Page 269 - Advanced Thermodynamics for Engineers, Second Edition

258 CHAPTER 12 CHEMICAL EQUILIBRIUM AND DISSOCIATION

0
Now DG is a function of T alone (having been defined at a standard pressure, p 0 ), therefore
T
¼ fðTÞ.
K p r
is related to the datum pressure used to
Equation (12.56) shows that the numerical value of K p r
0
define m . If the amounts of substance of reactants and products are the same then the value of K p is not
affected by the datum pressure (because y a þ y b y c y d ¼ 0). However, if the amounts of substance
1
of products and reactants are not equal, as is the case for the CO þ O 2 /CO 2 reaction, then the value
2
of K p will be dependent on the units of pressure. Hence the value of equilibrium constant, K p , is the
same for the water gas reaction ðCO þ H 2 O/CO 2 þ H 2 Þ in both SI and imperial units because K p is
dimensionless in this case.
12.5.1 K p DEFINED IN TERMS OF MOLE FRACTION
The definition of partial pressure is
p a ¼ x a p (12.60)

Hence replacing the terms for partial pressure in Eqn (12.57) by the definition in Eqn (12.60) gives:
( ) " ! #
p p y d x x y d
y c
y c
c
d
c
d
<T ln ¼<T ln p ðy c þy d y a y b Þ (12.61)
y a y b
p a p x a x
y a y b
b b
which results in the following expression for K p in terms of mole fraction
!
x x y d
y c
c
d
K p ¼ y a y b p ðy c þy d y a y b Þ (12.62)
x a x
b
The above expressions are known as the law of mass action.
12.6 VARIATION OF GIBBS ENERGY WITH COMPOSITION
Equations (12.57) and (12.62) show that the equilibrium composition of a mixture is defined by the
equilibrium constant that can be defined in terms of the partial pressures or mole fractions of the
constituents of the mixture: the equilibrium constant was evaluated by equating the change of Gibbs
¼ 0. It is instructive to examine how
energy at constant pressure and temperature to zero, i.e. dGÞ p;T
the Gibbs energy of a mixture varies with composition at constant temperature and pressure. Assume
that two components of a mixture, A and B, can combine chemically to produce compound C. This is a
slightly simplified form of Eqns (12.38) and (12.39). If the chemical equation is
A þ B/2C; (12.63)
then at some point in the reaction, defined by the fraction of reaction, ε, the chemical composition is
ð1 εÞA þð1 εÞB þ 2εC (12.64)

and the Gibbs energy is
G ¼ð1 εÞm þð1 εÞm þ 2εm c (12.65)
b
a