Poly(triazine imide) or PTI is a promising material for molecular sieving membranes, thanks to its atom-thick ordered lattice with an extremely high density (1.6 × 10^14 pores/cm2) of triangular-shaped nanopores of ~0.34 nm diameter. Here, we investigate the application of PTI nanopores in the purification of Kr from Xe to reduce the storage volume of the mixture of 85Kr/Xe. Using van-der-Waals density-functional theory (vdW-DFT) calculations, benchmarked against the random phase approximation (RPA), we calculate the potential energy profiles for Kr and Xe across the nanopores. For each gas, starting from the RPA potential-energy profile, the force-field parameters to be used in the classical molecular dynamics framework are trained to calculate the Helmholtz free energy barrier as a function of temperature, and therefore, the corresponding entropic loss. Overall, due to the much higher activation energy from the adsorbed state in Xe (17.61 and 42.10 kJ/mole for Kr and Xe, respectively), a large Kr/Xe separation selectivity is postulated from the PTI membrane. Furthermore, the combination of atom-thick PTI lattice and high pore density leads to extremely large yet selective permeances for Kr. For example, Kr permeance of 1000 gas permeation units (GPU) accompanying a large Kr/Xe selectivity (>10000) is calculated at 25 °C, significantly better than the state-of-the-art membranes for Kr/Xe separation, making PTI-based membranes a leading candidate to process the hazardous waste of 85Kr/Xe mixture.