10 kinetic models are studied in detail and used after to model the adsorption kinetics of lead on an activated carbon. All the kinetics parameters are determined: coefficients of diffusion, rate constants and maximum lead adsorption, then, compared to the literature data. The data are better simulated by the nonlinear models in the order: simplified Elovich>Elovich>Bangham> pseudo order n >Boyd, Crank long times >pseudo order 2 > Crank> Weber and Morris > Langmuir, pseudo order 1 > pore volume and surface diffusion model by Leyva Ramos > simplified Crank short times. It is one of the first times that the kinetics of adsorption are fitted by the entire true Crank model. The kinetics of lead adsorption by the activated carbon are best described by the Elovich equation: Q = (1/beta)Ln (alpha beta t) with a equal to 0.035 mg g(-1) s(-1) and beta to 0.134 g mg(-1). (C) 2016 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.