Abstract
The Variational theory of mixtures due to Mansoori and Leland is modified to account for translational quantum effects in solution, and this modified form of the theory is applied to the problem of gas solubilities in liquids. The theory is used to derive expressions for the Henry's law constant, the molar heat of solution at infinite dilution, and the partial molar volume at infinite dilution for a solute in a liquid solution. These expressions are applied, over a range of temperatures, to the following systems; H2 in each of Ar, N2, and CH4; He in each of Ar, N2, and CH4; and Ne in each of Ar and N2. Lennard-Jones 6–12 pair potentials are used for these calculations. The Lennard-Jones parameters are taken from gas-phase second virial coefficient data. The results obtained are compared with experimental data and with previous calculations on these systems based on the Leonard-Henderson-Barker theory. The variational results appear to be in better agreement with experiment for the He-containing systems, while the Leonard-Henderson-Barker theory seems better for the other systems. An explanation for this is suggested.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. A. Barker and D. Henderson,J. Chem. Phys. 47, 4714 (1967).
G. A. Mansoori and F. B. Canfield,J. Chem. Phys. 51, 4958 (1969).
J. D. Weeks, D. Chandler, and H. C. Andersen,J. Chem. Phys. 54, 5237 (1971).
P. J. Leonard, D. Henderson, and J. A. Barker,Trans. Faraday Soc. 66, 2439 (1970).
G. A. Mansoori and T. W. Leland, Jr.,J. Chem. Phys. 53, 1931 (1970).
L. L. Lee and D. Levesque,Mol. Phys. 26, 1351 (1973).
R. O. Neff and D. A. McQuarrie,J. Phys. Chem. 77, 413 (1973).
S. Goldman,J. Phys. Chem. 81, 608 (1977).
G. A. Mansoori,J. Chem. Phys. 56, 5335 (1972).
R. W. Zwanzig,J. Chem. Phys. 22, 1420 (1954).
H. S. Green,J. Chem. Phys. 19, 955 (1951).
S. Kim, D. Henderson, and J. A. Barker,Can. J. Phys. 47, 99 (1969).
T. L. Hill,An Introduction to Statistical Thermodynamics (Addison-Wesley, Reading, Massachusetts, 1960), p. 80.
G. A. Mansoori, N. F. Carnahan, K. E. Starling, and T. W. Leland, Jr.:J. Chem. Phys. 54, 1523 (1971).
J. L. Lebowitz,Phys. Rev. 133, A895 (1964).
H. L. Frisch, J. L. Katz, E. Praestgaard, and J. L. Lebowitz,J. Phys. Chem. 70, 2016 (1966).
F. S. Acton,Numerical Methods that Work (Harper and Row, New York, 1970), pp. 454–458.
J. S. Rowlinson,Liquids and Liquid Mixtures (Butterworths, London, 1969), pp. 46, 48, 51.
T. W. Leland, J. S. Rowlinson, G. A. Sather, and I. D. Watson,Trans. Faraday Soc. 65, 2034 (1969).
D. Henderson and P. J. Leonard, inPhysical Chemistry, An Advanced Treatise, Vol. VIIIB, H. Eyring, D. Henderson, and W. Jost, eds. (Academic Press, New York, 1971), pp. 420, 473, 489.
R. C. Miller,J. Chem. Phys. 55, 1613 (1971).
L. A. K. Staveley,J. Chem. Phys. 53, 3136 (1970).
W. B. Streett,J. Chem. Phys. 42, 500 (1965).
W. B. Streett,J. Chem. Phys. 46, 3282 (1967).
M. Orentlicher and J. M. Prausnitz,Chem. Eng. Sci. 19, 775 (1964).
K. A. Solen, P. L. Chueh, and J. M. Prausnitz,Ind. Eng. Chem. Process Des. Dev. 9, 310 (1970).
W. B. Streett,Cryogenics 5, 27 (1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Goldman, S. On the use of the variational method for interpreting the solubilities of gases in liquids. J Solution Chem 6, 461–474 (1977). https://doi.org/10.1007/BF00645840
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00645840