Display omitted •We present an explicit representation of molar Gibbs free energy for gaseous substances.•The molar Gibbs free energy calculation model is only related to three molecular constants.•Gibbs free energies of gaseous phosphorus dimer are excellently predicted. We establish an analytical representation for the prediction of the molar Gibbs free energies of gaseous diatomic molecule substances. By comparing the predicted values to the experimental data for the gaseous phosphorus dimer, the availability of the Gibbs free energy calculation model is verified. The present model is related to three molecular constants and away from the need of lots of experimental spectroscopy data.