal expansion and contraction explains why ice floats: solid water is less dense than the liquid water below it. As a result, frozen water stays at the top of a lake in winter; since ice is a poor conductor of heat, energy cannot escape from the water below it in sufficient amounts to freeze the rest of the lake water. Thus, the water below the ice stays liquid, preserving plant and animal life.
Gases T H E GAS LAW S . As discussed, liq-
uids expand by larger factors than solids do. Given the increasing amount of molecular kinetic energy for a liquid as compared to a solid, and for a gas as compared to a liquid, it should not be surprising, then, to learn that gases respond to changes in temperature with a volume change even greater than that of liquids. Of course, where a gas is concerned, “volume” is more difficult to measure, because a gas simply expands to fill its container. In order for the term to have any meaning, pressure and temperature must be specified as well. A number of the gas laws describe the three parameters for gases: volume, temperature, and pressure. Boyle’s law, for example, holds that in conditions of constant temperature, an inverse relationship exists between the volume and pressure of a gas: the greater the pressure, the less the volume, and vice versa. Even more relevant to the subject of thermal expansion is Charles’s law.
between volume and temperature. As a gas heats up, its volume increases, and when it cools down, its volume reduces accordingly. Thus, if an air mattress is filled in an air-conditioned room, and the mattress is then taken to the beach on a hot day, the air inside will expand. Depending on how much its volume increases, the expansion of the hot air could cause the mattress to “pop.”
Thermal Expansion
VOLUME GAS THERMOMET E R S . Whereas liquids and solids vary signif-
icantly with regard to their expansion coefficients, most gases follow more or less the same pattern of expansion in response to increases in temperature. The predictable behavior of gases in these situations led to the development of the constant gas thermometer, a highly reliable instrument against which other thermometers— including those containing mercury (see below)—are often gauged. In a volume gas thermometer, an empty container is attached to a glass tube containing mercury. As gas is released into the empty container, this causes the column of mercury to move upward. The difference between the former position of the mercury and its position after the introduction of the gas shows the difference between normal atmospheric pressure and the pressure of the gas in the container. It is, then, possible to use the changes in volume on the part of the gas as a measure of temperature. The response of most gases, under conditions of low pressure, to changes in temperature is so uniform that volume gas thermometers are often used to calibrate other types of thermometers.
Solids Many solids are made up of crystals, regular shapes composed of molecules joined to one another as though on springs. A spring that is pulled back, just before it is released, is an example of potential energy, or the energy that an object possesses by virtue of its position. For a crystalline solid at room temperature, potential energy and spacing between molecules are relatively low. But as temperature increases and the solid expands, the space between molecules increases—as does the potential energy in the solid.
Charles’s law states that when pressure is kept constant, there is a direct relationship
In fact, the responses of solids to changes in temperature tend to be more dramatic, at least when they are seen in daily life, than are the behaviors of liquids or gases under conditions of
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thermal expansion. Of course, solids actually respond less to changes in temperature than fluids do; but since they are solids, people expect their contours to be immovable. Thus, when the volume of a solid changes as a result of an increase in thermal energy, the outcome is more noteworthy. JA R L I D S A N D P O W E R L I N E S .
An everyday example of thermal expansion can be seen in the kitchen. Almost everyone has had the experience of trying unsuccessfully to budge a tight metal lid on a glass container, and after running hot water over the lid, finding that it gives way and opens at last. The reason for this is that the high-temperature water causes the metal lid to expand. On the other hand, glass—as noted earlier—has a low coefficient of expansion. Otherwise, it would expand with the lid, which would defeat the purpose of running hot water over it. If glass jars had a high coefficient of expansion, they would deform when exposed to relatively low levels of heat. Another example of thermal expansion in a solid is the sagging of electrical power lines on a hot day. This happens because heat causes them to expand, and, thus, there is a greater length of power line extending from pole to pole than under lower temperature conditions. It is highly unlikely, of course, that the heat of summer could be so great as to pose a danger of power lines breaking; on the other hand, heat can create a serious threat with regard to larger structures. E X PA N S I O N J O I N T S . Most large bridges include expansion joints, which look rather like two metal combs facing one another, their teeth interlocking. When heat causes the bridge to expand during the sunlight hours of a hot day, the two sides of the expansion joint move toward one another; then, as the bridge cools down after dark, they begin gradually to retract. Thus the bridge has a built-in safety zone; otherwise, it would have no room for expansion or contraction in response to temperature changes. As for the use of the comb shape, this staggers the gap between the two sides of the expansion joint, thus minimizing the bump motorists experience as they drive over it.
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of steel. Steel, as noted earlier, expands by a factor of 12 parts in 1 million for every Celsius degree change in temperature, and while this may not seem like much, it can create a serious problem under conditions of high temperature. Most tracks are built from pieces of steel supported by wooden ties, and laid with a gap between the ends. This gap provides a buffer for thermal expansion, but there is another matter to consider: the tracks are bolted to the wooden ties, and if the steel expands too much, it could pull out these bolts. Hence, instead of being placed in a hole the same size as the bolt, the bolts are fitted in slots, so that there is room for the track to slide in place slowly when the temperature rises. Such an arrangement works agreeably for trains that run at ordinary speeds: their wheels merely make a noise as they pass over the gaps, which are rarely wider than 0.5 in (0.013 m). A high-speed train, however, cannot travel over irregular track; therefore, tracks for high-speed trains are laid under conditions of relatively high tension. Hydraulic equipment is used to pull sections of the track taut; then, once the track is secured in place along the cross ties, the tension is distributed down the length of the track.
Thermometers and Thermostats MERCURY IN THERMOMETERS.
A thermometer gauges temperature by measuring a temperature-dependent property. A thermostat, by contrast, is a device for adjusting the temperature of a heating or cooling system. Both use the principle of thermal expansion in their operation. As noted in the example of the metal lid and glass jar above, glass expands little with changes in temperature; therefore, it makes an ideal container for the mercury in a thermometer. As for mercury, it is an ideal thermometric medium—that is, a material used to gauge temperature—for several reasons. Among these is a high boiling point, and a highly predictable, uniform response to changes in temperature.
Expansion joints of a different design can also be found in highways, and on “highways” of rail. Thermal expansion is a particularly serious problem where railroad tracks are concerned, since the tracks on which the trains run are made
In a typical mercury thermometer, mercury is placed in a long, narrow sealed tube called a capillary. Because it expands at a much faster rate than the glass capillary, mercury rises and falls with the temperature. A thermometer is calibrated by measuring the difference in height between mercury at the freezing point of water, and mercury at the boiling point of water. The interval
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Thermal Expansion
KEY TERMS COEFFICIENT:
A number that serves
as a measure for some characteristic or property. A coefficient may also be a factor
produced by the movement of molecules in relation to one another. The energy
POTENTIAL ENERGY:
against which other values are multiplied
that an object possesses by virtue of its
to provide a desired result.
position.
COEFFICIENT OF LINEAR EXPAN-
SYSTEM:
In physics, the term “system”
A figure, constant for any partic-
usually refers to any set of physical interac-
ular type of solid, used in calculating the
tions, or any material body, isolated from
amount by which the length of that solid
the rest of the universe. Anything outside
will change as a result of temperature
of the system, including all factors and
change. For any given substance, the coeffi-
forces irrelevant to a discussion of that sys-
cient of linear expansion is typically a
tem, is known as the environment.
SION:
number expressed in terms of 10-5/°C. TEMPERATURE: COEFFICIENT OF VOLUME EXPAN-
A measure of the
average kinetic energy—or molecular
A figure, constant for any partic-
translational energy in a system. Differ-
ular type of material, used in calculating
ences in temperature determine the direc-
the amount by which the volume of that
tion of internal energy flow between two
material will change as a result of tempera-
systems when heat is being transferred.
SION:
ture change. For any given substance, the coefficient of volume expansion is typically a number expressed in terms of 10-4/°C. HEAT:
Internal thermal energy that
flows from one body of matter to another. KINETIC ENERGY:
The energy that
an object possesses by virtue of its motion. MOLECULAR TRANSLATIONAL ENERGY:
The kinetic energy in a system
between these two points is then divided into equal increments in accordance with one of the well-known temperature scales.
THERMAL ENERGY:
Heat energy, a
form of kinetic energy produced by the movement of atomic or molecular particles. The greater the movement of these particles, the greater the thermal energy. THERMAL EXPANSION:
A property
in all types of matter that display a tendency to expand when heated, and to contract when cooled.
that is less responsive to temperature changes. As a result, the bimetallic strip will bend to one side.
tral component is a bimetallic strip, consisting of thin strips of two different metals placed back to back. One of these metals is of a kind that possesses a high coefficient of linear expansion, while the other metal has a low coefficient. A temperature increase will cause the side with a higher coefficient to expand more than the side
When the strip bends far enough, it will close an electrical circuit, and, thus, direct the air conditioner to go into action. By adjusting the thermostat, one varies the distance that the bimetallic strip must be bent in order to close the circuit. Once the air in the room reaches the desired temperature, the high-coefficient metal will begin to contract, and the bimetallic strip will straighten. This will cause an opening of the electrical circuit, disengaging the air conditioner.
