Air separation is challenging due to the similarities in the sizes and energetics of oxygen and nitrogen. Although polymer membrane-based technology has achieved some success in replacing conventional air separation methods, the effectiveness of polymers has been shown to fall short of the economically attractive region occupied by inorganic microporous materials. Koros and co-workers have recently proposed that this lack of performance is a manifestation of the low entropic selectivity in polymers, possibly due to chain mobility or free volume effects. In this work, we address the effects of chain mobility on selectivity using molecular models and transition-state theory. We employ the methodology recently developed by Greenfield and Theodorou in which the polymer degrees of freedom can be explicitly included in the hopping rate calculations. About 100 oxygen and nitrogen jump events are studied in three different glassy polypropylene configurations. To examine the effects of polymer rigidity, two separate cases are considered for each jump; in the first case, the polymer model is held completely rigid during the event, while in the second the polymer torsional degrees of freedom are allowed to participate. The results show that the effects of polymer flexibility are reflected most significantly in the energy barriers, with the entropy barriers only marginally affected. Whereas the energetic selectivity can be reduced by 4 orders of magnitude in going from the rigid model to the flexible one, the entropic selectivity generally shows little change. The results are discussed in the context of current experimental and theoretical understanding of these systems.