Abstract
Rigorous expressions based on the Lennard-Jones (6–12) potential, are presented for the Gibbs and Helmholtz free energy of a dilute mixture. These expressions give the free energy of the mixture in terms of the thermodynamic properties of the pure solvent, thereby providing a convenient means of correlating dilute mixture behavior with that of the pure solvent. Expressions for the following dilute binary solution properties are derived: Henry's constant, limiting activity coefficients with their derivatives, solid solubilities in supercritical gases, and mixed second virial coefficients. The Henry's constant expression suggests a linear temperature dependence; application to solubility data for various gases in methane and water shows a good agreement between theory and experiment. In the thermodynamic modeling of supercritical fluid extraction, we have demonstrated how to predict new solubility-pressure isotherms from a given isotherm, with encouraging results. The mixed second virial coefficient expression has also been applied to experimental data; the agreement with theory is good.
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References
J. H. Hildebrand and R. L. Scott, Regular Solutions (Prentice-Hall, Englewood Cliffs, N.J., 1962), Chap. 6.
J. H. Hildebrand, J. M. Prausnitz, and R. L. Scott, Regular and Related Solutions (Van Nostrand Reinhold, New York, 1970), Chaps. 6 and 8.
H. C. Longuet-Higgins, Proc. R. Soc. (Lond.) A205:247 (1951).
D. Cook and H. C. Longuet-Higgins, Proc. R. Soc. (Lond.) A209:28 (1951).
W. B. Brown and H. C. Longuet-Higgins, Proc. R. Soc. (Lond.) A209:416 (1951).
R. L. Scott, J. Chem. Phys. 25:193 (1956).
I. Prigogine, A. Bellemans, and A. Englert-Chwoles, J. Chem. Phys. 24:518 (1956).
P. J. Wojtowicz, Z. W. Salsburg, and J. G. Kirkwood, J. Chem. Phys. 27:505 (1957); 26:1553 (1957).
D. A. Jonah, K. S. Shing, and K. E. Gubbins, Proceedings 8th Symposium on Thermophysical Properties, Vol. 1, J. V. Sengers, ed. (Am. Soc. Mech. Eng., New York, 1982), p. 335.
T. L. Hill, Statistical Mechanics (McGraw-Hill, New York, 1956), Chap. 3.
J. J. Nicolas, K. E. Gubbins, W. B. Street, and D. J. Tildesley, Mol. Phys. 37:1429 (1979).
K. S. Shing and K. E. Gubbins, Molecular Based Study of Fluids, Adv. Chem. Ser. (Am. Chem. Soc., Washington, D.C., 1983) Chap. 4.
M. M. Abbott and H. C. Van Ness, AIChE J. 21:62 (1975).
D. A. Jonah and S. R. M. Ellis, J. Appl. Chem. 15:151 (1965); D. A. Jonah, Molecular Based Study of Fluids, Adv. Chem. Ser. (Am. Chem. Soc., Washington, D.C., 1983) Chap. 16.
R. T. Kurnik, S. J. Holla, and R. C. Reid, J. Chem. Eng. Data 26:47 (1981).
J. H. Dymond and E. B. Smith, The Virial Coefficients of Pure Gases and Mixtures (Clarendon Press, Oxford 1980).
J. L. Perez, Ph.D. thesis (Universidad Nacional de Mexico, Mexico City, 1977).
T. J. Edwards, G. Maurer, and J. M. Prausnitz, AIChE J. 24:966 (1978).
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Jonah, D.A. Consideration of some dilute-solution phenomena based on an expression for the Gibbs free energy. Int J Thermophys 7, 935–948 (1986). https://doi.org/10.1007/BF00503849
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DOI: https://doi.org/10.1007/BF00503849