Chemical Constants and Absolute Entropy

Voi. 13, 1927

CHEMISTR Y: W. H, RODEB USH

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The Correction to the Saha Formula.-Comparing our ionization formula with Saha's it is easy to find that the correcting factor for the latter is Lo hF Tk(T-To)1 1 A - e kT +!kTo I1 _+-. 2 To hpo In thermodynamic equilibrium this factor is naturally unity, and we have seen that for the sun it is very near to unity because To = T. lt, therefore, seems impossible to explain in this way certain anomalies in the solar spectrum such as the behavior of Ba+, which is to be explained rather by some atomic property (perhaps the "steric factor" introduced by Saha,6 or by the existence of a metastable D state). For the stars, especially for giants and early type stars which show emission lines, this correcting factor may be of some importance, but in view of the lack of precision of the available data on spectral line photometry it seems premature at present to discuss this question further. I Gerasimovic, Zeit. Phys., 39, 1926 (361). 2 Phil. Mag., 47, 1924 (224). Phil; Mag., 46, 1923 (843). 4Pub. Dom. A p. Obs., 2, 1923 (213). 5 M. N. R. A. S., 82, 1922 (368). 6 Phil. Mag., 40, 1920 (472). 3

CHEMICAL CONSTANTS AND ABSOLUTE ENTROPY By WORTH H. RODZBUSH UNIVZRSITY Or ILLINOIS

Communicated March 2, 1927

Recent calculations of the chemical constants for sodium and potassiumt'M23'45 have not been particularly concordant but in several cases new data have been contributed which reduce the uncertainty in the calculations. Thus Simon and Zeidler3 have obtained specific heat data at low temperatures for potassium and sodium which is in substantial agreement with that of Eastman and Rodebush.6 Egerton has confirmed the data obtained in this laboratoryv on the vapor pressures of these metal at low pressures. Finally Dr. A. L. Dixon has obtained in this laboratory satisfactory data on the specific heats of the liquid metals so that for the first time it is possible to calculate the entropies of the vapors of sodium and potassium with complete and seemingly reliable data. The only part of the calculation that requires elaboration is the fitting of an equation to the vapor pressure data. Dr. Dixon finds that Cp for molten potassium is nearly constant and equal to 7.80 in the temperature ,

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6CHEMISTR Y: W. H. RODEB USH

PRtOC. N. A. S.

range immediately above the boiling point. This would indicate that the vapor pressure equation should contain a term 1.40 log T'. When we 1 plot the data of Egerton and Fiock and Rodebush2 on a log pi diagram we find excellent agreement between the two sets of data but it is impossible to fit the data with any equation except a simple linear form which does not allow for variation of AH with the temperature. On the other hand if we disregard the boiling point we may fit all the other data surprisingly well with the equation: -

logio Pmm. =-_ 47r80- 1.40 log T + 11.670.

The justification for the above procedure is the assumption that the vapor at the boiling point can no longer be treated as a perfect gas. On the other hand we are of course assuming that the vapor at pressures below 30 to 40 mm. may be treated as a perfect gas. A similar situation is found in the case of sodium. The boiling point is disregarded as are the data of Rodebush and- DeVries at intermediate pressures. These latter data were obtained by the same method as those of Fiock and Rodebush on potassium but the apparatus had not been developed to a satisfactory degree and the results are probably high. The equation

logio Pmm.

5730 1 log T + 11.580 --1.25

fits the data of Egerton and Rodebush and DeVries,l at low pressures, in an entirely satisfactory manner and incidentally the data of Haber and Zisch7 at intermediate pressures. The entropies of the vapors at 2980 K. and 1 atmosphere are tabulated below. The value for potassium is in substantial agreement with that calculated by Fiock and Rodebush. The value for sodium is higher than the probable range estimated by Rodebush and DeVries because of an error made by them in the calculation of the entropy of fusion. The value for sodium is lower than that obtained by Simon3 and it appears difficult to justify Simon's vapor-pressure equation. For comparison the entropies of lead and mercury are included. The entropy of lead vapor is as calculated by Rodebush and Dixon8 while the value for mercury is taken from the paper by Fogler and Rodebush8 with a correction for the specific heat data at low temperatures obtained since by Simon.9 In the second column of table 1 are given the values predicted by the Tetrode equation. It will be noted that values for sodium and potassium are high by 1.3 units which is near the value Rin 2 predicted by Schottky,'0 Fowler" and others for atoms whose lowest quantum state has an a priori

CHEMISTR Y: W. H. RODEB USH

VOLc. 13, 1927

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probability of 2. Taylor12 has shown that sodium and potassium possess two possible orientations in a magnetic field and Van Vleck5 has suggested that the entropies of sodium and potassium should show this effect. ENTROPZS OP THU VAPORS AT 298 OK. AND 1 ATmsPosR: OBSERVED

