Critical of linear and nonlinear equations of pseudo-first order and pseudo-second order kinetic models

The experimental adsorption equilibrium of Cd(II) onto chitosan (Cd(II)/CS) and methyl orange onto bentonite (MO/Bt) were studied in batch adsorption experiments at room temperature for an initial concentration of 236.5 mg/L for Cd (II) (pH = 5) and 33 mg/L for MO (pH = 3). The adsorption rate increases rapidly for t < 30 min, and the equilibrium is reached after this contact time for both systems. The values of the experimental maximum amount of Cd(II) and MO adsorbed are qe = 56.70 and 56.55 mg/g for Cd/CS and MO/Bt, respectively. The obtained experimental data were analysed using the linear and the nonlinear forms of pseudo-first and pseudo-second order kinetic models (LPFO, NLPFO, LPSO, NLPSO). The appropriate model to describe the adsorption kinetics of each system was determined based on the comparison of R2 and the standard deviation Δq (%). It was found that the adsorption process of Cd(II)/CS followed NLPFO and that of MO/Bt can be described by both of NLPSO and LPSO. The results show that the nonlinear forms (NLPSO and NLPFO) are suitable for describing the kinetics adsorption reactions in the liquid phase and the LPSO (qt = f(1/t) model can also be suitable for some systems, depending on the experimental conditions. Because of qt values, determined from these models correspond well to the experimental data as confirmed by the error analysis values of R2 and Δq (%), it is noticed that the determination of R2 alone is insufficient to decide among the kinetic models.