An approach for the explicit determination of adsorption isotherms constants and its validation by experimental data

Adsorption behavior of most of the batch mode adsorption processes are defined by non-linear isotherms models such as Redlich-Peterson, Radke-Prausnitz, Sips, Koble–Corrigan- model, etc. To determine the isotherms’ parameters of this type of adsorption models, a trial and error based optimization methods are inevitable which are time consuming as usually are sensitive to the chosen first guess. Therefore, in the present paper an explicit method with no need to trial and error for the determination of the non-linear adsorption models’ parameters was presented. In this approach, first the differential form of the adsorption isotherm is achieved and then the exponential parameter is determined through the intercept of this equation. Having the exponential parameter in hand, the other constants of the isotherm are obtained from the slope and intercept of the linear plot of the concentration and the adsorption capacity. To validate the method, catecholamine modified polysulfone was synthesized for the adsorption of chromium (VI), and different adsorption models were fitted to the resultant data. In the exponential parameter determination, in comparison with the trial and error method, the relative error was less than one percent.