Study of a Refined Model for Aqueous 1-1 Electrolytes

Abstract

The hypernetted‐chain integral equation is used to calculate the ion–ion pair correlation functions and the thermodynamic properties of models for aqueous alkali halides based on an ion–ion pair potential function having four terms: the usual Coulomb term, a core repulsion term of order $r^{\text{−9}}$ , a well‐known dielectric repulsion term of order $r^{\text{−4}}$ , and a “Gurney” term to represent the effect of the overlap of the structure‐modified regions, “cospheres,” about the ions when the ions come close together. The only parameter in the potential which is adjusted to fit excess free energy data for solutions is the coefficient $A_{\mathrm{ij}}$ of the Gurney term for the interaction of ions of species $i$ and $j$ . This is scaled so it represents the molar free energy change of water displaced from the cospheres when they overlap. The corresponding entropy change $S_{\mathrm{ij}}$ and volume change $V_{\mathrm{ij}}$ are adjusted to fit, respectively, heat of dilution and apparent molal volume data. Some thermodynamic problems in this fitting process, due to the underlying McMillan–Mayer theory, are considered in detail. Good agreement is obtained between computed model properties and experiment for various sets of these parameters. Detailed results are given for one consistent set of $A_{\mathrm{ij}}$ , $S_{\mathrm{ij}}$ , and $V_{\mathrm{ij}}$ parameters for all the alkali halide solutions for which the required data are available. The $A_{\mathrm{ij}}$ parameters are in the range from 100 to − 200 cal/mole. Since this is small compared to RT, the thermodynamic data for these solutions can be interpreted without assuming rigid hydration of any of the ions, a conclusion previously reached by Rasaiah from the study of quite different models. The trends in $A_{\mathrm{+-}}$ with variation of species do seem to reflect hydration and structure‐breaking effects in the solutions. The sign of $S_{\mathrm{+-}}$ is paradoxical, also in agreement with Rasaiah's results, while $V_{\mathrm{+-}}$ and $S_{\mathrm{+-}}$ seem to be mutually consistent.