Gibbs Free Energy and Phases — Where Do Ice, Water, and Water Vapor Trade Places?

The same H₂O becomes ice, water, or water vapor depending on the temperature. The deciding quantity is the Gibbs free energy G = H − TS: the phase with the lowest G is the one that appears. In ① we plot G(T) for the three phases and confirm that the crossing points are the melting point and the boiling point. In ② we change the external pressure and follow the crossing points until the phase diagram emerges by itself. The model is built only from literature values of the heat capacity, standard entropy, and molar volume, and it gives a boiling point at 1 atm of 373.117 K (measured: 373.124 K).

Reference thermochemical values are from CODATA; the heat capacity of water vapor is given by NIST’s Shomate equation; the heat capacity of ice is from Giauque & Stout (1936); and the densities are standard steam-table values. The model cannot treat conditions above the critical point (647 K, 22.06 MPa) or above 200 MPa (just above that, from about 210 MPa, ice III appears).