A molecular theory of Setchenov's salting-out principle and applications in mixed-solvent electrolyte solutions

Abstract

An exact molecular theory is developed to express the salting-out behavior of solute species in mixed-solvent (more than one solvent) electrolyte solutions. The starting point is the Kirkwood-Buff solution theory. The Setchenov constant can be shown to be a special case (at infinite dilution) of the general theory. The new formula involves the partial molar volumes of the components and the isothermal compressibility of the medium. In addition, it contains the direct correlation function integrals for solvent-salt interactions. Furter's theory of relative volatilities is shown to be related to Setchenov's equation and the molecular-based equation. All these equations express the affinities of the solvent and cosolvents toward the salt in the solution. Low affinity (for a particular solvent-salt pair) means salting-out of this solvent. When combined with the Gibbs-Duhem relation, the affinity equations result in a differential equation for the activity of a single solvent which can be numerically solved. This affords a means of obtaining the activities of solvents individually in the mixture. We test the new approach for two ternary solutions, methanolwaterLiBr and methanolwaterLiCl, by applying an empirical affinity equation. For the ionic activities, we use the mean spherical approximation expressions. Comparison with experimental data shows that the agreement is close for the vapor-liquid equilibria of these ternary systems. Generalization to higher-component systems is outlined.