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T H E B I M E TA L L I C S T R I P I N T H E R M O S TAT S . In a thermostat, the cen-
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In cold weather, when the temperature-control system is geared toward heating rather than cooling, the bimetallic strip acts in much the same way—only this time, the high-coefficient metal contracts with cold, engaging the heater. Another type of thermostat uses the expansion of a vapor rather than a solid. In this case, heating of the vapor causes it to expand, pushing on a set of brass bellows and closing the circuit, thus, engaging the air conditioner.
Fleisher, Paul. Matter and Energy: Principles of Matter and Thermodynamics. Minneapolis, MN: Lerner Publications, 2002.
WHERE TO LEARN MORE
“Thermal Expansion Measurement” (Web site). (April 21, 2001).
Beiser, Arthur. Physics, 5th ed. Reading, MA: AddisonWesley, 1991.
252
NPL: National Physics Laboratory: Thermal Stuff: Beginners’ Guides (Web site). (April 18, 2001). Royston, Angela. Hot and Cold. Chicago: Heinemann Library, 2001. Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.
“Comparison of Materials: Coefficient of Thermal Expansion” (Web site). (April 21, 2001).
“Thermal Expansion of Solids and Liquids” (Web site). (April 21, 2001).
Encyclopedia of Thermodynamics (Web site). (April 12, 2001).
Walpole, Brenda. Temperature. Illustrated by Chris Fairclough and Dennis Tinkler. Milwaukee, WI: Gareth Stevens Publishing, 1995.
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S C I E N C E O F E V E RY DAY T H I N G S real-life Physics
W AV E M O T I O N A N D O S C I L L AT I O N WAVE MOTION O S C I L L AT I O N FREQUENCY RESONANCE INTERFERENCE DIFFRACTION DOPPLER EFFECT
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Wave Motion
W AV E M O T I O N
CONCEPT Wave motion is activity that carries energy from one place to another without actually moving any matter. Studies of wave motion are most commonly associated with sound or radio transmissions, and, indeed, these are among the most common forms of wave activity experienced in daily life. Then, of course, there are waves on the ocean or the waves produced by an object falling into a pool of still water—two very visual examples of a phenomenon that takes place everywhere in the world around us.
HOW IT WORKS Related Forms of Motion In wave motion, energy—the ability to perform work, or to exert force over distance—is transmitted from one place to another without actually moving any matter along the wave. In some types of waves, such as those on the ocean, it might seem as though matter itself has been displaced; that is, it appears that the water has actually moved from its original position. In fact, this is not the case: molecules of water in an ocean wave move up and down, but they do not actually travel with the wave itself. Only the energy is moved.
time that it takes an object orbiting another (as, for instance, a satellite going around Earth) to complete one cycle of orbit. With wave motion, a period is the amount of time required to complete one full cycle of the wave, from trough to crest and back to trough. H A R M O N I C M O T I O N . Harmonic motion is the repeated movement of a particle about a position of equilibrium, or balance. In harmonic motion—or, more specifically, simple harmonic motion—the object moves back and forth under the influence of a force directed toward the position of equilibrium, or the place where the object stops if it ceases to be in motion. A familiar example of harmonic motion, to anyone who has seen an old movie with a clichéd depiction of a hypnotist, is the back-and-forth movement of the hypnotist’s watch, as he tries to control the mind of his patient.
One variety of harmonic motion is vibration, which wave motion resembles in some respects. Both wave motion and vibration are periodic, involving the regular repetition of a certain form of movement. In both, there is a continual conversion and reconversion between potential energy (the energy of an object due to its position, as for instance with a sled at the top of a hill) and kinetic energy (the energy of an object due to its motion, as with the sled when sliding down the hill.) The principal difference between vibration and wave motion is that, in the first instance, the energy remains in place, whereas waves actually transport energy from one place to another.
A wave is an example of a larger class of regular, repeated, and/or back-and-forth types of motion. As with wave motion, these varieties of movement may or may not involve matter, but, in any case, the key component is not matter, but energy. Broadest among these is periodic motion, or motion that is repeated at regular intervals called periods. A period might be the amount of
O S C I L LAT I O N . Oscillation is a type of harmonic motion, typically periodic, in one or more dimensions. Suppose a spring is fixed in
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first spring is once again disturbed: the energy will pass through the rubber bands, from spring to spring, causing the entire row to oscillate. This is similar to what happens in the motion of a wave.
Wave Motion
Types and Properties of Waves There are some types of waves that do not follow regular, repeated patterns; these are discussed below, in the illustration concerning a string, in which a pulse is created and reflected. Of principal concern here, however, is the periodic wave, a series of wave motions, following one after the other in regular succession. Examples of periodic waves include waves on the ocean, sound waves, and electromagnetic waves. The last of these include visible light and radio, among others.
HEINRICH HERTZ. (Hulton-Deutsch Collection/Corbis. Reproduced by permission.)
place to a ceiling, such that it hangs downward. At this point, the spring is in a position of equilibrium. Now, consider what happens if the spring is grasped at a certain point and lifted, then let go. It will, of course, fall downward with the force of gravity until it comes to a stop—but it will not stop at the earlier position of equilibrium. Instead, it will continue downward to a point of maximum tension, where it possesses maximum potential energy as well. Then, it will spring upward again, and as it moves, its kinetic energy increases, while potential energy decreases. At the high point of this period of oscillation, the spring will not be as high as it was before it was originally released, but it will be higher than the position of equilibrium. Once it falls, the spring will again go lower than the position of equilibrium, but not as low as before—and so on. This is an example of oscillation. Now, imagine what happens if another spring is placed beside the first one, and they are connected by a rubber band. If just the first spring is disturbed, as before, the second spring will still move, because the energy created by the movement of the first spring will be transmitted to the second one via the rubber band. The same will happen if a row of springs, all side-by-side, are attached by multiple rubber bands, and the
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Electromagnetic waves involve only energy; on the other hand, a mechanical wave involves matter as well. Ocean waves are mechanical waves; so, too, are sound waves, as well as the waves produced by pulling a string. It is important to note, again, that the matter itself is not moved from place to place, though it may move in place without leaving its position. For example, water molecules in the crest of an ocean wave rotate in the same direction as the wave, while those in the trough of the wave rotate in a direction opposite to that of the wave, yet there is no net motion of the water: only energy is transmitted along the wave. F I V E P R O P E RT I E S O F WAV E S .
There are three notable interrelated characteristics of periodic waves. One of these is wave speed, symbolized by v and typically calculated in meters per second. Another is wavelength, represented as λ (the Greek letter lambda), which is the distance between a crest and the adjacent crest, or a trough and the adjacent trough. The third is frequency, abbreviated as f, which is the number of waves passing through a given point during the interval of 1 second. Frequency is measured in terms of cycles per second, or Hertz (Hz), named in honor of nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894). If a wave has a frequency of 100 Hz, this means that 100 waves are passing through a given point during the interval of 1 second. Higher frequencies are expressed in terms of kilohertz (kHz; 103 or 1,000 cycles per
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Wave Motion
TRANSVERSE
WAVES PRODUCED BY A WATER DROPLET PENETRATING THE SURFACE OF A BODY OF LIQUID. (Photograph
by Martin Dohrn/Science Photo Library, National Audubon Society Collection/Photo Researchers, Inc. Reproduced with permission.)
second) or megahertz (MHz; 106 or 1 million cycles per second.) Frequency is clearly related to wave speed, and there is also a relationship—though it is not so immediately grasped—between wavelength and speed. Over the interval of 1 second, a given number of waves pass a certain point (frequency), and each wave occupies a certain distance (wavelength). Multiplied by one another, these two properties equal the speed of the wave. This can be stated as a formula: v = fλ. Earlier, the term “period” was defined in terms of wave motion as the amount of time required to complete one full cycle of the wave. Period, symbolized by T, can be expressed in terms of frequency, and, thus, can also be related to the other two properties identified above. It is the inverse of frequency, meaning that T = 1/f. Furthermore, period is equal to the ratio of wavelength to wave speed; in other words, T = λ/v. A fifth property of waves—one not mathematically related to wavelength, wave speed, frequency, or period, is amplitude. Amplitude can be defined as the maximum displacement of oscillating particles from their normal position. For an ocean wave, amplitude is the distance
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from either the crest or the trough to the level that the ocean would maintain if it were perfectly still. WAV E S H A P E S . When most people think of waves, naturally, one of the first images that comes to mind is that of waves on the ocean. These are an example of a transverse wave, or one in which the vibration or motion is perpendicular to the direction the wave is moving. (Actually, ocean waves are simply perceived as transverse waves; in fact, as discussed below, their behavior is rather more complicated.) In a longitudinal wave, on the other hand, the movement of vibration is in the same direction as the wave itself.
