The law of corresponding states in its most general form

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It is shown that any two-body intermolecular potential function can be put into a dimensionless form involving only one energy parameter, e0, and only one length parameter, r0, in addition to any dimensionless intermolecular potential function-shape parameters C1, C2, . . . and any dimensionless electrostatic parameters μ2/e0r03, Q2/e0f05, . . . , where μ, Q, . . . are dipole, quadrupole, . . . moments. Use is made of this result to derive the most general form of the law of corresponding states for PVT behavior at moderate densities by means of a completely general and systematic dimensional analysis procedure. The result, readily transferable to any equilibrium or transport bulk property in reduced form, is Pv/nRT = f(v/r03 kT/e0, C1, C2, . . . , α/r03, μ2/e0r03, Q2/e0r05, . . . , M, Δ*) where Δ* is a new quantum-deviation parameter, combining into a single variable the quantum deviations from the classical law of corresponding states due to translation, rotation, vibration, and electronic transitions, the Ct's are intermolecular potential function-shape factors, and the other symbols have their usual meanings. Alternatively, PV/RT = f[V/Vc, T/Tc, w1, w2, . . . , αN/Vc, μ2N/VckTc, Q2(N/Vc)5/2/kTc, . . . , M, Δ(c)] where Δ(c) is another general quantum-deviation parameter related to Δ*, w1, w2, . . . are molecular geometry parameters, and the other symbols are standard. Inclusion of the molecular weight, M, is considered here for the first time.

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The Journal of Physical Chemistry