New statistical physicochemical interpretations of an adsorption process at molecular level were developed to explain the binary adsorption isotherms of lead and zinc ions on activated carbon derived from Styrax officinalis seeds (Balikesir, Turkey) and a commercial activated carbon at different temperatures, 298, 308 and 318 K. The extended Hill model was developed to explain heterogeneous model in terms of the grand canonical ensemble in statistical physics. Steric and energetic parameters, like the numbers of ions per site n(1) and n(2), the densities of receptor sites N-M1 and N-M2 and the adsorption energies (-epsilon(1)) and (-epsilon(2)) were directly obtained from the fitting of the experimental adsorption isotherms by numerical simulation to describe the process. The simulation results suggested that two adsorbates per site were anchored on activated carbon surface. The magnitudes of the calculated adsorption energies indicated that Zn2+ and Pb2+ were physically adsorbed by the activated carbon. Thermodynamic potential functions, namely entropy, enthalpy and internal energy were calculated to explain the order and disorder of the adsorbate at the adsorbent surface during the binary adsorption process. The values of the free enthalpy and the internal energy indicated spontaneous adsorption process. (C) 2015 Elsevier B.V. All rights reserved.