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 x 10(14)pores per cm(2)) of triangular-shaped nanopores of similar to 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(85)Kr/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 restrained 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 per mole for Kr and Xe, respectively), a large Kr/Xe separation selectivity is postulated from the PTI membrane. Furthermore, the combination of the atom-thick PTI lattice and high pore density leads to extremely large yet selective permeances for Kr. For example, a Kr permeance of 1000 gas permeation units (GPU) accompanying a large Kr/Xe selectivity (>10 000) is calculated at 25 degrees C, which is significantly better than that of the state-of-the-art membranes for Kr/Xe separation, making PTI-based membranes a leading candidate for processing the hazardous waste of(85)Kr/Xe mixture.