Transverse waves are easier to visualize, particularly with regard to the aspects of wave motion—for example, frequency and amplitude—discussed above. Yet, longitudinal waves can be understood in terms of a common example. Sound waves, for instance, are longitudinal: thus, when a stereo is turned up to a high volume, the speakers vibrate in the same direction as the sound itself. A longitudinal wave may be understood as a series of fluctuations in density. If one were to take a coiled spring (such as the toy known as the “Slinky”) and release one end while holding the
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other, the motion of the springs would produce longitudinal waves. As these waves pass through the spring, they cause some portions of it to be compressed and others extended. The distance between each point of compression is the wavelength. Now, to return to the qualified statement made above: that ocean waves are an example of transverse waves. We perceive them as transverse waves, but, in fact, they are also longitudinal. In fact, all types of waves on the surface of a liquid are a combination of longitudinal and transverse, and are known as surface waves. Thus, if one drops a stone into a body of still water, waves radiate outward (longitudinal), but these waves also have a component that is perpendicular to the surface of the water, meaning that they are also transverse.
REAL-LIFE A P P L I C AT I O N S Pulses on a String There is another variety of wave, though it is defined in terms of behavior rather than the direction of disturbance. (In terms of direction, it is simply a variety of transverse wave.) This is a standing wave, produced by causing vibrations on a string or other piece of material whose ends are fixed in place. Standing waves are really a series of pulses that travel down the string and are reflected back to the point of the original disturbance. Suppose you hold a string in one hand, with the other end attached to a wall. If you give the string a shake, this causes a pulse—an isolated, non-periodic disturbance—to move down it. A pulse is a single wave, and the behavior of this lone wave helps us to understand what happens within the larger framework of wave motion. As with wave motion in general, the movement of the pulse involves both kinetic and potential energy. The tension of the string itself creates potential energy; then, as the movement of the pulse causes the string to oscillate upward and downward, this generates a certain amount of kinetic energy.
In accordance with the third law of motion, there should be an equal and opposite reaction once the pulse comes into contact with the wall. Assuming that you are holding the string tightly, this reaction will be manifested in the form of an inverted wave, or one that is upside-down in relation to the original pulse. In this case, the tension on the end attached to the support is equal and opposite to the tension exerted by your hand. As a result, the pulse comes back in the same shape as before, but inverted. If, on the other hand, you hold the other end of the string loosely; instead, once it reaches the wall, its kinetic energy will be converted into potential energy, which will cause the end of the string closest to the wall to move downward. This will result in sending back a pulse that is reversed in horizontal direction, but the same in vertical direction. In both cases, the energy in the string is reflected backward to its source—that is, to the place from which the pulse was originally produced by the action of your hand. If, however, you hold the string so that its level of tension is exactly between perfect rigidity and perfect looseness, then the pulse will not be reflected. In other words, there will be no reflected wave. T RA N S M I SS I O N A N D R E F L E C T I O N . If two strings are joined end-to-end,
and a pulse is produced at one end, the pulse would, of course, be transmitted to the second string. If, however, the second string has a greater mass per unit of length than the first one, the result would be two pulses: a transmitted pulse moving in the “right” direction, and a reflected, inverted pulse, moving toward the original source of energy. If, on the other hand, the first string has a greater mass per unit of length than the second one, the reflected pulse would be erect (right side up), not inverted.
The speed of the pulse is a function of the string and its properties, not of the way that the pulse
For simplicity’s sake, this illustration has been presented in terms of a string attached to a wall, but, in fact, transmission and reflection occur in a number of varieties of wave motion—
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was originally delivered. The tighter the string, and the less its mass per unit of length, the faster the pulse travels down it. The greater the mass per unit of length, however, the greater the inertia resisting the movement of the pulse. Furthermore, the more loosely you hold the string, the less it will respond to the movement of the pulse.
AND
REFLECTION.
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not just those involving pulses or standing waves. A striking example occurs when light hits an ordinary window. The majority of the light, of course, is transmitted through the window pane, but a portion is reflected. Thus, as one looks through the window, one also sees one’s reflection. Similarly, sound waves are reflected depending on the medium with which they are in contact. A canyon wall, for instance, will reflect a great deal of sound, and, thus, it is easy to produce an echo in such a situation. On the other hand, there are many instances in which the desire is to “absorb” sound by transmitting it to some other form of material. Thus, for example, the lobby of an upscale hotel will include a number of plants, as well as tapestries and various wall hangings. In addition to adding beauty, these provide a medium into which the sound of voices and other noises can be transmitted and, thus, absorbed.
Sound Waves P R O D U C T I O N . The experience of sound involves production, or the generation of sound waves; transmission, or the movement of those waves from their source; and reception, the principal example of which is hearing. Sound itself is discussed in detail elsewhere. Of primary concern here is the transmission, and to a lesser extent, the production of sound waves.
In terms of production, sound waves are, as noted, longitudinal waves: changes in pressure, or alternations between condensation and rarefaction. Vibration is integral to the generation of sound. When the diaphragm of a loudspeaker pushes outward, it forces nearby air molecules closer together, creating a high-pressure region all around the loudspeaker. The loudspeaker’s diaphragm is pushed backward in response, thus freeing up a volume of space for the air molecules. These, then, rush toward the diaphragm, creating a low-pressure region behind the highpressure one. As a result, the loudspeaker sends out alternating waves of high pressure (condensation) and low pressure (rarefaction).
the sound wave, a vibration that the ear’s inner mechanisms translate and pass on to the brain. The range of audibility for the human ear is from 20 Hz to 20 kHz. The lowest note of the eightyeight keys on a piano is 27 Hz and the highest 4.186 kHz. This places the middle and upper register of the piano well within the optimal range for audibility, which is between 3 and 4 kHz. Sound travels at a speed of about 1,088 ft (331 m) per second through air at sea level, and the range of sound audible to human ears includes wavelengths as large as 11 ft (3.3 m) and as small as 1.3 in (3.3 cm). Unlike light waves, which are very small, the wavelengths of audible sound are comparable to the sizes of ordinary objects. This creates an interesting contrast between the behaviors of sound and light when confronted with an obstacle to their transmission. It is fairly easy to block out light by simply holding up a hand in front of one’s eyes. When this happens, the Sun casts a shadow on the other side of one’s hand. The same action does not work with one’s ears and the source of a sound, however, because the wavelengths of sound are large enough to go right past a relatively small object such as a hand. However, if one were to put up a tall, wide cement wall between oneself and the source of a sound—as is often done in areas where an interstate highway passes right by a residential community—the object would be sufficiently large to block out much of the sound.
Radio Waves Radio waves, like visible light waves, are part of the electromagnetic spectrum. They are characterized by relatively long wavelengths and low frequencies—low, that is, in contrast to the much higher frequencies of both visible and invisible light waves. The frequency range of radio is between 10 KHz and about 2,000 MHz—in other words, from 10,000 Hz to as much as 2 billion Hz—an impressively wide range.
medium such as air, they create fluctuations between condensation and rarefaction. These result in pressure changes that cause the listener’s eardrum to vibrate with the same frequency as
AM radio broadcasts are found between 0.6 and 1.6 MHz, and FM broadcasts between 88 and 108 MHz. Thus, FM is at a much, much higher frequency than AM, with the lowest frequency on the FM dial 55 times as great as the highest on the AM dial. There are other ranges of frequency assigned by the FCC (Federal Communications Commission) to other varieties of radio trans-
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FREQUENCY AND WAV E L E N GT H . As sound waves pass through a
Wave Motion
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Wave Motion
KEY TERMS The maximum displace-
means that 20,000 waves are passing
ment of particles in oscillation from their
through a given point during the interval
normal position. For an ocean wave,
of one second. Higher frequencies are
amplitude is the distance from either the
expressed in terms of kilohertz (kHz; 103
crest or the trough to the level that the
or 1,000 cycles per second) or megahertz
ocean would maintain if it were per-
(MHz; 106 or 1 million cycles per second).
AMPLITUDE:
fectly still. KINETIC ENERGY:
The energy that
The ability to perform work,
an object possesses due to its motion, as
which is the exertion of force over a given
with a sled when sliding down a hill. This is
distance. Work is the product of force and
contrasted with potential energy.