PREDICTED

Potassium

38.2

Sodium

36.7 41.7 42.9

36.9 35.4 41.8 41.9

Mercury

Lead

This seemingly excellent confirmation of the theory of thermodynamic probability justifies one or two observations from a theoretical standpoint. It is assumed in the case of potassium that only a single orientation is possible to an atom in the metallic crystal lattice. If more than one orientation were possible for a given atom in the solfd then the entropy of the solid would presumably be greater than zero at absolute zero. Since the magnetic moment is usually considered to be due to moving charges this hypothetical deviation from the third law could be explained as due to the existence of kinetic energy in the solid at 0°K. It is interesting to speculate as to whether all exceptions to the Third Law can be explained as due to the presence of kinetic energy in the condensed phase at absolute zero. Pauling and Tolman"3 have apparently proved that random orientation of molecules is sufficient to cause a positive deviation from the Third Law but their demonstration makes use of the vapor phase which in turn presupposes that the molecules possess kinetic energy to some extent even in the condensed phase. Another point which may be mentioned in this connection is that Ehrenfest and Trkal" and Fowler"5 take the position, that there is no such thing as absolute thermodynamic probability or absolute entropy. Ehrenfest applies the quantum conditions in a way that apparently leaves the thermodynamic probability of the vapor phase purely a relative number depending on the units used. It will be noted, however, that the mathematical expression obtained by Ehrenfest differs from that obtained by Tetrode chiefly in that Planck's constant h appears in the numerator with a negative exponent rather than in the denominator with a positive exponent. In order to obtain the expression for equilibrium between the vapor and the solid phase it is necessary to introduce the quantum constant of "action" with a definite value. This would certainly suggest that the thermodynamic probability of a system is a definite number and hence justify the concept of absolute entropy. Rodebush and De Vries, J. Amer. Chem. Soc., 47, 2488 (1925). 2 Fiock and Rodebush, Ibid., 48, 2522 (1926). ' Simon and Zeidler, Zeit. physik. Chem., 123, 383 (1926). ' Edmondson and Egerton, Proc. Roy. Soc., 113A, 520 (1927).

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' Van Vleck, Physic. Rev., 28, 980 (1926). IEastman and Rodebush, J. Amer. Chem. Soc., 40, 489 (1918). 7 Haber and Zisch, Zeit. Physik, 9, 325 (1922). s Rodebush and Dixon, Physic. Rev., 26, 851 (1925); Fogler and Rodebush, J. Amer. Chem. Soc., 40, 2080 (1923). 9 Simon, Ann. Physik, 68, 241 (1922). 10 Schottky, Physik. Zeit., 22, 1 (1921). 11 Fowler, Phil. Mag., 45, 32 (1923). 12 Taylor, Physic. Rev., 28, 576 (1926). 13 Pauling and Tolman, J. Amer. Chem. Soc., 47, 2148 (1925). "Ehrenfest and Trkal, Proc. Amsterdam Akad., 23, 162 (1920). 1 Fowler, Phil. Mag., 44, 823 (1922).

ON CHEMICAL ACTIVATION BY COLLISIONS By RICHARD C. TOiMAN, DON M. YOST AND Roscoi3 G. DICKINSON GATES CHIMICAL LABORATORY, CALIFORNIA INSTITUTE oF T}3CHNOLOGY

Communicated March 3, 1927

1. Introduction.-In the case of first order unimolecular gas reactions, such as the decomposition of nitrogen pentoxide, there is a well-known, theoretical difficulty' in discovering any process of activation rapid enough to maintain the full Maxwell-Boltzmann quota of activated molecules and thus to assure a first order course to the reaction. This problem has recently been treated anew by Fowler and Rideal,2 who consider, in a somewhat new light, the possibility of activation by molecular collisions. By assuming that activation occurs as the result of practically every collision in which the sum of the internal energies el and e2 carried by the two molecules and their relative kinetic energy v is greater than the energy necessary for activation e,, Fowler and Rideal find it possible, even using kinetic theory diameters, to obtain rates of activation considerably greater than known rates of reaction. The purpose of the present note is to emphasize, rather more strongly than has been done by Fowler and Rideal, the difficulties involved in making the assumption that activation occurs at every collision where the energy available is sufficient for the purpose. 2. General Plausibility of the Assumption.-The first difficulty concerns itself with the general plausibility of the assumption. Since the expression for the fraction of all collisions, in which the total energy available is greater than any value e, is mainly determined by an exponential factor of the form e- /kT it is evident, with the large values of the energy of activation actually encountered, that in the great majority of activating collisions the total energy available would only be slightly greater than that necessary for activation, and hence practically all the energy would have to flow into one of the two molecules.