Pseudo-first-order kinetics in water contaminant adsorption: a cautionary note

The pseudo-first-order (PFO) kinetic model, first introduced by Lagergren in 1898, remains one of the most widely applied tools in adsorption studies of water contaminant removal because of its simplicity and ease of use. However, recent publications have featured incorrect formulations of this model, encompassing both linearized and nonlinear versions. These errors range from typographical mistakes to equations that are mathematically unsound, and in some cases, a fundamentally different kinetic model has been misidentified and applied as the PFO equation. Such inaccuracies have serious consequences: they lead to incorrect parameter estimation, obscure data interpretation, and ultimately undermine the reliability and comparability of adsorption research. In this communication, we systematically present representative cases of these errors in articles published in Water, Air, & Soil Pollution during 2023 and 2024. Particular attention is given to the erroneous nonlinear formulations of the PFO model, which have not been thoroughly examined in previous critiques. By clarifying these misconceptions, we emphasize the importance of accurate kinetic modeling for ensuring scientific rigor, improving reproducibility, and advancing adsorption research in water contaminant removal.

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