Pseudo-Second-Order Kinetic Equation for Describing the Effect of Sorbent and Sorbate Concentrations

The sorbent concentration (C_s) effect and sorbate initial concentration (C₀) effect are common phenomena observed in the study of adsorption kinetics at solid-liquid interfaces. That is, adsorption rate constants simulated with classical kinetic equations, such as the pseudo-second-order (PSO) model, for a given system vary with C_s and C₀. The classical kinetic equations cannot predict or describe the "C_s-effect" and "C₀-effect" (called "C-effects" here). In the current work, the dynamic partition coefficient of sorbate between solid and liquid phases (K) was used to describe the adsorption kinetic processes. Based on the surface component activity (SCA) model, which assumes the activity coefficients of the surface components (f_s) are not equal to unity but rather a function of C_s and the adsorption capacity (or C₀) and referring to the classical PSO model, a new kinetic equation was established, called the "SCA-PSO kinetic model", and its two parameters, the intrinsic equilibrium partition coefficient (K_e⁰) and the intrinsic rate constant (k₂⁰), are independent of C_s and C₀. In addition, the new model relates K and the rate constant (k₂) to C_s and C₀ via f_s, and can thus describe the C-effects. The f_s can be estimated from the change of equilibrium partition coefficient (K_e) with C_s and C₀. The new model predicts that with the increase of C_s and C₀, K_e decreases while k₂ increases. Its rationality was confirmed by the literature-reported adsorption kinetic data of heavy metals on inorganic and biomass sorbents with the C-effects.