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The Thermodynamic Theory of Ion Exchange: A Single-Phase Mixture Formulation

Department of Agronomy and Soils, University of Puerto Rico, Mayaguez, PR

*Corresponding author (v_snyder{at}rumac.upr.clu.edu).

ABSTRACT

A longstanding problem in the thermodynamic theory of ion exchange has been lack of a general method for measuring activities of solid-ion complexes or exchanger species. Existing theory, based on integrating the Gibbs-Duhem relation for a solid exchanger phase immersed in an electrolyte solution, is often subject to uncertainties due to indeterminate amounts of solvent and electrolytes adsorbed onto the exchanger surface. We remove these difficulties by treating ion exchange systems as simple mixtures of solvent, electrolytes, and exchanger species, with no formal partitioning into phases. Through judicious choice of components, an integrable Gibbs-Duhem relation is obtained that can be solved for the activity of any arbitrary exchanger species, requiring only reversibility of the system and measurable solvent and electrolyte activities. The theory is very general in principle and is applicable to variable- and permanent-charge solid exchangers with positive and negative surface charge sites, in electrolyte environments containing any number of competing cation and anion species. In preliminary tests, the theory was used to calculate exchanger species activities and equilibrium constants from published data on binary and ternary NH₄⁺-Ba²⁺-La³⁺ exchange in aqueous montmorillonite suspensions, for constant water potential conditions where the conventional two-phase theory is also considered applicable. Results obtained with the mixture theory exhibited good internal consistency and were generally comparable to results obtained with the two-phase theory.

Received for publication November 20, 1995.