4410
NOTES
Solubility of Gases in Mixtures of Nonpolar Liquids -2s
by R. G. Linford and J. H. Hildebrand Department of Chemistry, University of California, Berkeley, California 94790 (Received June 19, 1969) xcu
-2.5
CT
Several experimental determinations have been published’ of the solubility of gases in mixtures of polar liquids, but the more fundamental problem of their solubility in nonpolar liquid mixtures appears to have been attacked only in a theoretical paper by O’Connell and Prausnitz.2 This investigation was undertaken in order to ascertain whether a successful regular solution correlation of values of the solubility of a gas in a series of pure liquids with their solubility parameters is applicable also to its solubility in mixtures of two of these liquids. A relationship between the logarithm of solubility of a gas and the solubility parameters of solvents was pointed out by Hildebrand3 in 1954 and subsequently expanded in later paper^.^ The lines for log xz ( 2 2 = mble fraction of gas) vs. 81, the solubility parameters of the solvents, proved to be curved. Hildebrand6 showed in 1967 that straight lines result by using A2 instead of 61. In the case of Ar, Table I: Solubility of Gases, Mole Fraction, xz a t 1 Atm and 25O, in Mixtures of (1) Benzene, Mole Fraction 21, with (3) CClzF.CClF2,and Square of Solubility Parameter of the Mixed Solvent, &-s2, Calculated from 62 and 68 by Eq 1
Hz
1.000 0.695 0.341 0 Ar 1.000 0.650 0,348 0 CPF6 1.000 0.674 0.359 0 CzHs 1.000 0.776 0.510 0.260 0
2.58” 3.96 5.35 6 . 556 8.77b 16.0 22.2 30. 5d 11.OBe 40.55
85.8 149.4O 151.o c 193.2 238.0 265.4 285. 8E
83.5 70.0 58.5 50.0 83.5 68.5 58.5 50.0 83.5 69.5 59.0
-3.c
-3.5
2 1-3 Figure 1. Linear correlation between the solubility of a gas, XZ, and the solubility parameters of solvents: open circles, pure liquids; closed circles, mixtures of (1) benzene with (3) CClzF CCIFz.
-
for which values of x2 are most abundant and accurate, the straight line extends through the whole range from C7F16 to CSz, with values of 812from 37 to 100. Scott6 in 1950 proposed calculating a solubility parameter for a solvent mixture as the volume fraction average of the parameter of the pure liquids. We follow our convention of designating a “solute,” in this case a gas, by subscript 2, and use subscripts 1 and 3 for the pure solvent liquids. The solubility parameters of our liquid mixtures are calculated by
where the a’s are volume fractions. Gordon and Scott7 applied this equation to solutions of phenanthrene in mixtures of cyclohexane and methylene iodide. Smith, Walkley, and Hildebrands determined the solubility of iodine in mixtures of C7F16 and CC1, and found eq 1 to be applicable. In this paper, we report determinations of the solubility of Hz, Ar, c2H6, and CZFBin mixtures of benzene and CClzF-CC1F2, “Freon 113.” We selected this
50.0 83.5 73.5 63.5 56.0 50.0
a H. W. Cook, D. N. Hansen, and B. J. Alder, J . Chem. Phys., 26,748 (1957). b H. L. Clever, R. Battino, J. H. Saylor, and P. M. Gross, J. Phys. Chem., 61,1078 (1957). J. Horiuti, Sei. Papers, Inst. Phys. Chem. Research, Tokyo, 17, No. 341, 125 (1931). d H . Hiraoka and J. H. Hildebrand, J. Phys. Chem., 68, 213 (1964). e Determined for this study by R. G. Linford; details to be published.
The Journal of Physical Chemistry
-0
(1) R. Battino and H. L. Clever, Chem. Rev., 66,395 (1966). (2) J. P. O’Connell and J. M. Prausnitz, Ind. Eng. Chem. Fundamentals, 3, 347 (1964). (3) J. H. Hildebrand, J . Phys. Chenz., 57,671 (1964). (4) J. H. Hildebrand and R. L. Scott, “Regular Solutions,” PrenticeHall, Englewood Cliffs, N. J., 1962. (5) J. H. Hildebrand, Proc. Nut. Acad. Sci. U.S., 57, 642 (1967). (6) R. L. Scott and J. H. Hildebrand, “Solubility of Nonelectrolytes,” Reinhold Publishing Corp., New York, N. Y.,1960; 2nd ed., Dover Publications, New York, N. Y., 1964, p 201. (7) L. J. Gordon and R. L. Scott, J . Anzer. Chem. floc., 74, 4138 (1952). (8) E. B. Smith, J. Walkley, and J. H. Hildebrand, J . Phys. Chem., 63, 703 (1969).
