Determination of Intermolecular Potentials from Thermodynamic Data and the Law of Corresponding States

It is shown that in classical statistical mechanics the second virial coefficient in the virial expansion of the equation of state of a gas uniquely determines the intermolecular potential provided that the potential is monotonic (i.e., everywhere repulsive or everywhere attractive). This result leads to a partial verification of a conjecture of H. Kammerlingh‐Onnes and W. H. Keesom concerning the Law of Corresponding States. An explicit formula for the potential is also obtained. If the potential is not monotonic it is not uniquely determined by the second virial coefficient. All potentials corresponding to a given second virial coefficient are determined explicitly.