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

Abstract

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.

A systematic study of hexavalent chromium adsorption and removal from aqueous environments using chemically functionalized amorphous and mesoporous silica nanoparticles

“…A linearized form of Eq. 8 has often been used to obtain adsorption kinetics parameters using linear regression, which has been most widely used to analyze pseudo-order adsorption kinetics 51,[53][54][55]…”

“…where q t fit (mg•g −1 ) is the amount of Cr(VI) adsorbed per mass of nanoparticles used at time t as predicted by best fit, and sd is the standard deviation of residuals (mg•g −1 ) 51 .…”

Sorption of Organic Pollutants by Humic Acids: A Review

“…A frequent mistake is to evaluate the applicability of the pseudo-second-order model from the linearity of the plot t/q vs. t without excluding adsorption data at (or very close to) equilibrium. The applicability of the pseudo-second order model, or of any other linearizable model, could be evaluated by fitting the data with the nonlinear form of the model and verifying that the residual errors are randomly distributed, as suggested by some authors [84,85].…”

Summary on Adsorption and Photocatalysis for Pollutant Remediation: Mini Review

“…[65] o Developed to compensate for the deficiencies of PFO and PSO, n can be an integer or non-integer rational number, and must be determined by an experiment. [66] Combined (Avrami* and General**) o Has multiple parallel routes that contribute to the total adsorbate uptake by different small and large sites, where k i is the rate coefficient for route i, a i is the weight coefficient that reflects the share of route i (N) and for N = 1, this model is reduced to the PFO model [35] constants without physicochemical meaning and provide little insights into adsorption mechanisms and no meaningful mechanism can be confidently postulated from these models. In addition to the mechanism of reaction, it is neces- Table 3.…”