Materials capable of cost-effective on-board hydrogen storage and delivery are currently being sought worldwide as a means to facilitate a hydrogen-based energy transition in the transportation sector. Among the solutions proposed, hydrogen storage by physisorption on porous solids constitutes a main avenue of research, and for intelligent design of such materials a detailed knowledge of gas adsorption thermodynamics is of the utmost importance. Analysis of the available data for hydrogen adsorption on alkali and alkaline-earth cation exchanged zeolites clearly shows that standard adsorption enthalpy (Delta H(0)) and entropy (Delta S(0)) are correlated, in the sense that larger Delta S(0) values correspond to larger Delta H(0) values. It was also shown that, referring to absolute values, the relative rate at which adsorption entropy changes decreases gradually as adsorption enthalpy increases thus resulting in a non-linear correlation between Delta H(0) and Delta S(0). These results are discussed and corresponding implications for hydrogen storage via physisorption are highlighted.