Statistical theory of solutions of salts in solvents with low dielectric constant

The statistical theory of solutions according to McMillan and Mayer is applied to solutions of salts in solvents with low dielectric constant. It is shown that the irreducible integrals B₂₀ and B₁₁, which characterize the interaction between two molecules of solvent and between a molecule of solvent and a molecule of dissolved substance, respectively, can be calculated through the partial molar volumes of the components and the isothermal compressibility of the solvent. Their contribution to the second virial coefficient is extremely small for solutions of salts in media with low dielectric constant. By means of a continuum model, the B₀₂ values are calculated as functions of the parameter x=²/DkT³, and an explanation is given for the relationships observed in the association of the salts. An approximate calculation of the effective diameter of the molecules x=²/DkT³ is given for some salts.