ENERGY:
distance, where force and distance are exerted in the same direction. FREQUENCY:
The number of waves
passing through a given point during the interval of one second. The higher the fre-
A wave in
which the movement of vibration is in the same direction as the wave itself. This is contrasted to a transverse wave. Physical substance that has
quency, the shorter the wavelength. Fre-
MATTER:
quency can also be mathematically related
mass; occupies space; is composed of
to wave speed and period.
atoms; and is ultimately convertible to
HARMONIC MOTION:
The repeated
energy.
movement of a particle about a position of
MECHANICAL WAVE:
equilibrium, or balance.
that involves matter. Ocean waves are
A type of wave
A unit for measuring frequen-
mechanical waves; so, too, are the waves
cy, equal to one cycle per second. If a sound
produced by pulling a string. The matter
wave has a frequency of 20,000 Hz, this
itself may move in place, but, as with all
HERTZ:
mission: for instance, citizens’ band (CB) radios are in a region between AM and FM, ranging from 26.985 MHz to 27.405 MHz. Frequency does not indicate power. The power of a radio station is a function of the wattage available to its transmitter: hence, radio stations often promote themselves with announcements such as “operating with 100,000 watts of power....” Thus, an AM station, though it has a much lower frequency than an FM station, may possess more power, depending on the wattage of the transmitter. Indeed, as we shall see, it is precisely because of its high frequency that an FM station lacks the broadcast range of an AM station.
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A M P L I T U D E A N D F R E Q U E N CY M O D U LAT I O N S . What is the difference
between AM and FM? Or to put it another way, why is it that an AM station may be heard halfway across the country, yet its sound on a car radio fades out when the car goes under an overpass? The difference relates to how the various radio signals are modulated. A radio signal is simply a carrier: it may carry Morse code, or it may carry complex sounds, but in order to transmit voices and music, its signal must be modulated. This can be done, for instance, by varying the instantaneous amplitude of the radio wave, which is a function of the radio station’s power. These variations in amplitude are called amplitude modulation, or
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Wave Motion
KEY TERMS
CONTINUED
types of wave motion, there is no net
PULSE:
movement of matter—only of energy.
turbance that takes place in wave motion of
OSCILLATION:
A type of harmonic
motion, typically periodic, in one or more
a type other than that of a periodic wave. A type of trans-
STANDING WAVE:
verse wave produced by causing vibrations
dimensions. PERIOD:
An isolated, non-periodic dis-
For wave motion, a period is
the amount of time required to complete
on a string or other piece of material whose ends are fixed in place. A wave that exhibits
one full cycle of the wave, from trough to
SURFACE WAVE:
crest and back to trough. Period can be
the behavior of both a transverse wave and
mathematically related to frequency, wave-
a longitudinal wave.
length, and wave speed.
TRANSVERSE
PERIODIC MOTION:
Motion that is
which the vibration or motion is perpendi-
repeated at regular intervals. These inter-
cular to the direction in which the wave is
vals are known as periods.
moving. This is contrasted to a longitudi-
PERIODIC WAVE:
A wave in which a
WAVE:
A wave in
nal wave. The distance between
uniform series of crests and troughs follow
WAVELENGTH:
one after the other in regular succession.
a crest and the adjacent crest, or the trough
By contrast, the wave produced by apply-
and an adjacent trough, of a wave. Wave-
ing a pulse to a stretched string does not
length, abbreviated λ (the Greek letter
follow regular, repeated patterns.
lambda) is mathematically related to wave
POTENTIAL ENERGY:
The energy
speed, period, and frequency. Activity that carries
that an object possesses due to its position,
WAVE MOTION:
as for instance with a sled at the top of a
energy from one place to another without
hill. This is contrasted with kinetic energy.
actually moving any matter.
AM, and this was the first type of commercial radio to appear. Developed in the period before World War I, AM made its debut as a popular phenomenon shortly after the war. Ironically, FM (frequency modulation) was developed not long after AM, but it did not become commercially viable until well after World War II. As its name suggests, frequency modulation involves variation in the signal’s frequency. The amplitude stays the same, and this— combined with the high frequency—produces a nice, even sound for FM radio. But the high frequency also means that FM signals do not travel as far. If a person is listening to an FM station while moving away from the
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station’s signal, eventually the station will be below the horizon relative to the car, and the car radio will no longer be able to receive the signal. In contrast to the direct, or line-of-sight, transmissions of FM stations, AM signals (with their longer wavelengths) are reflected off of layers in Earth’s ionosphere. As a result, a nighttime signal from a “clear channel station” may be heard across much of the continental United States. WHERE TO LEARN MORE Ardley, Neil. Sound Waves to Music. New York: Gloucester Press, 1990. Berger, Melvin and Gilda Berger. What Makes an Ocean Wave?: Questions and Answers About Oceans and Ocean Life. New York: Scholastic, 2001.
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Catherall, Ed. Exploring Sound. Austin, TX: SteckVaughn Library, 1990. Glover, David. Sound and Light. New York: Kingfisher Books, 1993. “Longitudinal and Transverse Wave Motion” (Web site). (April 22, 2001).
262
Ruchlis, Hyman. Bathtub Physics. Edited by Donald Barr; illustrated by Ray Skibinski. New York: Harcourt, Brace, and World, 1967. “Wave Motion” (Web site). (April 22, 2001). “Wave Motion and Sound.” The Physics Web (Web site). (April 22, 2001).
“Multimedia Activities: Wave Motion.” ExploreScience.com (Web site). (April 22, 2001).
“Wave Motion Menu.”Carson City-Crystal High School Physics and Chemistry Departments (Web site). (April 22, 2001).
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Oscillation
O S C I L L AT I O N
CONCEPT When a particle experiences repeated movement about a position of stable equilibrium, or balance, it is said to be in harmonic motion, and if this motion is repeated at regular intervals, it is called periodic motion. Oscillation is a type of harmonic motion, typically periodic, in one or more dimensions. Among the examples of oscillation in the physical world are the motion of a spring, a pendulum, or even the steady back-andforth movement of a child on a swing.
and an adult caught the child at the point of maximum displacement—this would be an example of unstable equilibrium. The swing is in equilibrium because the forces on it are balanced: it is being held upward with a force equal to its weight. Yet, this equilibrium is unstable, because a disturbance (for instance, if the adult lets go of the swing) will cause it to move. Since the swing tends to oscillate, it will move back and forth across the position of stable equilibrium before finally coming to a rest in the stable position.
Properties of Oscillation
HOW IT WORKS Stable and Unstable Equilibrium When a state of equilibrium exists, the vector sum of the forces on an object is equal to zero. There are three varieties of equilibrium: stable, unstable, and neutral. Neutral equilibrium, discussed in the essay on Statics and Equilibrium elsewhere in this book, does not play a significant role in oscillation; on the other hand, stable and unstable equilibrium do.
There are two basic models of oscillation to consider, and these can be related to the motion of two well-known everyday objects: a spring and a swing. As noted below, objects not commonly considered “springs,” such as rubber bands, display spring-like behavior; likewise one could substitute “pendulum” for swing. In any case, it is easy enough to envision the motion of these two varieties of oscillation: a spring generally oscillates along a straight line, whereas a swing describes an arc.
If, on the other hand, the swing were raised to a certain height—if, say, a child were swinging
Either case involves properties common to all objects experiencing oscillation. There is always a position of stable equilibrium, and there is always a cycle of oscillation. In a single cycle, the oscillating particle moves from a certain point in a certain direction, then reverses direction and returns to the original point. The amount of time it takes to complete one cycle is called a period, and the number of cycles that take place during one second is the frequency of the oscillation. Frequency is measured in Hertz (Hz), with 1 Hz—the term is both singular and plural—equal to one cycle per second.
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In the example of a playground swing, when the swing is simply hanging downward—either empty or occupied—it is in a position of stable equilibrium. The vector sums are balanced, because the swing hangs downward with a force (its weight) equal to the force of the bars on the swing set that hold it up. If it were disturbed from this position, as, for instance, by someone pushing the swing, it would tend to return to its original position.
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Oscillation
THE
BOUNCE PROVIDED BY A TRAMPOLINE IS DUE TO ELASTIC POTENTIAL ENERGY. (Photograph by Kevin Fleming/Corbis.
Reproduced by permission.)
It is easiest to think of a cycle as the movement from a position of stable equilibrium to one of maximum displacement, or the furthest possible point from stable equilibrium. Because stable equilibrium is directly in the middle of a cycle, there are two points of maximum displacement. For a swing or pendulum, maximum displacement occurs when the object is at its highest point on either side of the stable equilibrium position. For example, maximum displacement in a spring occurs when the spring reaches the furthest point of being either stretched or compressed. The amplitude of a cycle is the maximum displacement of particles during a single period of oscillation, and the greater the amplitude, the greater the energy of the oscillation. When an object reaches maximum displacement, it reverses direction, and, therefore, it comes to a stop for an instant of time. Thus, the speed of movement is slowest at that position, and fastest as it passes back through the position of stable equilibrium. An increase in amplitude brings with it an increase in speed, but this does not lead to a change in the period: the greater the amplitude, the further the oscillating object has to move, and, therefore, it takes just as long to complete a cycle.
