On the use of linearized pseudo-second-order kinetic equations for modeling adsorption systems

Applications of second-order kinetic models to adsorption systems were reviewed. An overview of second-order kinetic expressions is described in this paper based on the solid adsorption capacity. An early empirical second-order equation was applied in the adsorption of gases onto a solid. A similar second-order equation was applied to describe ion exchange reactions. In recent years, a pseudo-second-order rate expression has been widely applied to the adsorption of pollutants from aqueous solutions onto adsorbents. In addition, the earliest rate equation based on the solid adsorption capacity is also presented in detail.

The kinetics of sorption from a solution onto an adsorbent has been explored theoretically. The general analytical solution was obtained for two cases. It has been shown that at high initial concentration of solute (sorbate) the general equation converts to a pseudo-first-order model and at lower initial concentration of solute it converts to a pseudo-second-order model. In other words, the sorption process obeys pseudo-first-order kinetics at high initial concentration of solute, while it obeys pseudo-second-order kinetics model at lower initial concentration of solute. The theoretical results (derived equations) show that the observed rate constants of pseudo-first-order and pseudo-second-order models are combinations of adsorption and desorption rate constants and also initial concentration of solute. The obtained theoretical equations are used to correlate experimental data for sorption kinetics of some solutes on various sorbents. The predictions of the theory are in excellent agreement with the experimental data.