Page 326 - Advanced thermodynamics for engineers

14.4 CHEMICAL KINETICS OF NO 315

14.4.2 INITIAL RATE OF FORMATION OF NO
Heywood et al. (1971) derived the initial rate of formation of NO in the following way. It can be shown
that Eqn (14.31) is the dominant equation for the initial formation of NO. When the nitric oxide (NO)
starts to form the value of a ¼ 0, and Eqn (14.31) can be written
1 d
ð½NOŠVÞ¼ 2R 1 (14.32)
V dt
R 1 ¼ k f1 ½OŠ ½N 2 Š : (14.33)
e
e
Heywood states that, using a three equation set for the formation of NO, the value of the rate
constant for the reaction in the forward direction is

3
k f1 ¼ 7:6 10 13 e ð 38000=TÞ cm =mol s (14.34)
3
It is necessary to note two factors about Eqn (14.34): the rate constant for the reaction is in cm /mol
s, and the exponential term is significantly different from that in Eqn (14.19).
Hence,

1 d
ð½NOŠVÞ¼ 2k f1 ½OŠ ½N 2 Š : (14.35)
e
e
V dt
Heywood (1988) also shows that
1=2
K ½O 2 Š
pðOÞ e
½OŠ ¼ 1=2 ; (14.36)
e
ðRTÞ
where
1
K ¼ equilibrium constant for the reaction O 2 5O
pðOÞ
2
¼ 3:6 10 e atm 1=2
3 ð 31090=TÞ
Substituting this value into Eqn (14.34) gives

d½NOŠ 6 10 16 1=2 3
¼ e ð 69090=TÞ ½O 2 Š e ½N 2 Š cm =mol s (14.37)
e
dt T 1=2
3
The values of [O 2 ] e and [N 2 ] e , which should be in mol/cm , can be obtained from an equilibrium
analysis of the mixture. The value of [O] e can be calculated from the perfect gas law, because
n p x p
½O 2 Š e ½O 2 Š e ½O 2 Š e
½O 2 Š ¼ ¼ ¼ : (14.38)
e
V RT RT
Likewise,
x p
½N 2 Š e
½N 2 Š ¼ (14.39)
e
RT