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ABSTRACT
A rigorous, mathematical representation of a sorption isotherm as a Stieltjes transform is employed to prove a theorem about the "two-surface" Langmuir equation. This theorem states that, if the distribution coefficient for an ion sorbed by a soil is a finite, decreasing function of the amount sorbed, q, and extrapolates to zero at some finite value of q, then the sorption isotherm can always be represented mathematically by a two-surface Langmuir equation. Since the proof of this theorem does not depend on the chemical mechanism of ion sorption, it follows that the adjustable parameters in the two-surface Langmuir equation cannot be interpreted in terms of surface reactions without additional, independent evidence that only adsorption on two kinds of surface site actually is involved in the ion sorption reaction.
1 Contribution from the Institut National de la Recherche Agronomique, Station de Science du Sol, Versailles, France, and the Dep. of Soil and Environmental Sciences, University of California, Riverside, CA 92521.
2 Visiting fellow (I.N.R.A.) and Professor of Soil Science, Univ. of California.
Received for publication January 7, 1982. Accepted for publication July 20, 1982.
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