Abstract
The present paper deals with the application of fluctuation theory of solutions to the solubility of poorly soluble substances of environmental significance in aqueous mixed solvents. The fluctuation theory of ternary solutions was first used to derive an expression for the activity coefficient of a solute at infinite dilution in a binary mixed solvent. This equation contains the activity coefficients of the constituents of the solute-free mixed solvent and the molar volume of the solute-free mixed solvent. Further, the derived expression for the activity coefficient of a solute at infinite dilution was used to generate a number of expressions for the solubility of solids in aqueous mixed solvents. Several expressions for the activity coefficients of the components were considered: first, the mixed solvent was considered an ideal mixture; second, the activity coefficients of the constituents of the binary solvent were expressed using the two-suffix Margules equations; third, the activity coefficients of the constituents of the binary solvent were expressed using the Wilson equations. The obtained expressions were applied to 25 experimental data sets pertaining to the solubilities of hydrophobic organic pollutants (HOP) in aqueous mixed solvents. It was found that the suggested equations can be used for an accurate and reliable correlation of the solubilities in aqueous mixed binary solvents. The best results were obtained by combining our expression for the activity coefficient of a solute at infinite dilution in a mixed solvent with the Wilson equations for the activity coefficients of the constituents of a solute-free mixed solvent. The derived equations can also be used for predicting the solubilities of poorly soluble environmentally important compounds in aqueous mixed solvents using for the Wilson parameters those obtained from vapor-liquid equilibrium data. A similar methodology was applied to the solubility of poorly soluble substances of environmental significance in multicomponent (ternary and higher) aqueous mixed solvents. The expression for the activity coefficient of a solute in an ideal multicomponent mixed solvent was used to derive an equation for the solubility of a poorly soluble solute in an ideal multicomponent mixed solvent in terms of its solubilities in two subsystems of the multicomponent solvent and their molar volumes. Ultimately the solubility could be expressed in terms of those in binary or even in the individual constituents of the solvent and their molar volumes. The computational method was applied to predict the solubilities of naphthalene and anthracene in ternary, quaternary and quinary aqueous mixed solvents. The results were compared with experiment and good agreement was obtained.
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