  It can be fruitful to view two-component physical systems of attractive
monomers, A and B, ``chemically'' in terms of a reaction A + B <-> C, where C =
AB is an associated pair or complex. We show how to construct free energies in
the three-component or chemical picture which, under mass-action equilibration,
exactly reproduce any given two-component or ``physical'' thermodynamics.
Order-by-order matching conditions and closed-form chemical representations
reveal the freedom available to modify the A-C, B-C, and C-C interactions and
to adjust the association constant. The theory (in the simpler one-component,
i.e., A = B, case) is illustrated by treating a van der Waals fluid.
