Single-component permeances of six gases were measured on three different supported nanoporous carbon membranes prepared by spray coating and pyrolysis of poly(furfulyl alcohol) on porous stainless-steel disks. Global activation energies were regressed from data collected as a function of temperature. Permeances and global activation energies were correlated to molecular size, assuming that entropic affects dominated the transport. The permeance was best correlated to the minimum projected area of the molecule computed from first principles. The free-energy barriers to transport within the membranes were derived from the temperature dependence of the permeance data, after accounting for porosity differences between the membranes and differences in molecular adsorption. Using transition-state theory and an entropic model derived, the free energy, enthalpy, and entropic barriers to transport within the membrane were examined as a function of molecular size. Computed on the basis of size, the entropic component of this barrier did not account for the large differences in the transition-state free energies. However, when these entropic barrier values were used to compute the enthalpic portion of the barrier free energies, the minimum projected area of each molecule correlated strongly. Furthermore, these enthalpic components of the barriers were fitted nicely by the Everett-Powl mean field potential, using only the pore size as the adjustable parameter. These results shed light on the underlying mechanism by which shape-selective transport takes place in the NPC membranes and small molecules are separated.