This study presents a further examination of the relationship between the Langmuir kinetics and the Lagergren (first-order) and the second-order rate models of batch adsorption. The earlier work of Liu and Shen on the transformation of the Langmuir kinetic equation to a linear combination of the Lagergren rate expression and the second-order rate expression was given a rational treatment and solutions of the transformed equation were obtained. Based on the solutions, correct relationships between the Langmuir equation and the first-order and second-order equations were established and the significance of the relationships discussed. (C) 2014 Elsevier B.V. All rights reserved.