The present study modeled the adsorption process of the drug diclofenac sodium on activated charcoal. For this purpose, a mass balance-based model was used considering a fixed bed column. The mass transfer rate in the solid phase was represented by a driving force model proposed in this study, and a gamma exponent with a range of 0 > γ ≤ 2 was assigned to the model. Different isotherms were adopted to represent the equilibrium at the solid/liquid interface: the Langmuir, Freundlich, Sips and Redlich-Peterson isotherms. The modeling was approached from the perspective of Bayesian statistics, and the Markov chain Monte Carlo method was used for parameter estimation. Model validation was performed with experimental data obtained under different operating conditions of initial concentration ($C_{0.