Activity coefficients of electrolyte solutions in the modified mean spherical approximation

The Helmholtz free energy of ionic solutions is calculated in the dressed-ion theory (DIT) using a Gibbs–Helmholtz relation. The obtained expression naturally takes into account the occurrence of a process of renormalization of charges and screening length in the bulk which is described by means of the modified mean spherical approximation (MMSA). This process is shown to provoke a decreasing of the electrostatic attractions in the bulk. The chemical potentials and activity coefficients are also a matter of study and a c3/2 dependence on molar concentration is predicted for the deviations from Debye–Hückel limiting law (DHLL) values of these magnitudes, recovering the classical results of Fowler and Guggenheim. Finally, theoretical predictions for the mean activity coefficients of 1:1 restricted primitive model (RPM) electrolytes are seen to fit actual hypernetted chain calculations (HNC) and first- and second-order mode expansions.