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Restoring Force Imagine a spring hanging vertically from a ceiling, one end attached to the ceiling for support and the other free to hang. It would thus be in a position of stable equilibrium: the spring hangs downward with a force equal to its weight, and the ceiling pulls it upward with an equal and opposite force. Suppose, now, that the spring is pulled downward. A spring is highly elastic, meaning that it can experience a temporary stress and still rebound to its original position; by contrast, some objects (for instance, a piece of clay) respond to deformation with plastic behavior, permanently assuming the shape into which they were deformed. The force that directs the spring back to a position of stable equilibrium—the force, in other words, which must be overcome when the spring is pulled downward—is called a restoring force. The more the spring is stretched, the greater the amount of restoring force that must be overcome. The same is true if the spring is compressed: once again, the spring is removed from a position of equilibrium, and, once again, the restoring force tends to pull it outward to its “natural” position. Here, the example is a spring,
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but restoring force can be understood just as easily in terms of a swing: once again, it is the force that tends to return the swing to a position of stable equilibrium. There is, however, one significant difference: the restoring force on a swing is gravity, whereas, in the spring, it is related to the properties of the spring itself.
Oscillation
Elastic Potential Energy For any solid that has not exceeded the elastic limit—the maximum stress it can endure without experiencing permanent deformation— there is a proportional relationship between force and the distance it can be stretched. This is expressed in the formula F = ks, where s is the distance and k is a constant related to the size and composition of the material in question. The amount of force required to stretch the spring is the same as the force that acts to bring it back to equilibrium— that is, the restoring force. Using the value of force, thus derived, it is possible, by a series of steps, to establish a formula for elastic potential energy. The latter, sometimes called strain potential energy, is the potential energy that a spring or a spring-like object possesses by virtue of its deformation from the state of equilibrium. It is equal to 1⁄2ks2. POTENTIAL AND KINETIC ENE R GY. Potential energy, as its name suggests,
involves the potential of something to move across a given interval of space—for example, when a sled is perched at the top of a hill. As it begins moving through that interval, the object will gain kinetic energy. Hence, the elastic potential energy of the spring, when the spring is held at a position of the greatest possible displacement from equilibrium, is at a maximum. Once it is released, and the restoring force begins to move it toward the equilibrium position, potential energy drops and kinetic energy increases. But the spring will not just return to equilibrium and stop: its kinetic energy will cause it to keep going. A
In the case of the “swing” model of oscillation, elastic potential energy is not a factor. (Unless, of course, the swing itself were suspended on some sort of spring, in which case the object will oscillate in two directions at once.) Nonetheless, all systems of motion involve potential and kinetic energy. When the swing is at a position of maximum displacement, its
S C I E N C E O F E V E RY DAY T H I N G S
BUNGEE JUMPER HELPS ILLUSTRATE A REAL-WORLD
EXAMPLE OF OSCILLATION. (Eye Ubiquitous/Corbis. Reproduced
by permission.)
potential energy is at a maximum as well. Then, as it moves toward the position of stable equilibrium, it loses potential energy and gains kinetic energy. Upon passing through the stable equilib-
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rium position, kinetic energy again decreases, while potential energy increases. The sum of the two forms of energy is always the same, but the greater the amplitude, the greater the value of this sum.
REAL-LIFE A P P L I C AT I O N S Springs and Damping Elastic potential energy relates primarily to springs, but springs are a major part of everyday life. They can be found in everything from the shock-absorber assembly of a motor vehicle to the supports of a trampoline fabric, and in both cases, springs blunt the force of impact. If one were to jump on a piece of trampoline fabric stretched across an ordinary table—one with no springs—the experience would not be much fun, because there would be little bounce. On the other hand, the elastic potential energy of the trampoline’s springs ensures that anyone of normal weight who jumps on the trampoline is liable to bounce some distance into the air. As a person’s body comes down onto the trampoline fabric, this stretches the fabric (itself highly elastic) and, hence, the springs. Pulled from a position of equilibrium, the springs acquire elastic potential energy, and this energy makes possible the upward bounce. As a car goes over a bump, the spring in its shock-absorber assembly is compressed, but the elastic potential energy of the spring immediately forces it back to a position of equilibrium, thus ensuring that the bump is not felt throughout the entire vehicle. However, springs alone would make for a bouncy ride; hence, a modern vehicle also has shock absorbers. The shock absorber, a cylinder in which a piston pushes down on a quantity of oil, acts as a damper—that is, an inhibitor of the springs’ oscillation.
H O W DA M P I N G W O R K S . When the spring is first released, most likely it will fly upward with so much kinetic energy that it will, quite literally, bounce off the ceiling. But with each transit within the position of equilibrium, the friction produced by contact between the metal spring and the air, and by contact between molecules within the spring itself, will gradually reduce the energy that gives it movement. In time, it will come to a stop.
If the damping effect is small, the amplitude will gradually decrease, as the object continues to oscillate, until eventually oscillation ceases. On the other hand, the object may be “overdamped,” such that it completes only a few cycles before ceasing to oscillate altogether. In the spring illustration, overdamping would occur if one were to grab the spring on a downward cycle, then slowly let it go, such that it no longer bounced. There is a type of damping less forceful than overdamping, but not so gradual as the slow dissipation of energy due to frictional forces alone. This is called critical damping. In a critically damped oscillator, the oscillating material is made to return to equilibrium as quickly as possible without oscillating. An example of a critically damped oscillator is the shock-absorber assembly described earlier.
occurs when a particle or object moves back and forth within a stable equilibrium position under the influence of a restoring force proportional to its displacement. In an ideal situation, where friction played no part, an object would continue to oscillate indefinitely.
Even without its shock absorbers, the springs in a car would be subject to some degree of damping that would eventually bring a halt to their oscillation; but because this damping is of a very gradual nature, their tendency is to continue oscillating more or less evenly. Over time, of course, the friction in the springs would wear down their energy and bring an end to their oscillation, but by then, the car would most likely have hit another bump. Therefore, it makes sense to apply critical damping to the oscillation of the springs by using shock absorbers.
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SIMPLE HARMONIC MOTION A N D DA M P I N G . Simple harmonic motion
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Of course, objects in the real world do not experience perpetual oscillation; instead, most oscillating particles are subject to damping, or the dissipation of energy, primarily as a result of friction. In the earlier illustration of the spring suspended from a ceiling, if the string is pulled to a position of maximum displacement and then released, it will, of course, behave dramatically at first. Over time, however, its movements will become slower and slower, because of the damping effect of frictional forces.
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Bungee Cords and Rubber Bands Many objects in daily life oscillate in a spring-like way, yet people do not commonly associate them with springs. For example, a rubber band, which behaves very much like a spring, possesses high elastic potential energy. It will oscillate when stretched from a position of stable equilibrium.
One type of pendulum is a metronome, which registers the tempo or speed of music. Housed in a hollow box shaped like a pyramid, a metronome consists of a pendulum attached to a sliding weight, with a fixed weight attached to the bottom end of the pendulum. It includes a number scale indicating the number of oscillations per minute, and by moving the upper weight, one can change the beat to be indicated.
Rubber is composed of long, thin molecules called polymers, which are arranged side by side. The chemical bonds between the atoms in a polymer are flexible and tend to rotate, producing kinks and loops along the length of the molecule. The super-elastic polymers in rubber are called elastomers, and when a piece of rubber is pulled, the kinks and loops in the elastomers straighten.
early nineteenth century, but, by then, the concept of a pendulum was already old. In the second century A.D., Chinese mathematician and astronomer Zhang Heng (78-139) used a pendulum to develop the world’s first seismoscope, an instrument for measuring motion on Earth’s surface as a result of earthquakes.
The structure of rubber gives it a high degree of elastic potential energy, and in order to stretch rubber to maximum displacement, there is a powerful restoring force that must be overcome. This can be illustrated if a rubber band is attached to a ceiling, like the spring in the earlier example, and allowed to hang downward. If it is pulled down and released, it will behave much as the spring did.
Zhang Heng’s seismoscope, which he unveiled in 132 A.D., consisted of a cylinder surrounded by bronze dragons with frogs (also made of bronze) beneath. When the earth shook, a ball would drop from a dragon’s mouth into that of a frog, making a noise. The number of balls released, and the direction in which they fell, indicated the magnitude and location of the seismic disruption.
