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Thermodynamic Derivation of Equations of the Langmuir Type for Ion Equilibria in Soils¹

ABSTRACT

Classical thermodynamics was employed to derive equations of the Langmuir type with parameters having chemical meaning for homovalent and heterovalent ion exchange processes and for anion-fixation reactions wherein the anion is able to form an insoluble precipitate with some exchangeable cation. The analysis pointed out that the traditional equation of the Langmuir type is not the appropriate equation to describe ion exchange processes because the ion exchanger generally cannot be treated as an ideal solid solution. Nevertheless, for systems with low concentration of one ion in a supporting electrolyte, the solid-phase activity coefficient ratio should be a constant, and an equation of the Langmuir type may describe successfully this portion of the exchange isotherm. It was shown also that anion-fixation isotherms could be completely described by solving simultaneously three equations: a solubility product, a traditional equation of the Langmuir type for cation exchange, and an equivalence equation. Selected experimental data from the literature were utilized to demonstrate the applicability of the derived equations and to determine parameters for comparison and correlation with other data and for the identification of the ionic species undergoing ion exchange.

¹ Contribution from the Dep. of Soils & Water, King Faisal Univ., Alhasa, Saudi Arabia; and the Dep. of Soil & Environmental Sciences, Univ. of California, Riverside, CA 92521.

² Associate Professor of Soil Chemistry and Professor of Soil Science, respectively.

Received for publication November 5, 1979. Accepted for publication November 19, 1980.