Derivation of Pseudo-First-Order, Pseudo-Second-Order and Modified Pseudo-First-Order rate equations from Langmuir and Freundlich isotherms for adsorption

Abstract

• Kinetics study of Langmuir and Freundlich isotherms by Statistical Rate Theory. • Derivation of Pseudo-First-Order and Pseudo-Second-Order models. • Derivation of Modified Pseudo-First-Order model. • Derivation of a new kinetics model for adsorption. • Simulation of Humic Acid adsorption on Hematite and Kaolinite adsorbents. The kinetics of adsorption for Langmuir and Freundlich isotherms has been explored theoretically on the basis of Statistical Rate Theory (SRT). The Modified Pseudo-First-Order (MPFO) and Pseudo-First-Order (PFO) models were derived from Freundlich isotherm on the basis of Statistical Rate Theory at c 0 ≫ c e and at close to equilibrium respectively. Also, for a Langmuirian adsorption MPFO was derived at initial times of adsorption under condition c 0 ≫ c e and also Pseudo-First-Order (at close to equilibrium) and Pseudo-Second-Order (PSO) model (at close to equilibrium for c 0 ≫ c e and θ e ≅ 1 ) were obtained based on SRT. It has been proven that from Freundlich and Langmuir isotherms the fractional coverage is a linear function of t at very short initial times of adsorption. Also an useful rate equation was derived at condition c 0 ≅ c e from Freundlich isotherm. The theoretical obtained equations from Freundlich and Langmuir isotherms have been examined by several set of experimental data selected from literature.