The influence of dielectric saturation on the thermodynamic properties of aqueous ions

Abstract

An examination is made of the applicability of the simple electrostatic (Born) model for ions in aqueous solutions, with special reference to the expressions for free energy z$^{2}$e$^{2}$/2r$\epsilon $, and entropy, (z$^{2}$e$^{2}$/2r$\epsilon $) ($\partial $ ln $\epsilon $/$\partial $T). The model is found to be valid to a useful first approximation, but the deviations are significant, particularly for ions of high charge and small radius. Theories of the dielectric constant of water and of its variation with field strength are applied to the case of monatomic ions in aqueous solution, and give rise to an interpretation of the experimental free energies and entropies that is more satisfactory than the simple model. If $\overline{S}_{\text{e.s.}}^{0}$ is the electrostatic contribution to the entropy, $\overline{S}_{\text{e.s.}}^{0}$/z$^{\frac{3}{2}}$ is found to be a continuous function of z$^{\frac{1}{2}}$/r, and the Born equation is closely applicable to entropies for values of z$^{\frac{1}{2}}$/r less than about 0$\cdot $4. In the case of free energy the Born equation applies over a wider range, up to z$^{\frac{1}{2}}$/r values of about 0$\cdot $8.