The Thermodynamics of Ternary Cation Exchange Systems and the Subregular Model

Abstract

The thermodynamic theory of ternary exchange equilibria is developed. It is shown that the analogs of well‐known thermodynamic expressions for binary exchange systems can be derived for ternary systems as well. The subregular model of ternary cation exchange systems, which was applied recently to NH4‐Ba‐La exchange on montmorillonite, is examined critically within the thermodynamic context. It is found that the subregular model for a ternary system cannot be expressed solely in terms of parameters that depend only on data obtained for binary systems, in contradiction with claims made recently in the literature. The subregular model is shown to contain one parameter that requires ternary exchange data for its evaluation. A calculation of this ternary constant for NH4‐Ba‐La exchange on montmorillonite indicated that its value was zero within experimental precision. Nonetheless, in general it must be concluded that the behavior of ternary exchange systems cannot be predicted from data on binary exchange systems alone.

Ca-K-Na exchange equilibria on a smectitic soil: Modeling the variation of selectivity coefficient

“…Modeling the variation of the selectivity coefficient The subregular solution model introduced by Elprince et al (1980) and Chu and Sposito (1981) to descri be the variation of the exchanger phase activity coefficients in ternary exchange systems contains a model parameter which needs to be determined from ternary experimental data. Fletcher et al (1984), Sposito et al (1983), and Sposito and Fletcher (1985) showed that the magnitude of the parameter is negligible in view of the experimental error involved in the determination of the equilibrium ionic composition.…”

Sodium-calcium, calcium-potassium, and potassium-sodium exchange equilibria on a montmorillonitic soil

“…This restriction in the thermodynamics of ion exchange was removed by Chu and Sposito (1981) who extended these general thermodynamic relations so Present address: Division of Soils and Agronomy, Regional Agricultural Research Center, Bombuwela, Kaltara, Sri Lanka. that activity coefficients in ternary cation exchange systems could be computed from relevant experimental data.…”

A Multiresponse method for fitting solid-phase activity coefficient models to ternary ion-exchange data

“…(5). One is the popular method of fitting a polynomial to plots of K v as a function of composition and then integrating the polynomial (Barri and Rees, 1980;Sposito, 1981;Chu and Sposito, 1981). The result of this integration is the K eq .…”

“…There are a number of models available for the activities of the solid-phase ions (Truesdell 1966;Smith and Woodburn, 1978;Chu and Sposito, 1981;Pabalan, 1994;Bond, 1995;Snyder and Cavallaro, 1997), all of which have some empirically determined parameters. This study uses the class of polynomials introduced by Cox (1971) to model mixtures, augmented with the inverse-terms model proposed by Draper and St. John (1977).…”

“…A number of models are available for estimating both the solid and aqueous-phase activity coefficients (Truesdell 1966;Smith and Woodburn, 1978;Chu and Sposito, 1981;Zemaitis et al, 1986;Pabalan, 1994;Bond, 1995;Snyder and Cavallaro 1997). A large amount of data is available to calculate the aqueous-phase activity coefficients for most ions of interest under the most common concentration ranges (Zemaitis et al, 1986).…”