Is one performing the treatment data of adsorption kinetics correctly?

In the literature, the linear form of the pseudo-first-order (PFO) and pseudo-second-order (PSO) models are often applied for fitting the data of adsorption kinetics. Many authors have applied the linear form of the PSO model and concluded that such a kinetics is better fitted, based on the values of adsorption capacity at the equilibrium (q_e) and the high value (which should be close to 1.0) of the coefficient of determination (R²). The linearized PFO model is usually ruled-out because the values of q_e and R² are worse than those obtained by the linearized PSO. On the other hand, the nonlinear fitting of data is highly recommended for the use of equations that are not typically linear such as kinetics data. In this communication, the data of 52 articles (containing 225 experiments of adsorption kinetics) were collected, and the kinetic data were treated using the linear and nonlinear PFO and PSO models. Results indicated that the values of k₂ (the rate constant of the PSO model) calculated from the nonlinear fitting method were quite different from those acquired from the linear one. However, the values of q_e2 (adsorption capacity at the equilibrium of the PSO model) are in complete agreement, which induces users to an erroneous decision. Using a linearized kinetic model, all the 225 values of R² of the PSO model were closer to 1.0 than PFO. However, when nonlinearized fitting of the data was used, 122 out of 225 cases (54.22%) showed that the nonlinear PFO is better fitted than the PSO kinetic model.