Analysis of the heterogeneous rate of dissociation of Cu(II) from humic and fulvic acids by statistical deconvolution

Abstract

Pseudo first-order rate constant data of the dissociation of Cu(II) species from humic substances in a variety of chemical environments is considered. This data is observed to be widely heterogeneous under moderate environmental conditions, and a continuous distribution of rate constants is needed to adequately model the data. The rate constant distribution is optimally estimated with regularized least-squares and expectation-maximization (EM), and the different methods of solution yield different degrees of heterogeneity for each experiment. This behavior distinctly illustrates the pitfalls of widely heterogeneous rate constant analysis. Under these circumstances the solution of maximum entropy is dictated by the precepts of information theory. This solution corresponds to the EM solution for all the data considered in this study. The EM spectra of Cu(II) dissociation from humic and fulvic acids under various environmental conditions are reported. Interpretation of the spectra in terms of plausible humic chemistry is offered, and cautions appropriate for this type of kinetic analysis are delineated.