Binary solutions of consolute liquids

8

CHEMISTR Y: BANCROFT AND DAVIS

PRoc. N. A. S.

anhydride (SiO2. 12WO3). Phosphodecimolybdic acid similarly forms a body-centered cube with a side length of 14.31 A.U. 3. A modified formula for the acid-2H20(6H20 . SiOC2. 12W03) or H[(SiO4)(Wo2030)(0H)n]I-and a new spatial structure have been deduced to correlate adequately the x-ray and chemical data. 1Throughout this paper the term silicotungstic acid will be understood to refer to silicoduodecitungstic acid. 2 This communication is an abstract of a portion of a thesis submitted by Arthur 0. Scroggie in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Chemistry at the University of Illinois. 3Rosenheim and Jaenicke, Zeits. anorg. Chem., 100, 319, 1917. Asch and Asch, The Silicates in Chemistry and Commerce, Van Nostrand, New York, 1911, p. 95. 4 See paper No. II of this series, J. Am. Chem. Soc. (in press). 6 Rosenheim and Jaenicke, Zeits. anorg. Chem., 101, 242, 1918. Astbury and Yardley, Phil. Trans. R. Soc. London, A224, 221, 1924. 7 Asch and Asch, ref. 3. 8 Glocker, Materialprafung mit RMntgenstrahen, Springer, Berlin, 1927, p. 274. 9 Asch and Asch, The Silicates in Chemistry and Commerce, Van Nostrand, New York, 1911, p. 281. Rosenheim and Jaenicke, Zeit. anorg. Chem., 100, 319, 1917.

BINARY SOLUTIONS OF CONSOLUTE LIQUIDS* By WILDER D. BANCROFr AND H. L. DAVIS DSPARTMONT oF CHEMaSTRY, CORNALL UNIVSRSITY Communicated November 26, 1928

It has long been known that the change of the partial pressure with the concentration for ideal solutions can be given accurately over the whole range of concentrations by the so-called Raoult law'

N1

_

p2-P 2

N1 + N2

I

P2

where the first term is the mol fraction in the liquid phase and P2 and P'2 are the vapor pressure of the pure solvent and the partial pressure of the solvent in the solution, respectively. We have found empirically that the behavior of other pairs of solutions can be represented with unexpected accuracy by the equation

(G/M

a

=

2P2-

II

P2p'2 \G2/M2/ where M1 and M2 are the gram-molecular weights of the two components in the vapor, while a and K are empirical constants, which are obtained,

CHEMISTRY: BANCROFT AND DAVIS

Vo.O. 15, 1929

9

at present from the experimental data. Of course the ratio (Ml/M2)5 can be combined with the K to form a new constant if desired. The value of K varies with the units selected; but that of a is independent of the units. If a and K are each unity, equation II becomes identical with equation I and therefore equation I is merely a special case under equation II. The units, in which the concentrations are expressed, can be adjusted so as to make K equal to unity. If Si and 52 are values so adjusted, we have

(S1Y = (p2p P2)

III

By a simple transformation this becomes Sa,S +S02 + Sa2

-PP2i2IV

which is probably the form to be used for a thermodynamical deduction. In tables 1 and 2 we give some data to show the validity of equation II in selected cases where at least one of the components is an associated liquid. In table 1 are the data by Dobson2 for ethyl alcohol and water at 250C. and in table 2 the data by Sameshima3 for acetone and ethyl ether at 30'C. and 200C. TABLE 1

ETHYL ALCOHOL AND WATER AT 250 pw, - P'Iw = log K1 = 0.6670 0.61 log Gals IP Gw - log - log pale

0.55 log W

Glac

GRAM % ALCOHOL in LIQUID

0.0 12.36 20.51 28.40 33.90 39.92 50.46 56.50 71.09 78.07 90.12 100

LOG K1 CALCD.

