THERMODYNAMICS OF SOLUBILITY IN MIXED-SOLVENT SYSTEMS

A general equation for the solubility of a completely-ionized solute which dissolves congruently in a mixed solvent in terms of (a) the solubilities of the solute in the individual solvents, (b) properties of the pure mixed solvent system, and (c) parameters which have molecular significance has been deduced using both classical thermodynamics and exact statistical thermodynamic theory of liquids. The equation from classical thermodynamics contains three terms which sum to zero: an excess logarithmic solubility relative to a defined ideal logarithmic solubility, an excess logarithmic activity coefficient, and an excess standard chemical potential. The ideal logarithmic solubility is linear in the solvent mole fraction. A method is described for estimation of the excess logarithmic activity coefficient if the Pitzer parameters for the salt in one pure solvent and the dielectric constant and density of the pure solvent mixture are known. The remaining term, the excess standard chemical potential, can be correlated with the theory of Kirkwood and Buff to define selective solvation term for the salt as a whole, and this term can be evaluated if the molar volume and the excess Gibbs energy of the solvent mixture are known. Examples from published experimental data are discussed.