Metal-Humate Interactions. 1. Discrete Ligand and Continuous Distribution Models

In this paper we examine critically the theory underlying discrete and continuous multiligand models for metal-humate binding. The concepts and equations that unify the various models are presented, and a general solution to the fundamental integral equation for ion binding in a multiligand system is given. Particular attention is paid to the continuous distribution models (normal distribution, affinity spectrum, and continuous stability function) which are relatively new tools in the field of metal-humate complexation. It is shown that the lower half and extreme right of the Gaussian ligand distribution assumed in the normal distribution model never affect metal speciation measurably and hence are not “knowable”. It is also shown that an affinity spectrum does not correspond to an actual distribution of ligands; rather, each peak in the spectrum indicates the most probable stability constant controlling metal binding in a particular region of the experimental formation function. Application of the affinity spectrum model leads to a set of discrete ligands. A close examination of the continuous stability function model shows that it contains implicitly the same assumption as the affinity spectrum approach and thus leads also to discrete ligands.