Methods for kinetic analysis of simultaneous, first-order reactions in waters: The kinetic model and methods for data analysis

Abstract The graphical method and the iterative method for analysing kinetic data for metal speciation in waters are described. The graphical method involves successive subtractions of one component from the total concentration of the metal remaining, beginning with the slowest component. The iterative method uses nonlinear regression of the experimental data assuming different numbers of components to obtain the weighted residuals. The number of components which gives a minimum to the sum of squares of the weighted residuals represents the number of kinetically distinguishable components. The weighted residuals should also have a normal distribution throughout the course of the reaction. These methods were applied to simulated data for systems containing three components whose rate constants differed by a factor of two and for some cases by a factor of three. When the concentrations of each component were equal and the ratio of the rate constants equal to two, the values of the rate constants obtained by these analyses ranged from 2 to 19% of the assigned values, but the values for the initial concentrations were as much as 40% different from the assigned values. When the concentration of one component was altered the reliability of its recovered rate constant and initial concentration decreased. The advantage of the iterative method is that no prior knowledge of the number of components, rate constants and initial concentrations is required. It is demonstrated that both of these methods provide simple, reliable ways of analysing kinetic data for characterization of metal species in waters.