A new insight into the pseudo-second-order model and the physical meaning of its rate constant in adsorption

In this research, an exact mathematical expression for the rate constant of the pseudo-second-order (PSO) model was obtained based on the general rate equation related to the adsorption mechanism of Coleman et al. This expression is capable of accurately calculating the ionic radius of divalent metal ions adsorbed on the adsorbent surface. It was also shown that the PSO model is more accurate under the conditions of low adsorbent dosage, low specific surface area of adsorbent, high molecular weight of adsorbate, and equilibrium coverage fraction close to 1. The validity of the obtained results was confirmed through experimental data selected from the literature.