The adsorption of methane, ethane, and argon on sodium mordenite (Na-MOR) at ambient and cryogenic conditions is investigated experimentally and with grand canonical Monte Carlo (GCMC) simulations. Two different Na-MOR samples with silicon-to-aluminum (Si/Al) ratios of similar to 5 and similar to 9 are used in the experiments. Simulations are conducted on models with close to the experimentally observed Si/Al ratios and also on a purely siliceous model of MOR. In addition, the impact of varying the zeolite crystal symmetry from Cmcm to Pbcn is examined with GCMC. The agreement between the GCMC simulations and previous and current experimental measurements is quite good at ambient conditions. Differences between the ambient isotherms computed with the Cmcm and Pbcn structures are slight. However, the two structures exhibit qualitatively different argon adsorption behavior at cryogenic temperatures (87.3 K). The structure based on symmetry Pbcn shows a much better match with experimental isotherms than does the Cmcm structure. Cryogenic adsorption measurements are shown to be sensitive to subtle structural differences in the zeolite lattice. They also provide a rigorous test of force fields used in simulations. It is demonstrated that inclusion of cations and framework Al atoms with realistic charge distributions in the simulations is required to adequately match experimental results.