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_t) 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_t 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.