The oscillation of a rubber band will be even more appreciable if a weight is attached to the “free” end—that is, the end hanging downward. This is equivalent, on a small scale, to a bungee jumper attached to a cord. The type of cord used for bungee jumping is highly elastic; otherwise, the sport would be even more dangerous than it already is. Because of the cord’s elasticity, when the bungee jumper “reaches the end of his rope,” he bounces back up. At a certain point, he begins to fall again, then bounces back up, and so on, oscillating until he reaches the point of stable equilibrium.
C LO C K S , S C I E N T I F I C I N S T R U M E N T S , A N D “FAX M AC H I N E ” . In
The Pendulum As noted earlier, a pendulum operates in much the same way as a swing; the difference between them is primarily one of purpose. A swing exists to give pleasure to a child, or a certain bittersweet pleasure to an adult reliving a childhood experience. A pendulum, on the other hand, is not for play; it performs the function of providing a reading, or measurement.
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Oscillation
ZHANG HENG’S SEISMOS C O P E . Metronomes were developed in the
718 A.D., during a period of intellectual flowering that attended the early T’ang Dynasty (618-907), a Buddhist monk named I-hsing and a military engineer named Liang Ling-tsan built an astronomical clock using a pendulum. Many clocks today—for example, the stately and imposing “grandfather clock” found in some homes—likewise, use a pendulum to mark time. Physicists of the early modern era used pendula (the plural of pendulum) for a number of interesting purposes, including calculations regarding gravitational force. Experiments with pendula by Galileo Galilei (1564-1642) led to the creation of the mechanical pendulum clock—the grandfather clock, that is—by distinguished Dutch physicist and astronomer Christiaan Huygens (1629-1695). In the nineteenth century, A Scottish inventor named Alexander Bain (1810-1877) even used a pendulum to create the first “fax machine.” Using matching pendulum transmitters and receivers that sent and received electrical
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Oscillation
KEY TERMS The maximum displace-
AMPLITUDE:
For a particle experi-
FREQUENCY:
ment of particles from their normal posi-
encing oscillation, frequency is the number
tion during a single period of oscillation.
of cycles that take place during one second.
One full repetition of oscilla-
CYCLE:
tion. In a single cycle, the oscillating particle moves from a certain point in a certain direction, then switches direction and moves back to the original point. Typically, this is from the position of stable equilibri-
Frequency is measured in Hertz. FRICTION:
The force that resists
motion when the surface of one object comes into contact with the surface of another. The repeated
um to maximum displacement and back
HARMONIC MOTION:
again to the stable equilibrium position.
movement of a particle within a position of
DAMPING:
The dissipation of energy
equilibrium, or balance.
during oscillation, which prevents an
HERTZ:
object from continuing in simple harmon-
cy. The number of Hertz is the number of
ic motion and will eventually force it to
cycles per second.
A unit for measuring frequen-
stop oscillating altogether. Damping is KINETIC ENERGY:
usually caused by friction.
The energy that
an object possesses due to its motion, as ELASTIC
POTENTIAL
ENERGY:
The potential energy that a spring or a spring-like object possesses by virtue of its
is contrasted with potential energy. For an
deformation from the state of equilibrium.
MAXIMUM DISPLACEMENT:
Sometimes called strain potential energy, it
object in oscillation, maximum displace-
is equal to
⁄2KS2,
WHERE S is the distance
ment is the furthest point from stable equi-
stretched and k is a figure related to the
librium. Since stable equilibrium is in the
size and composition of the material in
middle of a cycle, there are two points of
question.
maximum displacement. For a swing or
1
A state in which the
pendulum, this occurs when the object is at
vector sum for all lines of force on an
its highest point on either side of the stable
object is equal to zero.
equilibrium position. Maximum displace-
EQUILIBRIUM:
impulses, he created a crude device that, at the time, seemed to have little practical purpose. In fact, Bain’s “fax machine,” invented in 1840, was more than a century ahead of its time.
length, he was able to demonstrate that Earth rotates on its axis.
By far the most important experiments with pendula during the nineteenth century, however, were those of the French physicist Jean Bernard Leon Foucault (1819-1868). Swinging a heavy iron ball from a wire more than 200 ft (61 m) in
Foucault conducted his famous demonstration in the Panthéon, a large domed building in Paris named after the ancient Pantheon of Rome. He arranged to have sand placed on the floor of the Panthéon, and placed a pin on the bottom of the iron ball, so that it would mark the sand as the pendulum moved. A pendulum in oscillation maintains its orientation, yet the Foucault pen-
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THE
268
with a sled, when sliding down a hill. This
F O U C A U LT
PENDULUM.
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Oscillation
KEY TERMS
CONTINUED
ment in a spring occurs when the spring is
position under the influence of a restoring
either stretched or compressed as far as it
force proportional to its displacement.
will go.
Simple harmonic motion is, in fact, an
OSCILLATION:
A type of harmonic
motion, typically periodic, in one or more
ideal situation; most types of oscillation are subject to some form of damping.
dimensions. STABLE EQUILIBRIUM:
A type of
The amount of time required
equilibrium in which, if an object were dis-
for one cycle in oscillating motion—for
turbed, it would tend to return to its origi-
instance, from a position of maximum dis-
nal position. For an object in oscillation,
placement to one of stable equilib-
stable equilibrium is in the middle of a
rium, and, once again, to maximum dis-
cycle, between two points of maximum
placement.
displacement.
PERIOD:
PERIODIC MOTION:
Motion that is
repeated at regular intervals. These inter-
VECTOR:
A quantity that possesses
both magnitude and direction.
vals are known as periods. POTENTIAL ENERGY:
The energy
that an object possesses due to its position, as for instance, with a sled at the top of a hill. This is contrasted with kinetic energy.
VECTOR
SUM:
A calculation that
yields the net result of all the vectors applied in a particular situation. Because direction is involved, it is necessary when calculating the vector sum of forces on an
A force that
object (as, for instance, when determining
directs an object back to a position of sta-
whether or not it is in a state of equilibri-
ble equilibrium. An example is the resist-
um), to assign a positive value to forces in
RESTORING FORCE:
ance of a spring, when it is extended.
one direction, and a negative value to Har-
forces in the opposite direction. If the
monic motion, in which a particle moves
object is in equilibrium, these forces will
back and forth about a stable equilibrium
cancel one another out.
SIMPLE HARMONIC MOTION:
dulum (as it came to be called) seemed to be shifting continually toward the right, as indicated by the marks in the sand.
Earth itself was moving beneath the pendulum, providing an additional force which caused the pendulum’s plane of oscillation to rotate.
The confusion related to reference point: since Earth’s rotation is not something that can be perceived with the senses, it was natural to assume that the pendulum itself was changing orientation—or rather, that only the pendulum was moving. In fact, the path of Foucault’s pendulum did not vary nearly as much as it seemed.
Ehrlich, Robert. Turning the World Inside Out, and 174 Other Simple Physics Demonstrations. Princeton, N.J.: Princeton University Press, 1990.
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WHERE TO LEARN MORE Brynie, Faith Hickman. Six-Minute Science Experiments. Illustrated by Kim Whittingham. New York: Sterling Publishing Company, 1996.
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“Foucault Pendulum” Smithsonian Institution FAQs (Web site). (April 23, 2001).
Shirley, Jean. Galileo. Illustrated by Raymond Renard. St. Louis: McGraw-Hill, 1967. Suplee, Curt. Everyday Science Explained. Washington, D.C.: National Geographic Society, 1996.
Kruszelnicki, Karl S. The Foucault Pendulum (Web site). (April 23, 2001).
Topp, Patricia. This Strange Quantum World and You. Nevada City, CA: Blue Dolphin, 1999.
Schaefer, Lola M. Back and Forth. Edited by Gail Saunders-Smith; P. W. Hammer, consultant. Mankato, MN: Pebble Books, 2000.
Zubrowski, Bernie. Making Waves: Finding Out About Rhythmic Motion. Illustrated by Roy Doty. New York: Morrow Junior Books, 1994.
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Frequency
CONCEPT Everywhere in daily life, there are frequencies of sound and electromagnetic waves, constantly changing and creating the features of the visible and audible world familiar to everyone. Some aspects of frequency can only be perceived indirectly, yet people are conscious of them without even thinking about it: a favorite radio station, for instance, may have a frequency of 99.7 MHz, and fans of that station knows that every time they turn the FM dial to that position, the station’s signal will be there. Of course, people cannot “hear” radio and television frequencies— part of the electromagnetic spectrum—but the evidence for them is everywhere. Similarly, people are not conscious, in any direct sense, of frequencies in sound and light—yet without differences in frequency, there could be no speech or music, nor would there be any variations of color.
HOW IT WORKS Harmonic Motion and Energy In order to understand frequency, it is first necessary to comprehend two related varieties of movement: oscillation and wave motion. Both are examples of a broader category, periodic motion: movement that is repeated at regular intervals called periods. Oscillation and wave motion are also examples of harmonic motion, or the repeated movement of a particle about a position of equilibrium, or balance.
