Collective-Coordinate Treatment of Electrolytes

Abstract

The configuration integral for an electrolyte in a continuous dielectric medium is calculated using the method of collective coordinates. The pair potential energy is taken to be Coulombic (with fixed dielectric constant) for all interionic distances outside some separation a and zero inside. This form permits handling the potential energy completely within the collective-coordinate framework, but has the disadvantage of limiting the concentration to which the treatment is applicable. For low concentrations, the configurational partition function can be approximated to yield an analytic expression for the activity coefficient. For higher concentrations a numerical integration is used to calculate the mean molal activity coefficients for univalent salts in water at 25°C. The theoretical values obtained from the numerical integrations are within experimental error of the observed values up to molalities of 0.30 to 1.0, depending on the salt considered. As the concentration of the electrolyte goes to zero, the activity coefficient correctly tends to the Debye—Hückel limiting law.