April, 1962
PARTIAL
MOLALVOLUME
OF
GASES I N SOLUTION
597
THE THERMODYNAMIC PROPERTIES OF GASES IN SOLUTION. I. THE PARTIAL MOLAL VOLUME BY E. B. SMITH Physical Chemistry Laboralory, South Parka Road, Oxford AND
JOHNWALKLEY
Departmat of Chemistry, Imperial College, London, S.W. 7 Remind October 7.1981
An understanding of the partial molal volume of gases in solution is of considerable importance ih the study of the thermodynamic properties of such solutions. The available experimental data for gases in non-polar solvents are summarized and the applicability of various theories is examined. An inconsistency in the predictions of regular solution theory is observed. Finally, a simple free volume model is presented which enables the partial molal volume of diasolved gases to be prediatted in a satisfactory manner.
Largely as a result of the research of Professor J. H. Hildebrand over the last half-century, a general understaliding of the properties of solutions is now possible. Regular solution theory has provided a basis by which solubility can be predicted with a remarkable over-all success. Many details remain t b be filled in and we may be confident that Professor Hildebrand will, in future years, be active in their solution as he has been in the past. The more recent research of Professor Hildebrand and co-workers on the properties of gases dissolved in non-polar solvents has shown that the develdpment of an adequate theory for these systems remains one of the outstanding problems of solution theory. Progress in this field long has been hampered by a lack of reliable data, but the recent research of Hildebrand,' of Clever,2 and of Gjaldbaeka now has produced accurate solubility data extending over a wide range of solvent and solute molecules. These workers confirm, in general, the earlier data of Lannung4and of Horiuti.6 As yet no detailgd theoretical analysis has been made for gases in solution though several workersZlshave applied regular solution theory to their experimental results. In all cases, however, the actual prediction of gs~ssolubility has involved the use of most unrealistic parameters which, as will be discussed later, lead to completely unacceptable values when used in the prediction of other relevant data. The volume change on mixing for a dissolved gas is a most important thermodynamic property, yet only tl few workers have produced experimental values for the partial molal volumes of gases dissolved in non-polar solvents (Table I), and these of limited a c c ~ r a c y . ~ ~ No ,~-~ attempt has been made to interpret such data on the basis of an ac(1) (a) L. W. Reevea and J. H. Hildebrand, J . Am. Chem. Sac., 79, 1313 (1957); (b) J. E. Jolley and J. H. Hildebrand, ibid., 80, 1050 (1958); (c) Y. Kobatake and J. H. Hildebrand. J. Phys. Chem., 66, 331 (1961). (2) (a) H. L. Clever, R. Battino. J. H. Saylor, and P. M. Gross, ibid., 81, 1078 (1957): (b) H. I,. Clever. J. H. Saylor. and P. M. Grosa, ibid., 62, 89 (1958); (0) H. L. Clever. ibid., 62, 375 (1958). (3) (a) J. C. Gjaldbaek and J. H. Hildebrand, J . A m . Chum. SOC.. 71, 3147 (1949): (b) J. C. Gialdbaek, Acta Chem. Scand., 6 , 1398 (1952). (4) A. Lannung, J . A m . Chem. SOC.,62, 68 (1930). (5) J. Horiuti. Sci. Papers Inat. Phua. Chem. Ressarch Tokyo, 17, 125, No. 341 (1931). (6) R. H. Schumm and 0. L. I. Brown, J . A m . Cham. SOC.,76,2520 (1953). (7) J. walkley and J. E. Hidebrand, ibid.. 81,4439 (1959).
ceptable model using fundamental gas and solvent parameters. TABLE I EXPERIMENTAL PARTIAL MOLALVOLUMEAT 25' a
GFio CiFid i-C& C&
cc4
Cs&
cs2
6.0 6.1 6.9 7.5 8.6 9.2 10.0
Ar
54 51 50 44 43 45 CO
Ccl,
Nt
CHI
CF4
HI
(CM.)) DI
66.1 68.4
54.4 52.9
56.6 55.4 52.5 52.4 53 52 56.1
85.4 86.4 79.7 38 83.2 35.2 32.7 85.4
Os
CIHI
8 . 6 52.5 45.3 61
CO:
NO
48
47
Regular Solution Theory.-In the case of liquid and solid solutes considerable success in the understanding of solubility has been obtained by the use of the regular solution theory.+'O This theory gives for the solubility of a gas" -log Xt = -log
Xl'd
+
v2 (8,
- 6*)'/4.575T
(1)
where X2is the mole fraction of a gas in a saturated solution, X 2 i d is the ideal solubility, Vn is the molal volume of the gas in its reference state (the pure liquid), and 61 and 62 are the solubility parameters of the solvent and solute, respectively. The main diaculty in the application of eq. 1 is the choice of a suitable value for VZ. Clever2 selected the critical volume of the gas and was able to find a solubility parameter for each gas which gave a reasonable prediction of the solubility in a series of solvents, using a comparative method to eliminate Xp. Gjaldbaeks took V Zto be equal to the partial molal volume of the gas in CClr solvent and evaluated directly, since Xzidcan be estimated for the gases he examined. For a gas in a series of solvents a reasonably consistent value of 62 was obtained. I gives a list of the values obtained by the Table X above mentioned workers. Using the assumptions of regular solution theory it is possible to evaluate the excess volume change on mixing.lZ In terms of solubility parameters the (8) J. E. Jolley and J. H. Hildebrand, J. Phus. Cham., 61, 791 (1957). (9) E. 8hinoda and J. H. Hildebmnd, ;bid., 61, 789 (1857). (10)'E. B. Smith and J. Walkley, T r a m . Poroday SOC.,118, 220 (1960). (11) Hidebrand and Scott, "Solubility of Non-eleotrolytes," Reinhold Publishing Corporation, New York, N. Y., 1950, p. 224, (12) Reference 11, p. 138.
__ - - ((:as)
111
6
l
t
02
COz
5 1 5 7 c f .
TAHLE I1
- -cas-
(’0
Ik
Xe
.4r
1
