Refined Langmuir–Hinshelwood Kinetics for Heterogeneous Photocatalytic Systems: Analytical Closed-Form Solution, Enhanced Approximations and Experimental Validation

This study takes a further step forward in the analytical treatment of Langmuir–Hinshelwood (LH) kinetics for heterogeneous catalysis by deriving its closed-form solution. Unlike previous studies, we present a general solution that does not impose severe restrictions on the experimental conditions. This solution not only recovers the typical first- and zeroth-order regimes but also enables the simultaneous determination of the reaction rate constant and absorption–desorption equilibrium constant, unlike the traditional approaches to this equation, which needed additional isotherm experiments. The final solution requires a fine mathematical treatment for its numerical implementation, but enhanced approximations of the closed-form solution overcome this problem without losing the main advantage of calculating both constants at the same time. A parameter called “critical time” has been introduced, whose calculation allows us to distinguish quantitatively between kinetic regimes. Finally, the validation of these approximations has been carried out with experiments on zinc oxide and anatase (TiO2) under different conditions. Anatase experiments undoubtedly show a first-order tendency, regardless the quantity of powder. On the other hand, the degradation regime of the ZnO case cannot be easily ascribed to the zeroth or first order by simple inspection, but the model can mathematically rule out the zeroth order and confirm that it undergoes first-order degradation.