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

The sorbent concentration ( C s ) effect and sorbate initial concentration ( C 0 ) 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 C 0 . The classical kinetic equations cannot predict or describe the " C s -effect" and " C 0 -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 C 0 ) 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 e 0 ) and the intrinsic rate constant ( k 2 0 ), are independent of C s and C 0 . In addition, the new model relates K t and the rate constant ( k 2 ) to C s and C 0 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 C 0 . The new model predicts that with the increase of C s and C 0 , K e decreases while k 2 increases. Its rationality was confirmed by the literature-reported adsorption kinetic data of heavy metals on inorganic and biomass sorbents with the C -effects.