FREQUENCY
conversion of energy from one form to another. On the one hand is potential energy, or the energy of an object due to its position and, hence, its potential for movement. On the other hand, there is kinetic energy, the energy of movement itself. Potential-kinetic conversions take place constantly in daily life: any time an object is at a distance from a position of stable equilibrium, and some force (for instance, gravity) is capable of moving it to that position, it possesses potential energy. Once it begins to move toward that equilibrium position, it loses potential energy and gains kinetic energy. Likewise, a wave at its crest has potential energy, and gains kinetic energy as it moves toward its trough. Similarly, an oscillating object that is as far as possible from the stable-equilibrium position has enormous potential energy, which dissipates as it begins to move toward stable equilibrium. V I B RAT I O N . Though many examples of periodic and harmonic motion can be found in daily life, the terms themselves are certainly not part of everyday experience. On the other hand, everyone knows what “vibration” means: to move back and forth in place. Oscillation, discussed in more detail below, is simply a more scientific term for vibration; and while waves are not themselves merely vibrations, they involve— and may produce—vibrations. This, in fact, is how the human ear hears: by interpreting vibrations resulting from sound waves.
types of periodic motion, there is a continual
Indeed, the entire world is in a state of vibration, though people seldom perceive this movement—except, perhaps, in dramatic situations such as earthquakes, when the vibrations of plates beneath Earth’s surface become too force-
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KINETIC AND POTENTIAL ENE R GY. In harmonic motion, and in some
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In oscillation, whether the oscillator be spring-like or swing-like, there is always a cycle in which the oscillating particle moves from a certain point in a certain direction, then reverses direction and returns to the original point. Usually a cycle is viewed as the movement from a position of stable equilibrium to one of maximum displacement, or the furthest possible point from stable equilibrium. Because stable equilibrium is directly in the middle of a cycle, there are two points of maximum displacement: on a swing, this occurs when the object is at its highest point on either side of the stable equilibrium position, and on a spring, maximum displacement occurs when the spring is either stretched or compressed as far as it will go.
Frequency
Wave Motion
GRANDFATHER VARIETIES
OF
CLOCKS ARE ONE OF THE BEST-KNOWN A
PENDULUM .
(Photograph by Peter
Harholdt/Corbis. Reproduced by permission.)
ful to ignore. All matter vibrates at the molecular level, and every object possesses what is called a natural frequency, which depends on its size, shape, and composition. This explains how a singer can shatter a glass by hitting a certain note, which does not happen because the singer’s voice has reached a particularly high pitch; rather, it is a matter of attaining the natural frequency of the glass. As a result, all the energy in the sound of the singer’s voice is transferred to the glass, and it shatters.
Wave motion is a type of harmonic motion that carries energy from one place to another without actually moving any matter. While oscillation involves the movement of “an object,” whether it be a pendulum, a stretched rubber band, or some other type of matter, a wave may or may not involve matter. Example of a wave made out of matter—that is, a mechanical wave—is a wave on the ocean, or a sound wave, in which energy vibrates through a medium such as air. Even in the case of the mechanical wave, however, the matter does not experience any net displacement from its original position. (Water molecules do rotate as a result of wave motion, but they end up where they began.) There are waves that do not follow regular, repeated patterns; however, within the context of frequency, our principal concern is with periodic waves, or waves that follow one another in regular succession. Examples of periodic waves include ocean waves, sound waves, and electromagnetic waves.
Oscillation Oscillation is a type of harmonic motion, typically periodic, in one or more dimensions. There are two basic types of oscillation: that of a swing or pendulum and that of a spring. In each case, an object is disturbed from a position of stable equilibrium, and, as a result, it continues to move back and forth around that stable equilibrium position. If a spring is pulled from stable equilibrium, it will generally oscillate along a straight path; a swing, on the other hand, will oscillate along an arc.
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Periodic waves may be further divided into transverse and longitudinal waves. A transverse wave is the shape that most people imagine when they think of waves: a regular up-and-down pattern (called “sinusoidal” in mathematical terms) in which the vibration or motion is perpendicular to the direction the wave is moving. A longitudinal wave is one in which the movement of vibration is in the same direction as the wave itself. Though these are a little harder to picture, longitudinal waves can be visualized as a series of concentric circles emanating
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from a single point. Sound waves are longitudinal: thus when someone speaks, waves of sound vibrations radiate out in all directions.
Frequency
Amplitude There are certain properties of waves, such as wavelength, or the distance between waves, that are not properties of oscillation. However, both types of motion can be described in terms of amplitude, period, and frequency. The first of these is not related to frequency in any mathematical sense; nonetheless, where sound waves are concerned, both amplitude and frequency play a significant role in what people hear. Though waves and oscillators share the properties of amplitude, period, and frequency, the definitions of these differ slightly depending on whether one is discussing wave motion or oscillation. Amplitude, generally speaking, is the value of maximum displacement from an average value or position—or, in simpler terms, amplitude is “size.” For an object experiencing oscillation, it is the value of the object’s maximum displacement from a position of stable equilibrium during a single period. It is thus the “size” of the oscillation. In the case of wave motion, amplitude is also the “size” of a wave, but the precise definition varies, depending on whether the wave in question is transverse or longitudinal. In the first instance, amplitude is the distance from either the crest or the trough to the average position between them. For a sound wave, which is longitudinal, amplitude is the maximum value of the pressure change between waves.
Period and Frequency Unlike amplitude, period is directly related to frequency. For a transverse wave, a period is the amount of time required to complete one full cycle of the wave, from trough to crest and back to trough. In a longitudinal wave, a period is the interval between waves. With an oscillator, a period is the amount of time it takes to complete one cycle. The value of a period is usually expressed in seconds. Frequency in oscillation is the number of cycles per second, and in wave motion, it is the number of waves that pass through a given point per second. These cycles per second are called Hertz (Hz) in honor of nineteenth-century Ger-
S C I E N C E O F E V E RY DAY T H I N G S
MIDDLE C—WHICH IS AT THE MIDDLE OF A PIANO KEYBOARD—IS THE STARTING POINT OF A BASIC MUSICAL SCALE. IT IS CALLED THE FUNDAMENTAL FREQUENCY, OR THE FIRST HARMONIC . (Photograph by Francoise Gervais/Corbis. Reproduced by permission.)
man physicist Heinrich Rudolf Hertz (18571894), who greatly advanced understanding of electromagnetic wave behavior during his short career. If something has a frequency of 100 Hz, this means that 100 waves are passing through a given point during the interval of one second, or that an oscillator is completing 100 cycles in a second. Higher frequencies are expressed in terms of kilohertz (kHz; 103 or 1,000 cycles per second); megahertz (MHz; 106 or 1 million cycles per second); and gigahertz (GHz; 109 or 1 billion cycles per second.). A clear mathematical relationship exists between period, symbolized by T, and frequency (f): each is the inverse of the other. Hence,
T
= 1
f
= 1
f ,
and
T .
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If an object in harmonic motion has a frequency of 50 Hz, its period is 1/50 of a second (0.02 sec). Or, if it has a period of 1/20,000 of a second (0.00005 sec), that means it has a frequency of 20,000 Hz.
REAL-LIFE A P P L I C AT I O N S Grandfather Clocks and Metronomes One of the best-known varieties of pendulum (plural, pendula) is a grandfather clock. Its invention was an indirect result of experiments with pendula by Galileo Galilei (1564-1642), work that influenced Dutch physicist and astronomer Christiaan Huygens (1629-1695) in the creation of the mechanical pendulum clock—or grandfather clock, as it is commonly known. The frequency of a pendulum, a swing-like oscillator, is the number of “swings” per minute. Its frequency is proportional to the square root of the downward acceleration due to gravity (32 ft or 9.8 m/sec2) divided by the length of the pendulum. This means that by adjusting the length of the pendulum on the clock, one can change its frequency: if the pendulum length is shortened, the clock will run faster, and if it is lengthened, the clock will run more slowly. Another variety of pendulum, this one dating to the early nineteenth century, is a metronome, an instrument that registers the tempo or speed of music. Consisting of a pendulum attached to a sliding weight, with a fixed weight attached to the bottom end of the pendulum, a metronome includes a number scale indicating the frequency—that is, the number of oscillations per minute. By moving the upper weight, one can speed up or slow down the beat.
Harmonics As noted earlier, the volume of any sound is related to the amplitude of the sound waves. Frequency, on the other hand, determines the pitch or tone. Though there is no direct correlation between intensity and frequency, in order for a person to hear a very low-frequency sound, it must be above a certain decibel level. The range of audibility for the human ear is from 20 Hz to 20,000 Hz. The optimal range for hearing, however, is between 3,000 and 4,000 Hz.
