copyright by Philip A. Candela, 1997.

The** ***chemical potential*, µ, of a component in a
solution can be
thought of
in
many ways:

1. A measure of the "escaping tendency" for a component in a solution;
2. A measure of the reactivity of a component in a solution;
3. For a one component (pure) phase, the chemical potential can be thought
of as:
** µ = U + PV - TS** (note, in this equation,
µ,U,S,V, as well as T and P, are
**intensive** quantities).

That is, the chemical potential increases as
the internal energy, U, of the phase increases, and as the entropy, S, of
the phase decreases at a given temperature, T. Further, the µ increases
as the volume, V increases for a given pressure, P. So, components that
possess HIGHER internal energies are *de*stabilized relative to
those with
LOWER internal energies, and components with LOWER entropies are
*de*stabilized relative to those with HIGHER entropies.

4. The chemical potential of a component in a solution is defined as the
rate at which the (extensive) internal energy of the solution increases as
the number
of moles (extensive) of the component in question increases, for a given
entropy and volume of the solution. That is, for the chemical potential
of a component (i) in a solution (e.g., SrCO_{3} in the aragonite
(CaCO_{3}) of sponge spicules in the ocean, or of fish
otoliths from the
Chesapeake Bay):

µ_{i} =
{dU/dn_{i}}_{S,V,nj}

where d = the *partial* differential operator, U = the internal energy of
the phase, n_{i} is one component of phase, n_{j}
represents all the other
components of the system or phase; all variables to the right of the
"}" are held constant during the partial differentiation. U,n,S,V must be
extensive in this definition; the chemical potential, µ is ALWAYS
intensive. IF X (mole fraction) is subbed for n in this, the most basic,
fundamental and precise of all definitions for chemical potential, the
expression is rendered INCORRECT!

5. Yes, it does happen to be true that the chemical potential is equal to
the partial molar Gibbs Free Energy (or, Gibbs Potential), BUT... that is
NOT a good way to define µ because chemical potential ** is
more** fundamental than the Gibbs Potential, G, (defined as G = H -
TS, where H = U + PV). G, A, and H were defined by Gibbs as Auxiliary
Functions AFTER he defined chemical potential. What most people call
"free energy calculations" (i.e., free energy of products minus reactants
is greater or less than zero) are really** chemical potential
calculations**. This equivalence is due to that fact that the free
energy of a pure phase is equal to the chemical potential of the single
component of the pure phase. The use of what is REALLY an auxiliary
function (G) to fill a primary role in thermodynamics that is actually
better filled by **the more fundamental ****chemical potential** is
one of the many reasons why student have trouble with the subject. Read
Gibbs.
6. The chemical potential always refers to components in a (solid,
liquid
or gaseous) solution, or to the one component in a pure phase. When
considering say, dissolved alcohol in aqueous solution, the chemical
potential of alcohol= µ(alcohol in solution) = µ(pure alcohol)
+ RT ln (a), where
a = activity of the component (alcohol in this case) in the solution, and
where either a = jm or
a = j X (where j = activity coefficient, m = molality or molarity, and X
= mole fraction). In geology, we might be concerned with the chemical
potential of enstatite component in orthorhombic pyroxene, which, skipping
some complexities, may be represented by: µ(MgSiO_{3}) =
µ(pure MgSiO_{3}) + Rt ln X(MgSiO_{3}), when the
solution is ideal
(activity coefficent ~ 1).

7a.The chemical potential of ethanol increases to the right in
the following series of solutions: beer -> wine -> scotch whisky
->white lightning

7b. The chemical potential of O_{2} increases (all
corrected to the same T and P) progressing from a lunar basalt that has
accessory native iron, to an awaruite (Fe-Ni alloy) + magnetite-bearing
serpentinized ultramafic rock, to fayalite bearing granites, to fayalite
+ magnetite bearing granites, to granites with magnetite + quartz BUT no
fayalite, to hematitically altered granites! O_{2} chemical potential also
increases in going from Po + Mag ores, to Py + Mag ores to Py + hematite
bearing ores to jarosite + hematite bearing ores; not to mention from
black shales to red sandstones, and from oxygen depleted ground water to
an O_{2}-bearing vadose zone!