Recently, a method for estimating the excess Henry's law constant of a single solid solute in a mixed, binary solvent has been developed [1]. The excess Henry's law constant is defined through
Here index 1 indicate the solute whereas other are for the solvent species. At low solubilities this is essentially equal to the negative ‘excess' solubility. The method is based in statistical mechanical fluctuation solution theory [2,3], which deploys spatial integrals of the radial (pair) distribution function. Using this theoretical approach a simple, linear expression was developed, requiring only a single parameter describing the non-ideality of the solute/solvent pair. The method was successful in describing a wide variety of excess solubility behavior, including nearly ideal systems with small excess Henry's constants, excess Henry's constants that apply to many solutes, and systems which deviate from these simple rules. However, successful the method relied substantially upon an accurate description of the solvent/solvent non-ideality. This was approximated with the Wilson equation [4], which is useful for describing strongly non-ideal mixtures. It was found that some mixtures exhibited behavior which gave excess solubility estimates that was inconsistent with experimental data. To cure this problem, we have investigated the solvent/solvent description through comparison of the Wilson equation with other GE-models. We have also initiated efforts into describing the excess solubility using the integrals of the centers direct correlation function, defined by the Ornstein-Zernike equation [5]. Use of the direct correlation function enables estimation of the direct interaction between molecular pairs, indicating a more precise method. This approach still contains one parameter for each solute/solvent pair, due to the symmetry of the correlation functions.
References
[1] M.E. Christensen, J. Abildskov, J.P. O'Connell, AIChE J. Pending publication.
[2] J.P. O'Connell, Mol. Phys. 20 (1971) 27-33.
[3] J.P. O'Connell, AIChE J. 17 (1971) 658-663.
[4] G.M. Wilson, J. Am. Chem. Soc. 86 (1964) 127-130.
[5] L.S. Ornstein, F. Zernike, Ver. Academ. Wet. 23 (1914) 587-595.
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