In this study, the first quantum corrections to the second virial coefficient (SVC) is analytically evaluated with the Morse potential for noble gases of He, Ne, Ar, Kr, Xe and also for CH4, CO2, N-2 atoms and molecules for low temperatures. This exact analytical quantum correction method includes the series expansion formula and special functions, allowing more accurate and exact evaluation of the any thermodynamic properties of matter using the second virial coefficient at wide range of temperature. To our knowledge, except for some different approximation approaches, this study is the first analytical method for the calculation of the quantum correction to second virial coefficient with Morse potential and valid for all values of parameters. The SVC quantum correction results of Morse potential are compared with the literature especially with Lennard-Jones (12-6) and indicate a good agreement at high temperatures, but the Morse potential results heavily dominate over the Lennard-Jones (12-6) potential especially for light atoms and molecules at low temperatures. (C) 2019 Elsevier Ltd.