  The Helmholtz free-energy W is calculated as a function of separation
distance for two molecules in a fluid, A and B, whose mutual interaction is
described by a spherically symmetric potential. For the equilibrium A + B = AB
occurring in a dilute solution or gas, W is used to evaluate the association
constant K, which for ionic A and B is identical to the Bjerrum result. The
criterion defining the bound species is not arbitrary; i.e., the cutoff
separation distance in the configuration integral used to calculate K arises
directly from the definition of W. For a one-component dense fluid, W permits
the derivation of the phase-condensation temperature, which for a gas is the
critical temperature and for a liquid the freezing temperature. For ionic A and
B (e.g., Sodium and Chloride ions in molten NaCl), an expression for the
freezing temperature is obtained, which is similar to the expression for the
melting temperature derived by Kosterlitz and Thouless for two-dimensional
systems.
