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On the Use of the Langmuir Equation in the Interpretation of "Adsorption" Phenomena¹

ABSTRACT

A theoretical discussion in terms of molecular theory and the results of model experiments are employed to demonstrate that the conventional analysis of "anion fixation" data, through linear least squares regression of the points in a Langmuir plot, usually will not be sensitive enough to show the failure of the Langmuir equation whenever solubility product considerations are essential in the fixation reaction. The theoretical discussion points out that although the Langmuir equation is not restricted to two-dimensional phenomena (i.e., adsorption), it cannot apply if the reacting anions must be present at some threshold concentration before fixation occurs. An analysis of model experiments on the reactions of OH^- with Al- or Fe-resin and of Cl^- with Ag-resin shows that secondary precipitation phenomena always result in a statistically significant, linear correlation of the variables in a Langmuir plot if the concentration of the reacting anions is much larger than the threshold value needed to initiate precipitation of the secondary solid phase. This condition generally can be expected to be met when anions such as o-phosphate react with soils or soil constituents. Therefore, the Langmuir equation usually will appear to apply, on the basis of a statistical analysis, even when its applicability is impossible in principle. It follows that the Langmuir equation cannot be used statistically to determine whether adsorption or precipitation (formation of secondary minerals) is occurring during anion fixation reactions in soils and that the parameters in the Langmuir equation cannot be interpreted in terms of surface reactions without additional, independent evidence that only adsorption is involved in anion fixation.

¹ Contribution from the Institut für Ökologie-Bodenkunde der Technischen Universität, Berlin, 1 Berlin 33, Engerallee 19–21, West Germany, and the Dep. of Soil and Env. Sci., Univ. of California, Riverside, CA 92521.

² Soil Scientist and Associate Professor of Soil Science, respectively. Present address of the senior author: Institut für Anorganische Chemie der Freien Universität, Berlin, 1 Berlin 33, Fabeckstrasse 34/36, West Germany.

Received for publication December 19, 1975. Accepted for publication April 6, 1977.

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