The law of corresponding states in its most general form
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.
The Journal of Physical Chemistry
The law of corresponding states in its most general form.
The Journal of Physical Chemistry,
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