Asymptotic connections between Elovich, PFO and PSO adsorption kinetics in a coverage-dependent rate model

The Elovich, pseudo-first-order (PFO), and pseudo-second-order (PSO) equations are widely used in adsorption kinetics, although the connection among them is often treated empirically. Here, we analyze a generalized adsorption rate equation in which the apparent adsorption coefficient decreases exponentially with surface coverage. The model recovers Elovich behavior at low coverage and yields effectively PFO- or PSO-like relaxation near equilibrium, depending on the magnitude of a composite coverage parameter. It also predicts an intermediate regime in which neither pseudo-order approximation is fully adequate. Application to representative literature datasets shows that this approach provides a practical tool for interpreting why different empirical fits succeed in different coverage domains and why some kinetic curves require direct numerical treatment. The framework is therefore best viewed as an effective tool for kinetic interpretation and regime classification rather than as a microscopic theory of surface heterogeneity.