At 0.26667 Pa, the common value of Gibbs free energy (ΔG) for the catalytic hydrogen evolution reaction (HER) on Pt-doped graphene can be attributed to the exothermic nature of the system, which is influenced by the enthalpy (ΔH) of the reaction. In an exothermic reaction, where ΔH<0, the reaction releases heat as protons (H + ) are reduced to hydrogen gas (H2) on the catalyst surface. This release of heat lowers the overall free energy of the system, making the reaction thermodynamically favorable.