Extended geometric method: A simple approach to derive adsorption rate constants of Langmuir–Freundlich kinetics

A new and simple equation has been presented here for calculation of adsorption and desorption rate constants of Langmuir–Freundlich kinetic equation. The derivation of new equation is on the basis of extension and correction to the geometric method which has been presented by Kuan et al. [Kuan, W.-H., Lo, S.-L., Chang, C.M., Wang, M.K., 2000. A geometric approach to determine adsorption and desorption kinetic constants. Chemosphere 41, 1741–1747] for the kinetics of adsorption/desorption in aqueous solutions. The correction is to consider that the concentration of solute is not constant and changes as adsorption proceeds. The extension is that we applied Langmuir–Freundlich kinetic model instead of Langmuir kinetic model to consider the heterogeneity and therefore it is more applicable to the real systems. For solving Langmuir–Freundlich kinetic model, some geometric methods and also Taylor expansion were used and finally a simple and novel equation was derived (Eq. (20)) for calculation of adsorption rate constant. This new method was named “extended geometric method”. The input data of the obtained equation can be simply derived from initial data of adsorption kinetics. Finally the adsorption of methyl orange onto granular activated carbon was carried out at dynamic and equilibrium conditions and the capabilities of extended geometric method were examined by the experimental data.