Predicting equilibrium time by adsorption kinetic equations and modifying Langmuir isotherm by fractal-like approach

In this work, the pseudo-first-order (PFO), pseudo-second-order (PSO) and Vermeulen equations were modified by introducing an adjustable parameter i.e. the fractional surface coverage θ. The Langmuir kinetic equation was modified by the fractal-like approach and the separation factor RH was proposed to express essential characteristics of the fractal-like Langmuir isotherm. The kinetic and isotherm data obtained from nitrate adsorption on the PAN/AC composite were used to evaluate the validity of these models. Results indicated that the modified PSO equation could accurately predict the equilibrium time at different initial nitrate concentrations (R2 > 0.998) and that the fractal-like Langmuir isotherm could better describe the equilibrium data at different temperatures (R2 > 0.994). The magnitude of parameter b reflected the affinity of the adsorbent for the adsorbates. The innovation and significance of the present study was that the modified kinetic and isotherm models could predict the equilibrium time and describe the heterogeneous surfaces, respectively. Therefore, this work is expected to extend the application scope of the PFO, PSO and Vermeulen equations and Langmuir isotherm.