Exact solution of the Langmuir rate equation: New Insights into pseudo-first-order and pseudo-second-order kinetics models for adsorption.

The Langmuir adsorption rate equation was obtained in its exact, linear, and simple form. Using Stochastic Numerical Simulation, it was demonstrated that this equation can accurately calculate the adsorption rate constant (k a), which is more precise than the values obtained using pseudo-first-order (PFO) and pseudo-second-order (PSO) models. The derivation conditions of the PFO and PSO kinetics models from Langmuir kinetics were also investigated. The results showed that the PFO model can be obtained at two limit states: at C e ≅ C 0 and at C e ≪ C 0 with a very low fractional coverage. Also, the PSO model is derived under the condition C e → 0 and θ e → 1. The accuracy of the exact Langmuir model, both linear and nonlinear, and the theoretical derivation conditions of the PFO and PSO models were examined using several sets of kinetics data generated by the Stochastic Numerical Simulation method. The simulation results supported the theoretical approaches of this study. • Obtaining the exact solution of the Langmuir kinetics (EIL). • Deriving the Pseudo-First-Order model under the condition of C e ≅ C 0. • Deriving the Pseudo-First-Order model at short initial times of adsorption under C e ≪ C 0 condition. • Deriving the Pseudo-Second-Order model under the condition of C e → 0 and θ e → 1. • Evaluating the derivation conditions of PFO and PSO models using the Stochastic Numerical Simulation method. [ABSTRACT FROM AUTHOR]