4.10 Summary
We have introduced the last two energy quantities, the Helmholtz energy and
the Gibbs free energy. Both are related to the maximum amount of work a sys-
tem can perform. When all four energies are written in terms of their natural
variables, a startling number of useful relationships can be developed by judi-
cious application of partial derivatives. These derivatives, Maxwell’s relation-
ships among them, are very useful because they allow us to express quantities
that are difficult to measure directly in terms of changes in state variables that
can be easily measured.
We defined the chemical potential . It is called a partial molar quantity be-
cause it is a partial derivative with respect to the number of moles of material
in our system. We can define other partial molar quantities;is the first one
defined, because of its usefulness as we look into chemical reactions and chem-
ical equilibria.
Finally, we defined fugacity as a necessary description of real gases and
showed how we can determine fugacity experimentally in a somewhat simple
fashion. It is relatively simple because we have been able to derive a lot of ex-
pressions from the basic ideas of thermodynamics and use them to obtain
otherwise inaccessible information about our system.114 CHAPTER 4 Free Energy and Chemical Potential