3. Kinetic and Equilibrium Models of Adsorption

In adsorption study, isotherms and kinetics of adsorption process provide pieces of information underlying the mechanisms and dynamics of the process. Several equilibrium and kinetic models are usually employed for performing the experimental design of an adsorption system. In this chapter, the Langmuir, Freundlich, Sips, Liu, Redlich–Peterson nonlinear equations, as well as other unusual isotherm models (Hill, Khan, Radke–Prausnitz, Toth) are discussed. For the kinetics of adsorption, the pseudo-first-order, pseudo-second-order, general-order, Avrami fractionary order, and Elovich chemisorption models are explained. The importance of statistical parameters such as coefficient of determination (\(R^{2}\)), adjusted coefficient of determination (\(R_{\text{adj}}^{2}\)), and standard deviation (root of mean square error) are highlighted. The usage of linearized and nonlinearized equations are illustrated and explained. Some common mistakes commonly committed in the literature using linearized equilibrium and kinetic adsorption models as well as other polemic points in adsorption research are pointed out. Analytical techniques together with thermodynamical data of enthalpy and entropy changes are needed to ascertain if an adsorption process is a chemical or a physical process.