A Proposal for the Incorporation of Temperature into the Langmuir Model in Adsorption Isotherms

Adsorption is a frequently used technique for pollutant removal due to its efficiency and versatility. Mathematical modeling of these processes enables understanding of adsorbent and adsorbate interactions and prediction of system dynamics, especially when experimental data are limited. Among adsorption isotherm models, the Langmuir model is one of the most applied; however, its formulation does not explicitly consider temperature variation, limiting predictive capability in practical applications. This article proposes an adaptation of the Langmuir model by incorporating temperature dependence, enabling inference of isotherms at temperatures without experimental data. The model was first validated using data from the literature at different temperatures, considering the adsorption of amoxicillin, phosphate, methylene blue, and caffeine. Subsequently, it was applied to experimental data of copper ion adsorption by 5A zeolite obtained in this work, allowing estimation of Qmax and KL. Based on these estimates, hypotheses regarding their temperature dependence were formulated, and isotherms at 55 °C, 65 °C, and 75 °C were inferred and compared with experimental data. Finally, the model was applied to infer isotherms from 25 °C to 95 °C, demonstrating its ability to represent experimental dynamics and predict adsorption at temperatures without available data, contributing to the analysis and optimization of adsorption processes.