The hydrogen adsorption isotherms at equilibrium on four adsorbents (MOF-5 and three modified MOF-5s named, CH3-MOF-5, Br-MOF-5 and Cl-MOF-5) were studied using a monolayer model with four adsorption sites energies. The analytical expression of this model was developed using the grand canonical ensemble in statistical physics by taking some working hypotheses involving some physicochemical parameters which can describe the adsorption process. These parameters are: four numbers of hydrogen adsorbed molecules per site (n(1), n(2), n(3) and n(4)), four receptor site densities (N-M1, N-M2, N-M3 and N-M4), four saturation adsorbed quantities (Q(1), Q(2), Q(3) and Q(4)) and four adsorption energies (-epsilon(1), -epsilon(2), -epsilon(3) and -epsilon(4)). The evolutions of these parameters in relation with temperature were discussed to understand and interpret the adsorption process at different temperatures. Fitting results revealed that the adsorption of hydrogen on MOF-5 is an exothermic physisorption process. The adsorption surface is inhomogeneous with many site energies. The fitting of the adsorption site is achieved by an aggregate of hydrogen molecules. The adopted model expression is used to derive the thermodynamic potential functions which govern the sorption mechanism such as entropy S-a, free enthalpy of Gibbs G and internal energy E-int. (C) 2017 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.