Review of the theory of electrolytic conductance

Abstract

The Ostwald dilution law, based on the Arrhenius hypothesis of electrolytic dissociation, was the first theoretical formulation of the dependence of conductance on concentration. While it adequately described the conductance of weak electrolytes, it could not account for the observation by Kohlrausch that, at low concentrations, the equivalent conductance Λ of strong electrolytes approached linearity inc 1/2, the square root of concentration. Debye and Huckel (1923) assumed complete dissociation and calculated the theoretical behavior of rigid charged spheres moving in a continuum (the primitive model); the result was prediction of the Kohlrausch result. Onsager (1927) predicted the exact numerical value of the limiting slope for the Λ vs.c 1/2 curves. Bjerrum (1926) suggested association of ions to pairs which would not contribute to the long-range interionic effects considered by Debye and Huckel. Fuoss and Kraus (1933) corrected the Ostwald dilution law for the DHO square-root terms and obtained a Λ(c) function which satisfactorily accounted for conductance curves which lay below the limiting tangent. Investigations of the effects of higher terms which had been neglected in the classical DHO treatment of the primitive model led to Λ(c) functions which lay above the limiting tangent for completely dissociated electrolytes. By combining these higher-term equations with Bjerrum pairing, a generally useful conductance function was obtained (Fuoss-Hsia, 1957). In order to eliminate a number of inconsistencies between the properties of real systems and those of the primitive model, a new model (Fuoss, 1975) was proposed: Ion pairs are defined as those whose center-to-center distance lies in the rangea≤r≤R, whereR is the diameter of the Gurney cosphere. Later (1977) the paired ions were divided into two categories: ions which have only solvent molecules as nearest neighbors, and ions which have one ion of opposite charge as a member of the inner shell. The latter contribute only to charging current.