Modeling of the complex formation of metal ions with humic acids

Based on the conceptual model of cation-humic interactions considering the heterogeneous composition and polyelectrolyte nature of humic acids, the description of the interaction by the expression, log K_app = log K - m log [M] + a log α b log [Na⁺], is proposed, where K _app = [M··(zR)]/([M][R]), [M··(zR)] is the concentration of the cation bound to the humic acid, [M] is the concentration of the free cation with charge z, and [R] is the concentration of the free anionic sites of the humic acid, [R] = (C_R - z[M··(zR)])α (C_R is a total concentration of proton exchanging sites and α is a degree of dissociation), log K, m, a and b are the constant parameters depending on the cation and the humic acid. The expression is successfully applied to the experimental results on the complex formation (or protonation) of humate and polyacrylate (a homogeneous polymeric weak acid) with H⁺, NpO2⁺, Eu³⁺, Ca²⁺, Fe²⁺ and Fe³⁺ obtained under the condition where hydrolysis of cations and saturation of the reacting sites can be neglected.