Binding stoichiometry in sorption of divalent metal ions: A theoretical analysis based on the ion-exchange model

Abstract

Two stoichiometric assumptions have been compared for describing divalent metal ion binding by protonated sorbent/biosorbent. The first one corresponds to the classical model in which each metal ion (M) binds to two binding sites (X) forming a single MX(2) complex while the second one, proposed by Schiewer and Volesky and used for description of biosorption equilibria, assumes the existence of M(1/2)X complexes. Mathematical expressions corresponding to both these models have been developed by applying the ion-exchange model and methods of statistical thermodynamics. The M(1/2)X model appears to be nonphysical because it does not take into account the basic fact that two sites binding one metal ion must be neighboring. On the other hand, this latter assumption is the part of the MX(2) model which has been shown using Nitta's approach. Nevertheless, equations associated with the M(1/2)X model can be successfully used for description of the experimental data as they can simulate quite well the behavior predicted by the MX(2) model. This is especially true when considering the range of relatively high metal concentrations in the bulk solution and significant degree of surface heterogeneity characteristic of the sorbent surface.