.... 0.8030 0.6847 0.6653 0.6697 0.6636 0.6791 0.6724 0.6678 0.6663

0.4979 ....

P

- log K2 = 0.0030

Palo p' WATER

POUND, 1M.

CALMD.,

23.75 22.67 21.78 21.15 20.79 20.36 19.60 19.01 17.31 16.18 10.68 0

LOG

K2

p 'ACOHOL CALCD.,

POUND,

CALCD.

MM.

...

....

22.39 21.70 21.13 20.77 20.38 19.50 18.95 17.30 16.19 12.98

1.8034 1.9185 0.0035 0.0028 0.0260 0.0048 0.0160 1.9948 0.0037 0.0829

0.0 10.50 16.66 22.27 24.90 26.85 30.73 32.16 36.64 39.53 47.40

....

59.01

.

MM.

...

15.1 19.07 22.26 24.25 27.3 30.68

31.73 36.89 39.51 45.50

The equation gives Dobson's values for the partial pressures of water

10 10CHEMISTR Y: BA NCROFT AND DA VIS

PRoc. N. A. S.

very well through 78 gram per cent of alcohol. The equation describes Sameshima's data very well over practically the whole range. If we know the equations for acetone and methyl alcohol, and for acetone and water, for instance, we can calculate what solutions will have the same partial pressures of acetone and consequently what solutions would be in TABLE 2 ACETONE AND ETHYL ETHER AT 30 AND AT 200 NEt - log No - P'Ac = log K 0.88ogNAo P'Ac = log K80 0.17; log K20 = 0.20 MOL

%

Y8a

FOR

ACSTONS

LOG Kao

POUND

IN LIQUID

CALW.

MM.

0.0

3.87 13.27 25.09 34.54 49.58 65.07 70.47 83.81 93.37 95.28 97.99 100.00

....

0.1601 0.2029 0.2011 0.1772 0.1675 0.1556 0.1663 0.1593 0.2224 0.2048 0.1712 ....

0.0

21.8 66.2 106.7 132.4 167.5 201.2 213.7 243.1 266.8 270.6 276.6 282.7

ACSTON$

CALCD.

MOL % ACETONE

MM.

IN LIQUID

...

22.3 62.4 102.0 131.4 167.9 203.2 214.0 243.8 265.0 269.4 276.6 ...

0.0

5.2 12.71 24.90 45.70 61.21 66.62 84.16 88.83 93.17 93.58 97.90 99.59 100.00

LOG Kso CALC. ....

0.1828 0.2012 0.1916 0.1706 0.1623 0.1677 0.1544 0.1946 0.2137 0.2103 0.2032 0.1244 ....

P'g FOR ACSTONS CALCD.

FOUND MM.

MM.

0.0

19.6 41.8 70.2 105.2 126.8 135.2 160.5 167.9 174.5 175.0 181.4 184.1 185.2

20.3 41.7 71.0 106.8 127.5 137.9 162.6 168.1 174.2 174.8 181.3 184.3

equilibrium if methyl alcohol and alcohol water were, and could be kept, completely immiscible. If the concentration of acetone in grams per gram of methyl alcohol is G1 and in grams per gram of water is G2 we can deduce the equation for the distribution of acetone between methyl alcohol and water GIGl °82 = const. In the Cornell laboratory Mr. Morton measured this distribution using a rubber membrane to keep the methyl alcohol and water apart. The experimentally found value was 1.09 as against the value of 1.08 calculated from the ratio of the exponents in the two-component systems. From this it follows that the exponent "a" in equation II is some measure of the relative polymerizations. * This paper is part of a program now being carried out at Cornell University under a grant to Professor Bancroft from the Heckscher Foundation for the Advancement of Research, established by August Heckscher-at Cornell University. 1 Cf. Hildebrand, Solubility, 24, 59, 1924. 2 J. Chem. Soc., 27, 2866, 1925. 3J. Am. Chem. Soc., 40, 1482, 1918.