Erroneous Application of Pseudo-Second-Order Adsorption Kinetics Model: Ignored Assumptions and Spurious Correlations

In this research note, we revisit the pseudo-second-order model for adsorption kinetics, its assumptions, and its application to simulated, random, and published data. In particular, a widely used linear form of the pseudo-second-order model plotting t/q(t) against t-is shown to result in spurious correlations for typical adsorption experimental data. Depending on the range of data used, data from pseudo-first-order and pseudo-third-order models can also appear to be well-fit by the pseudo-second-order model. Inspection of the residual errors, however, indicates that the errors are not randomly distributed, as they should be. Based on this study, it is recommended to always verify the assumptions of a model, fit the data with the nonlinear form of the model equation, and inspect the residual plot to determine the goodness of fit.