Abstract
The general adsorption kinetic model, also called pseudo-\(n\) order (PNO) equation, is revisited using random differential equations. We provide a full probabilistic solution of the model, which is a stochastic process, by computing its first probability density function under very general hypotheses on its parameters, that are treated as absolutely continuous random variables with an arbitrary joint probability density function. The analysis is based on the so called Random Variable Transformation technique. From the first probability density function, we compute relevant information of the PNO model, such that, the mean, the variance and confidence interval. We also provide explicit expressions for the probability density functions of other significant quantities as the time required to reach a specific level of absorbed substance or the rate coefficient of the chemical reaction. All the theoretical findings are illustrated by means of real data. The application includes a thorough discussion about two important uncertainty quantification inverse methods, namely, the Random Least Mean Square and the Bayesian technique, to assign appropriate probability density functions to all the PNO model parameters so that the solution captures data uncertainties.
