Addressing mathematical discrepancies in the adsorption model of Hashem et al. (2024): A technical commentary

This letter provides a critical technical analysis of the application of the Freundlich isotherm in the study by Hashem et al. (2024), entitled "Chromium adsorption capacity from tannery wastewater on thermally activated adsorbent derived from kitchen waste biomass." While the study presents an innovative approach by utilizing pumpkin peel as an adsorbent for chromium removal, a critical issue was identified in the formulation and application of the Freundlich isotherm. The authors presented an incorrect mathematical modification of the isotherm, which significantly impacts the validity of the adsorption parameters derived, such as KF and 1/n, and ultimately affects the conclusions drawn about the system's adsorption capacity. Additionally, the assertion that the adsorption process can continue indefinitely is fundamentally flawed based on the principles of adsorption thermodynamics. This letter aims to rectify these discrepancies by revisiting the correct formulation of the Freundlich isotherm and highlighting the importance of accurate mathematical modeling in ensuring scientifically sound and replicable results. Despite these issues, the study remains a valuable contribution to the field, and the suggested revisions would further strengthen its impact.