NOTES pair of liquids because they are nonpolar, noncomplexing with the above gases, and very different in solvent power as indicated by their solubility parameters, 9-15 (cal cm-3 mo1-1)L/2for benzene and 7.05 for the Freon. The latter figure is a revision of one given in ref 4; we now have for its heat of vaporization 35.07 cal g-l from Du Pont Bulletin FST-1; from this and the molal volume, 119.9 cm3 a t 25’, we obtain the new value for its solubility parameter given above. The two solvents were “Spectroquality,” from Matheson Coleman and Bell. The mixtures were degassed in the apparatus by repeated freezing and evacuating; their composition was determined from the density of a degassed sample. The gases were of the highest purity commercially obtainable; they were dried before use. Solubilities were determined in the apparatus designed by Dymond and Hildebrand9 and since used extensively. Table I gives our measured values of the solubility of the four gases in the two pure liquids and 2 or 3 mixtures at 25’, together with values of 61-3’. Figure 1 plots log x2 us. 81-3’ for the mixtures (solid circles) and the pure liquids (open circles) with points added for other pure liquids in order to illustrate the linear relationship existing in both cases. We included C2F6 in order to learn whether its solubility in mixtures of liquids would show peculiarities such as are seen in the zig-zag line for CF4 in different pure liquids. VVe see only that the points for C2F6 in the two mixtures are not so close to the line joining the points for the pure liquids as they are for the other gases. We conclude that the linear relation between the solubility of a gas as log x2 in pure liquids and the square of their solubility parameters is equally valid for its solubility in liquid mixtures if their solubility parameters are calculated as volume fraction averages of the parameter of the component liquids. Acknowledgment. This research was supported by the National Science Foundation. (9) J. H. Dymond and J. H . Hildebrand, Ind. Eng. Chem. Fundamentals, 6 , 130 (1967).
The Limiting Behavior of the Integrand in the Robinson and Sinclair Equation
by Chai-fu Pan Department of Chemistry, Alabama State University, Montgomery, Alabam,a 36101 (Received June 86,1969)
The isopiestic vapor pressure method of studying aqueous solutions gives directly the osmotic Coefficient of the solution and the activity coefficient of the solute
441 1
can be calculated by means of some form of the GibbsDuhem equation. One convenient form is the Robinson and Sinclair equation’
(1)
where y is the activity coefficient, R denotes the reference electrolyte, m is the molal concentration, and R is the isopiestic ratio. The integrand in eq 1 can be evaluated by graphical methods. In the case of the reference and the test electrolytes are 1: 1 salts, it is stated2 that the limiting value of the integrand in this equation is zero. This, however, has not been proved, nor has the behavior of the integrand for electrolytes of other charge type been investigated. The problem, however, can be solved. The limiting Debye-Huckel equation for the osmotic coefficient is3
where 4 is the osmotic coefficient, Z is the charge number, v is the number of ions per molecule of electrolyte, and for aqueous solutions a t 25”, A = 0.5107 mo1-1/2 The condition for equilibrium in an isopiestic experiment is VRmR$R = Vm4
or R = - V-Rm -R - 4 vm 4~
(3)
From eq 2 and 3 and with the limiting behavior yR + 1, 4~ + 1, and m/mR --t VR/V when mR + 0, we obtain
(4) for an aqueous solution at 25’. The limiting value in eq 4 is obviously zero if both electrolytes are of the same charge type. If the reference electrolyte is of the 1: 1 charge type and the other is of the 2 : 1 charge type, the limiting value is -0.716. An example can be cited to show the validity of this derivation. The isopiestic measurements of Stokes4 on calcium chloride solutions, with sodium chloride as reference salt, include data for four solutions between (1) R.A. Robinson and D. A. Sinclair, J . Amer. Chem. Soc., 56, 1830 (1934). (2) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” revised ed, Butterworth and Co. Ltd., London, 1965,pp 180, 181. (3) G. N. Lewis and M. Randall (revised by K. S. Pitner and L. Brewer), “Thermodynamics,” 2nd ed, McGraw-Hill Book Co., Inc., New York, N. Y., 1961,pp 338,339. (4) R. H. Stokes, Trans. Faraday Soc., 41,637 (1945). Volume 73, Number 12 December 1969
