Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 26

2.3 CHEMICAL EQUILIBRIUM AND GIBBS FREE ENERGY
Gibbs free energy, G , is of significance for most environmental problems since G is
a variable of temperature, T , and pressure, p . Many environmental processes occur
at atmospheric pressure, which is a constant. Hence it is important to develop our
concept of equilibrium in terms of Gibbs free energy. J. Willard Gibbs, considered by
many to be the father of modern chemical thermodynamics, invented the function. It
has units of kilojoules (kJ). Utilizing the fundamental definition of G

= H − TS =

U + PV − TS , and further if P and T are constant, we have

d G = δ q − δ w + P d V − T d S = δ q − T d S . (2.34)

Since we know that, for spontaneous processes, T d S from the second law, at

constant T and P if only PV work of expansion is considered, we have the following
criterion for any change in independent variables of the system:

δ q ≤

d G = 0. (2.35)

For a reversible process in a closed system at constant temperature and pressure, if
only PV expansion work is allowed, there is no change in the Gibbs function (d G 0)

at equilibrium. Spontaneous processes will occur in such a system at constant T and
P when it is not at equilibrium with a consequent decrease in free energy (d G < 0).
The above inequality for a spontaneous change represents the criteria used in
equilibrium models in environmental science and engineering. For a finite change in
a system at constant temperature T , we can write

=

Δ G = Δ H − T Δ S . (2.36)

To assess whether a process in the natural environment is spontaneous or not, one
estimates the difference in Gibbs free energies between the final and initial states of
the system,

G is negative, the process is spontaneous. In other words, the
tendency of any system toward an equilibrium position at constant T and P is driven
by its desire to minimize its free energy. The free energy change for any system is,
therefore, given by the inequality

Δ G .If Δ

Δ H − T Δ S ≤ 0. (2.37)

For an exothermic process, there is a release of heat to the surroundings (enthalpy
change,

Δ Δ Δ

H < 0). For an endothermic process, since H > 0, T S has to be

greater than zero and positive and larger than H . Thus, an endothermic process

is accompanied by a very large increase in entropy of the system.

Δ

2.3.1 F REE E NERGY V ARIATION WITH T EMPERATURE AND P RESSURE
Since environmental processes occur at varying temperatures, it is useful to know
how the criterion for spontaneity and equilibrium for chemical processes vary with
temperature. Since at constant pressure ( ∂G/∂T) P =−

S , and S is always positive, it