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This places the piano, whose 88 keys range from 27 Hz to 4,186 Hz, well within the range of human audibility. Many animals have a much wider range: bats, whales, and dolphins can hear sounds at a frequency up to 150,000 Hz. But humans have something that few animals can appreciate: music, a realm in which frequency changes are essential. Each note has its own frequency: middle C, for instance, is 264 Hz. But in order to produce what people understand as music—that is, pleasing combinations of notes—it is necessary to employ principles of harmonics, which express the relationships between notes. These mathematical relations between musical notes are among the most intriguing aspects of the connection between art and science. It is no wonder, perhaps, that the great Greek mathematician Pythagoras (c. 580-500 B.C.) believed that there was something spiritual or mystical in the connection between mathematics and music. Pythagoras had no concept of frequency, of course, but he did recognize that there were certain numerical relationships between the lengths of strings, and that the production of harmonious music depended on these ratios. RAT I O S O F F R E Q U E N CY A N D P L E AS I N G T O N E S . Middle C—located,,
appropriately enough, in the middle of a piano keyboard—is the starting point of a basic musical scale. It is called the fundamental frequency, or the first harmonic. The second harmonic, one octave above middle C, has a frequency of 528 Hz, exactly twice that of the first harmonic; and the third harmonic (two octaves above middle C) has a frequency of 792 cycles, or three times that of middle C. So it goes, up the scale. As it turns out, the groups of notes that people consider harmonious just happen to involve specific whole-number ratios. In one of those curious interrelations of music and math that would have delighted Pythagoras, the smaller the numbers involved in the ratios, the more pleasing the tone to the human psyche. An example of a pleasing interval within an octave is a fifth, so named because it spans five notes that are a whole step apart. The C Major scale is easiest to comprehend in this regard, because it does not require reference to the “black keys,” which are a half-step above or below the “white keys.” Thus, the major fifth in the CMajor scale is C, D, E, F, G. It so happens that the
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Frequency
KEY TERMS For an object oscillation,
(1857-1894). Higher frequencies are
amplitude is the value of the object’s max-
expressed in terms of kilohertz (kHz; 103
imum displacement from a position of sta-
or 1,000 cycles per second); megahertz
ble equilibrium during a single period. In a
(MHz; 106 or 1 million cycles per second);
transverse wave, amplitude is the distance
and gigahertz (GHz; 109 or 1 billion cycles
from either the crest or the trough to the
per second.)
AMPLITUDE:
average position between them. For a sound wave, the best-known example of a longitudinal wave, amplitude is the maximum value of the pressure change between waves. CYCLE:
In oscillation, a cycle occurs
when the oscillating particle moves from a certain point in a certain direction, then switches direction and moves back to the
KINETIC ENERGY:
The energy that
an object possesses due to its motion, as with a sled when sliding down a hill. This is contrasted with potential energy. LONGITUDINAL WAVE:
A wave in
which the movement of vibration is in the same direction as the wave itself. This is contrasted to a transverse wave.
original point. Typically, this is from the
MAXIMUM DISPLACEMENT:
position of stable equilibrium to maxi-
object in oscillation, maximum displace-
mum displacement and back again to the
ment is the farthest point from stable equi-
stable equilibrium position.
librium.
FREQUENCY:
For a particle experi-
OSCILLATION:
For an
A type of harmonic
encing oscillation, frequency is the number
motion, typically periodic, in one or more
of cycles that take place during one second.
dimensions.
In wave motion, frequency is the number of waves passing through a given point during the interval of one second. In either case, frequency is measured in Hertz. Period (T) is the mathematical inverse of frequency (f) hence f=1/T.
In oscillation, a period is the
PERIOD:
amount of time required for one cycle. For a transverse wave, a period is the amount of time required to complete one full cycle of the wave, from trough to crest and back to trough. In a longitudinal wave, a period
The repeated
is the interval between waves. Frequency is
movement of a particle about a position of
the mathematical inverse of period (T):
equilibrium, or balance.
hence, T=1/f.
HARMONIC MOTION:
HERTZ:
A unit for measuring fre-
PERIODIC MOTION:
Motion that is
quency, named after nineteenth-century
repeated at regular intervals. These inter-
German physicist Heinrich Rudolf Hertz
vals are known as periods.
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Frequency
KEY TERMS that an object possesses due to its position,
between two points of maximum displacement.
as, for instance, with a sled at the top of
TRANSVERSE
POTENTIAL ENERGY:
The energy
a hill. This is contrasted with kinetic energy. STABLE EQUILIBRIUM:
A position
in which, if an object were disturbed, it would tend to return to its original position. For an object in oscillation, stable equilibrium is in the middle of a cycle,
ratio in frequency between middle C and G (396 Hz) is 2:3. Less melodious, but still certainly tolerable, is an interval known as a third. Three steps up from middle C is E, with a frequency of 330 Hz, yielding a ratio involving higher numbers than that of a fifth—4:5. Again, the higher the numbers involved in the ratio, the less appealing the sound is to the human ear: the combination E-F, with a ratio of 15:16, sounds positively grating.
The Electromagnetic Spectrum
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A wave in which the vibration or motion is perpendicular to the direction in which the wave is moving. This is contrasted to a longitudinal wave. WAVE:
A type of harmonic motion that carries energy from one place to another without actually moving any matter.
WAVE MOTION:
of gamma rays, reaching to frequencies as high as 1025. The latter value is equal to 10 trillion trillion. Obviously, these ultra-ultra high-frequency waves must be very small, and they are: the higher gamma rays have a wavelength of around 10-15 meters (0.000000000000001 m). For frequencies lower than those of visible light, the wavelengths get larger, but for a wide range of the electromagnetic spectrum, the wavelengths are still much too small to be seen, even if they were visible. Such is the case with infrared light, or the relatively lower-frequency millimeter waves.
Everyone who has vision is aware of sunlight, but, in fact, the portion of the electromagnetic spectrum that people perceive is only a small part of it. The frequency range of visible light is from 4.3 • 1014 Hz to 7.5 • 1014 Hz—in other words, from 430 to 750 trillion Hertz. Two things should be obvious about these numbers: that both the range and the frequencies are extremely high. Yet, the values for visible light are small compared to the higher reaches of the spectrum, and the range is also comparatively small.
Only at the low end of the spectrum, with frequencies below about 1010 Hz—still an incredibly large number—do wavelengths become the size of everyday objects. The center of the microwave range within the spectrum, for instance, has a wavelength of about 3.28 ft (1 m). At this end of the spectrum—which includes television and radar (both examples of microwaves), short-wave radio, and long-wave radio—there are numerous segments devoted to various types of communication.
Each of the colors has a frequency, and the value grows higher from red to orange, and so on through yellow, green, blue, indigo, and violet. Beyond violet is ultraviolet light, which human eyes cannot see. At an even higher frequency are x rays, which occupy a broad band extending almost to 1020 Hz—in other words, 1 followed by 20 zeroes. Higher still is the very broad range
RA D I O A N D M I C R O WAV E F R E Q U E N C I E S . The divisions of these sections
of the electromagnetic spectrum are arbitrary and manmade, but in the United States—where they are administered by the Federal Communications Commission (FCC)—they have the force of law. When AM (amplitude modulation) radio first came into widespread use in the early
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1920s—Congress assigned AM stations the frequency range that they now occupy: 535 kHz to 1.7 MHz. A few decades after the establishment of the FCC in 1927, new forms of electronic communication came into being, and these too were assigned frequencies—sometimes in ways that were apparently haphazard. Today, television stations 2-6 are in the 54-88 MHz range, while stations 7-13 occupy the region from 174-220 MHz. In between is the 88 to 108 MHz band, assigned to FM radio. Likewise, short-wave radio (5.9 to 26.1 MHz) and citizens’ band or CB radio (26.96 to 27.41 MHz) occupy positions between AM and FM. In fact, there are a huge variety of frequency ranges accorded to all manner of other communication technologies. Garage-door openers and alarm systems have their place at around 40 MHz. Much, much higher than these—higher, in fact, than TV broadcasts—is the band allotted to deep-space radio communications: 2,290 to 2,300 MHz. Cell phones have their own realm, of course, as do cordless phones; but so too do radio controlled cars (75 MHz) and even baby monitors (49 MHz).
S C I E N C E O F E V E RY DAY T H I N G S
WHERE TO LEARN MORE
Frequency
Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991. Allocation of Radio Spectrum in the United States (Web site). (April 25, 2001). DiSpezio, Michael and Catherine Leary. Awesome Experiments in Light and Sound. New York: Sterling Juvenile, 2001. Electromagnetic Spectrum (Web site). (April 25, 2001). “How the Radio Spectrum Works.” How Stuff Works (Web site).