It is shown that none of the Lermard-Jones n,m intermolecular potentials can represent any of the gases, neon, argon, krypton, xenon, nitrogen, oxygen, hydrogen, methane, ethane, and propane. In particular, the second and third virial coefficients B* and C*, and V-T* = T*(dB*/dT*), computed for these potentials cannot describe the experimental behavior of B, C, and V-T. This is demonstrated by their inability to match the temperature dependence of the dimensionless variable, h = V-T(2)/C, thus failing to satisfy a necessary condition for representing the PVT behavior of these gases. (c) 2008 Elsevier B.V. All rights reserved.