McKay, Donald. "Front matter" Multimedia Environmental Models ...

We are concerned with systems in which a chemical migrates from phase to
phase. These phase changes involve input or output of energy, thus this energy
exchange can compensate for entropy loss or gain. It can be shown that, whereas
entropy maximization is the criterion of equilibrium for a system containing constant
energy at constant volume, the criterion at constant temperature and pressure (the
environmentally relevant condition) is minimization of the related function, the
Gibbs free energy, which serves to combine energy and entropy in a common
currency.
Return to the example presented in Figure 5.1, of benzene diffusing from water
into an air bubble and striving to achieve equilibrium. The basic concept is that, if
we start with a benzene concentration in the water and none in air, the free energy
of the system will decrease as benzene migrates from water to air, because the
increase in free energy associated with the rise in benzene concentration in the air
is less that of the decrease associated with benzene loss from the water. The process
is thus spontaneous and irreversible. Benzene continues to diffuse from water into
the air until it reaches a point at which the free energy increase in the air is exactly
matched by the free energy decrease in the water. At this point, the system comes
to rest or equilibrium.
Likewise, if the system started with a higher benzene concentration
in the air phase and approached equilibrium, it would reach exactly the
same point of equilibrium with a particular ratio of concentrations in each phase.
The system thus seeks a minimum in free energy at which its derivative with
respect to moles of benzene is equal in both air and water phases. This derivative
is of such importance that it is called the chemical potential. The underlying principle
of phase equilibrium thermodynamics is that, when a solute such as benzene achieves
equilibrium between phases such as air, water, and fish, it seeks to establish an equal
chemical potential in all phases. The net diffusion flux will always be from high to
low chemical potential. Thus, we can use chemical potential for deductions of mass
diffusion in the same way that we use temperature in heat transfer calculations.
5.1.3 Fugacity
Unfortunately, chemical potential is logarithmically related to concentration,
thus doubling the concentration does not double the chemical potential. A further
complication is that a chemical potential cannot be measured absolutely, therefore
it is necessary to establish some standard state at which it has a reference value. It
was when addressing this problem that G.N. Lewis introduced a new equilibrium
criterion in 1901, which he termed fugacity, and which has units of pressure and is
assigned the symbol f. The term fugacity comes from the Latin root fugere, describing
a “fleeing” or “escaping” tendency. It is identical to partial pressure in ideal
gases and is logarithmically related to chemical potential. It is thus linearly or nearly
linearly related to concentration. Absolute values can be established because, at low
partial pressures under ideal conditions, fugacity and partial pressure become equal.
Thus, we can replace the equilibrium criterion of chemical potential by that of
fugacity. When benzene migrates between water and air, it is seeking to establish
an equal fugacity in both phases; its escaping tendency, or pressures, are equal in
both phases.
©2001 CRC Press LLC