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The kinetics of solute adsorption at the solid/solution interface has been studied by statistical rate theory (SRT) at two limiting conditions, one at initial times of adsorption and the other close to equilibrium. A new kinetic equation has been derived for initial times of adsorption on the basis of SRT. For the first time a theoretical interpretation based on SRT has been provided for the modified pseudo-first-order (MPFO) kinetic equation which was proposed empirically by Yang and Al-Duri. It has been shown that the MPFO kinetic equation can be derived from the SRT equation when the system is close to equilibrium. On the basis of numerically generated points ( t, q) by the SRT equation, it has been shown that we can apply the new equation for initial times of adsorption in a larger time range in comparison to the previous q vs radical t linear equation. Also by numerical analysis of the generated kinetic data points, it is shown that application of the MPFO equation for modeling of whole kinetic data causes a large error for the data at initial times of adsorption. The results of numerical analysis are in perfect agreement with our theoretical derivation of the MPFO kinetic equation from the SRT equation. Finally, the results of the present theoretical study were confirmed by analysis of an experimental system.

Removal of pollutants from aqueous solution is an important process, and adsorption is one of the most popular methods for this. Wastewater usually contains several solutes, and therefore the adsorption process in some systems is competitive. The lack of an adequate model for kinetics of competitive adsorption and also difficulties in modeling led only to the reporting of experimental data in most publications. Here we propose the first description of the competitive adsorption kinetics at the solid/solution interface based on the statistical rate theory (SRT) approach. For derivation of rate equations based on the SRT approach, at first we derived the chemical potential of adspecies for a competitive adsorption based on statistical thermodynamics from the partition function of a canonical ensemble. The derived kinetic equations for competitive adsorption are able to describe quantitatively the kinetics of some experimental data. Since the analytical solution of the derived rate equations led to complex expressions, we used stochastic numerical simulation for modeling of experimental data by the derived SRT equations. The present study shows that the stochastic numerical simulation is a powerful technique for modeling adsorption kinetics based on statistical rate theory.

Desorption is one of the popular methods for the design and regeneration of catalysts. For better understanding and modeling of this process, it is important to have models with theoretical basis. In the present work, the statistical rate theory (SRT) approach was used for the description of desorption kinetics at the solid/solution interface. Based on the SRT approach, two rate equations at initial times of desorption have been derived. A comparison between these two rate equations was done based on numerically generated kinetic data points ( t, q) by the SRT equation. On the basis of experimental data, it has been shown that the kinetics of desorption can be analyzed by the SRT rate equation. Also, the experimental data approve the accuracy of derived rate equations at initial times of desorption.

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