Untitled - Aerobib - Universidad Politécnica de Madrid

∆G 0 j = ∑ i
1.7. CASE OF A MIXTURE OF IDEAL GASES 25
and
(
Hi − T Si
0 )
νij (1.108)
is the increase in free energy due to reaction j at temperature T of the mixture and
at standard pressure p 0 . Thus ∆G 0 j depends only on T . Table 1.2 gives the values of
for several species corresponding to their formation from the chemical elements
∆G 0 j
at the standard state. Therefore Eq. (1.106) can be written
∏
( ) νj
X νij p0
i = Kj 0 (T ) , (j = 1, 2, . . . , r), (1.109)
p
i
where Kj 0 is called the equilibrium constant of reaction j depending only on temperature
T . The values of Kj 0 versus T are given in Fig. 1.6, for several typical reactions
of interest in combustion problems.
30
25
1
2H2 +OH ↔ H2O
20
log 10
(K p
)
15
10
5
0
CO
H 2 + 1 2O2 ↔ H2O
CO 2 +H 2 ↔ CO +H 2O
+ 1 2O2 ↔ CO2
1
2N2 +H2O ↔ NO +H2O
H 2O ↔ H 2 +O
1
2 N2 + 1 2O2 ↔ NO
1
2 H2 ↔ H
−5
1
2 N2 ↔ N
−10
0 400 800 1200 1600 2000 2400 2800 3200 3600
T(K)
Figure 1.6: Equilibrium constant of reaction vs temperature, for several typical reactions of
interest in combustion problems.
The chemical equations (1.84) used for this calculation can be any ones within
the following limitations: a) they must be linearly independent; b) their number must
be the maximum that can exist between species. This number can be determined when
the phase rule is applied. Be l ′ < l the number of components of the mixture, then
the number of independent reactions will be l − l ′ . In turn l ′ can be determined as
follows: let E j , (j = 1, 2, . . . , l), be the chemical elements forming the species and
a ij be the number of atoms of element E j in species A i . The number of components