Simulation of chemical element adsorption, release, and transport is possible without the need to perform time consuming, detailed adsorption studies on multiple samples by incorporating prediction equations into chemical speciation–transport models before simulating. Adsorption models also assume that the chemical species in a mixture is at chemical equilibrium which is the state in which the chemical activities or concentrations of the reactants and products have no net change over time. By the second law of thermodynamics, a mixture of chemicals satisfies its chemical equilibrium state (at a constant temperature and pressure) when the free energy of the mixture is reduced to a minimum. In this study a constant capacitance chemical surface complexation model was applied to simulate selenate (Se(IV)) adsorption on iron and aluminum oxides by optimizing monodentate Se(IV) surface complexation constants and surface protonation constants. Samples selected for variation in chemical properties were used. The composition of the chemicals satisfying its chemical equilibrium state was found by minimizing the function of the free energy of the mixture using PROC IML. Non linear least squares optimization was developed using PROC NLP to fit the equilibrium surface complexation constants specifying initial and boundary values. A general non linear multiple regression model was fit ted using PROC NLMIXED to the measured adsorption using easily measured soil parameters. Good fit of the model predicted and the experimental data indicated success of the protocol
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