Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 30

Chemical potential is the partial molar Gibbs free energy representing the change
in the total Gibbs energy due to the addition of a differential amount of species i to
a finite amount of solution at constant temperature and pressure. For a single pure
substance the chemical potential is the same as its molar Gibbs energy. Thus, the
chemical potential of benzene in pure water is different from that in a mixture of
water and alcohol. As its very name indicates,

μ i is an indicator of the potential for a
molecule (e.g., movement from one phase to another or a chemical reaction). Thus,
it is analogous to a hydrostatic potential for liquid flow, an electrostatic potential for
charge flow, and a gravitational potential for mechanical work.The chemical potential
is thus a kind of “chemical pressure” and is an intensive property of the system, such
as T and P . When the chemical potential of a molecule is the same in states a and b,
then equilibrium is said to exist. This satisfies the criterion for equilibrium defined
earlier, that is,

0. If the chemical potential is greater in state a than in state b,
then a transfer or reaction of species i occurs spontaneously to move from a to b. This
satisfies the criterion for a spontaneous process, that is,

Δ G =

G < 0.
The above formalism suggests that at constant T and P , the total free energy of a
system is given by

Δ

i μ i n i .

G = (2.52)

E XAMPLE 2.6 S IGNIFICANCE OF C HEMICAL P OTENTIAL

Problem : Calculate the change in chemical potential for the vaporization of water at
1 atm and 25 ◦ C.
Solution : The reaction is H 2 O(l) → H 2 O(g). The free energy of formation per mole is
− 237 kJ/mol for liquid water and − 229 kJ/mol for water vapor. For a pure substance
the free energy per mole is the same as the chemical potential. Hence,

Δμ =− 229 − ( − 237 ) = 8 kJ/mol. (2.53)

The chemical potential of the vapor is higher, indicating that there is useful work
available. It is clear that water vapor is more “potent” compared with liquid water.

2.5.1 G IBBS -D UHEM R ELATIONSHIP FOR A S INGLE P HASE
In equilibrium calculations, an important problem is the estimation of the chemi-
cal potential of different components in a single phase. Upon differentiation of the
expression for total Gibbs free energy given by Equation 2.43,

i μ i d n i +

d G = n i d μ i . (2.54)

i