Why Is the Linearized Form of Pseudo-Second Order Adsorption Kinetic Model So Successful in Fitting Batch Adsorption Experimental Data?

There is a vast amount of literature devoted to experimental studies on adsorption from liquids examining the adsorption potential of various adsorbents with respect to various solutes. Most of these studies contain not only equilibrium but also kinetic experimental data. The standard procedure followed in the literature is to fit the kinetic experimental adsorption data to some models. Typically empirical models are employed for this purpose and among them, the pseudo-first and pseudo-second order kinetic models are the most extensively used. In particular, the linear form of their integrated equations is extensively employed. In most cases, it is found that the pseudo-second order model is not only better than other models but also leads to high fitting quality. This is rather strange since there is no physical justification for such a model, as it is well accepted that adsorption kinetics is dominated by a diffusion process. In the present work, it will be shown through examples and discussion that the success of the linearized pseudo-second order model in fitting the data is misleading. Specific suggestions on appropriate adsorption data treatment are given.