Page 69 - Modeling of Chemical Kinetics and Reactor Design

Reaction Mechanisms and Rate Expressions 39
( +r * ) = k C CH 4 C H 2 + k C C H 4 C H * − k C * C H 2
1
3
2
2
2
CH 5
2
C H 5
2
net
(1-162)
− kC * C *
4
CH 5 H
2
The overall rate of reaction of C is
H*
( +r ) = k C C + k C C − k C C
2
2
H ∗ net 1 CH 4 H 2 3 CH 5 * H 2 2 C H 4 H ∗
2
(1-163)
− kC * C *
4
2
CH 5 H
The overall rate of reaction of C is
H 2
− ( r ) = k C C + k C C (1-164)
H 2 1 CH 4 H 2 3 * H 2
2
net CH 5
2
)
)
Assuming that (+r * net and (+r * net are zero, equating Equa-
2
CH 5 H
tions 1-162 and 1-163 gives:
kC CH 4 C H 2 + k C C H 4 C H * − k C C H 5 * C H 2 − k C CH 5 * C H *
4
1
2
3
2
2
2
2
(1-165)
= k C C + k C C − k C C − k C C
1 CH 4 H 2 3 CH 5 * H 2 2 C H 4 H * 4 C H 5 * H *
2
2
2
2
Therefore,
2kC CH 4 C H * = 2 k C C 2 H * 5 C H 2 (1-166)
2
3
2
kC CH 4 = C CH 5 *
2
2
2
kC C (1-167)
3 H 2 H *
From Equation 1-164
)
− ( r = k C C + k C C
2
H 2 1 CH 4 H 2 3 * H 2
net CH 5
2
Substituting Equation 1-167 into Equation 1-164 gives