The separation of individual component gases from a mixture of CO2, N-2, CH4, C2H6, and SF6 along with the selective permeation of CO2 from a mixture of CO2/N-2 through Na-zeolite-Y membrane have been investigated using reactivity descriptors and interaction energy calculations by density functional theory (DFT). To locate the active site of zeolite-Y, three different cluster models are considered to propose the role of zeolite framework in the selectivity of gaseous molecular separation. All the interacting molecules were optimized with respect to the framework cluster to compare the stability of the adsorption complex. We have analyzed the effect of affinities of gas molecules for the membrane wall on the permeation to predict the optimal affinity strength, e.g., for higher selectivity of CO2. We investigated the local softness of the interacting species with the zeolite framework cluster models. The order of activity as obtained from reactivity index values of individual molecules was compared with interaction energy calculations using DFT to validate the proposition. The result successfully predicts the experimental observation of selective permeation of gaseous molecules through Na-Y-zeolite pore in the order C2H6 < CH4 < SF6 < CO2 < N-2 and also proposes the plausible mechanism of zeolite membrane functionality.