Critical theoretical and thermodynamic comments on the paper "Enhanced adsorption of methyl orange using polyaniline-modified hydroxyapatite derived from natural Moroccan phosphate; https://doi.org/10.1016/j.cherd.2026.01.051"

This commentary highlights key theoretical, statistical, and thermodynamic errors in the recently published article by Benchhiba et al., 2026, concerning the adsorption of methyl orange onto polyaniline-modified hydroxyapatite. We highlight fundamental misapplications in the mathematical evaluation of adsorption kinetics, equilibrium isotherms, and thermodynamics. Specifically, the original study relies on the statistical fallacy of linearizing inherently nonlinear adsorption models, which distorts error structures and invalidates R² comparisons. Furthermore, this commentary exposes severe dimensional inconsistencies in the calculation of the Dubinin-Radushkevich, Temkin, and Freundlich isotherms. Most critically, the derivation of standard thermodynamic parameters (ΔG°, ΔH°, ΔS°) is fundamentally flawed due to the erroneous use of a dimensional distribution coefficient (K d ) instead of a dimensionless thermodynamic equilibrium constant ( K e 0 ), leading to extreme physical contradictions regarding the nature of adsorption (physisorption vs. chemisorption). By elucidating the correct mathematical and dimensional frameworks, this commentary aims to rectify the scientific record.