Derivation of the Langmuir Equation for Ion Exchange Reactions in Soils

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Abstract
The form of the Langmuir adsorption isotherm equation that is appropriate for ion exchange reactions is derived rigorously using statistical mechanics. It is shown that, in addition to the usual assumptions of localized, monolayer adsorption and no interactions between adsorbed ions, the restriction that the exchange process be one‐to‐one must be imposed. However, there is no inequality condition on the equilibrium solution concentrations and affinity parameters for the exchanging ions as has been suggested previously by several investigators. The Langmuir equation is valid for all nonzero values of the ion activities and affinity parameters.

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