The experimental isosteric heat, Qst, for molecular hydrogen adsorption in a Cu-exchanged zeolite ZSM-5 was determined as a function of the hydrogen loading. Qst was found to vary in a stepwise manner between 73 ± 5 and 39 ± 4 kJ/mol H2. This behaviour suggests the presence of different groups of adsorption sites, some of which have the appropriate thermodynamics necessary for an ambient conditions sorption based H2 storage medium. Our data can be directly related to model calculations and inelastic neutron scattering spectra. From a thermodynamic point of view, they confirm the feasibility of hydrogen storage applications based on molecular chemisorption of hydrogen.