Estimation of Thermodynamic Equilibrium Constant for Binary and Ternary Cation Exchange Reactions Using Rothmund–Kornfeld and Regular Solution Models in Some Soils and Soil Clays

Abstract

ABSTRACT Rothmund–Kornfeld selectivity coefficient (KRK) and regular solution model are rarely used to describe soil exchange data but it seems to be able to satisfactorily predict the true thermodynamic equilibrium constant (Kex). We tested the ability of Rothmund–Kornfeld and regular solution models to predict Kex in binary (K–NH4, Ca–Mg, and K–Ca) and ternary (Na–Ca–Mg) cation exchange systems in clays and soils with different dominant mineralogies. Applying the Rothmud–Kornfeld model to the exchange data indicated the preference of K over Ca and NH4, and Ca over Mg in binary, and Ca over Mg in ternary exchange systems. Similar results were obtained on the preference of cations by different exchangers when the regular solution model was applied to describe the exchange data. Despite the different assumptions of Rothmund–Kornfeld and regular solution models to approximate the activity coefficient of the ions on the exchange phase, similarity between the value of selectivity coefficients obtained by these two models was observed in homovalent cation exchange reactions. Also, a close agreement was observed between the value of selectivity coefficients obtained by these two models and Kex. However, in heterovalent cation exchange reactions, Rothmund–Kornfeld and regular solution models did not provide accurate estimation of the Kex. But these models can correctly indicate the overall preference of one ion to another as Kex. The results suggested Rothmund–Kornfeld and regular solution models can be applied satisfactorily in clay and soil systems as a rapid method to estimate Kex, especially in homovalent exchange reactions. Abbreviation KRK : Rothmund–Kornfeld selectivity coefficient; Kex: True thermodynamic equilibrium constant; ƒ: Exchange-phase activity coefficients; NP: Thermodynamic non-preference; E: Equivalent fractions of ion in exchange phases; Ẽ: Equivalent fractions of ion in solution phases; KRS: Regular solution selectivity coefficient; Kv: Vanselow selectivity coefficient; ∆Gex: Gibbs free energy change