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On the Use of the Langmuir Equation in the Interpretation of “Adsorption” Phenomena: II. The “Two‐Surface” Langmuir Equation
Author(s) -
Sposito Garrison
Publication year - 1982
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1982.03615995004600060006x
Subject(s) - langmuir , sorption , langmuir adsorption model , adsorption , langmuir equation , thermodynamics , surface (topology) , freundlich equation , ion , sorption isotherm , function (biology) , distribution function , mathematics , chemistry , materials science , physics , organic chemistry , geometry , evolutionary biology , biology
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.