Page 267 - Advanced Thermodynamics for Engineers, Second Edition

256 CHAPTER 12 CHEMICAL EQUILIBRIUM AND DISSOCIATION

and
¼ m dm 1 þ m dm 2 þ .m dm n : (12.42)
dGÞ p;T 1 2 n
From here on the mass form of the equation (Eqn (12.5a)) will be replaced by the mole form of the
equation (Eqn (12.5b)), because this is more appropriate for chemical reactions. It is possible to relate
the amount of substance of each constituent in terms of ε, viz.
n a ¼ ð1 εÞy a þ A
ð1 εÞy b þ B
n b ¼
(12.43)
εy c þ C
n c ¼
εy d þ D
n d ¼
where A, B, C and D allow for the excess amount of substance in nonstoichiometric mixtures.
Hence
dn a ¼ y a dε (12.44)
and applying similar techniques
dn a dn b dn c dn d
¼ dε: (12.45)
¼ ¼ ¼
y a y b y c y d
This is known as the equation of constraint because it states that the changes of amount of sub-
stance (or mass) must be related to the stoichiometric equation (i.e. changes are constrained by the
stoichiometry).
Hence

c
d
a
b
dGÞ p;T ¼ m y a dε m y b dε þ m y c dε þ m y d dε (12.46)
giving

vG
c
b
a
d
¼ m y a m y b þ m y c þ m y d
vε (12.47)
p;T
¼ 0; for equilibrium:
Therefore at equilibrium
m y a þ m y b ¼ m y c þ m y d : (12.48)
d
a
c
b
Since m is numerically equal to g, it is possible to describe m in a similar way to g, see Chapter 9
Section 9.2.4.
viz.
0
m ¼ m þ<Tlnp r (12.49)
where

0
m ¼ m þ m T (12.50)
0
and this is the value of m at temperature, T, and the datum pressure, p 0 .