A distribution model for binding of protons and metal ions by humic substances

Abstract

A mathematical model is proposed for the binding of protons and metal ions by humic substances. The totally empirical nature of simple, discrete models that treat humic substances as a mixture of two or three ligands (often erroneously referred to as “classesn of ligands) is clearly demonstrated. The extreme complexity of the mixture of ligands in humic substances suggests that a continuous ligand distribution model would be more appropriate, i.e., a model in which a continuum of log K values for proton or metal binding could be treated. In the proposed model, it is assumed that ligand concentrations are normally distributed with respect to their log K values. A “class” of ligands can then be characterized by its mean log K value (p) and the standard deviation (a) of log K values about the mean. This model has been successfully applied to the complexation of copper(I1) by aquatic humus and by sewage sludge derived fulvic acids. Proton binding by aquatic humus is efficiently described by a similar model that contains two classes of functional groups.