Page 84 - Modeling of Chemical Kinetics and Reactor Design

54 Modeling of Chemical Kinetics and Reactor Design

dC *
CH 5 = kC C + k C C
2
2
2
dt 2 CH 3 * CH 6 4 H * CH 6
(1-232)
− kC − k C C = 0
3
CH 5 * 5 CH 5 * H *
2
2
dC *
H = kC − k C C − k C C = 0 (1-233)
2
dt 3 CH 5 * 4 H * CH 6 5 H * C H 5 *
2
2
Adding Equations 1-231, 1-232, and 1-233 gives
kC = k C C
1 CH 6 5 H * C H 5 * (1-234)
2
2
This shows that the rate of initiation equals the rate of termina-
tion. Thus,

kC
1
2
C * = CH 6
H kC (1-235)
5 *
2
CH 5
Substituting Equation 1-235 into Equation 1-233 gives
kC kC
1
1
2
2
kC * − k C • CH 6 − kC * • CH 6 = 0
3
5
4
2
CH 5 CH 6 kC * CH 5 kC *
2
2
5
5
CH 5 CH 5
2
2
kk C 2 * − k k C 2 − k C = 0 (1-236)
14
3 5
1
2
2
2
CH 5 CH 6 CH 6
The rate of production of ethylene C H is:
2
4
dC
2
+ ( r ) = CH 4 = kC * (1-237)
2
CH 4 dt 3 CH 5
2
Introducing the chain length,
kC *
3
Chain length = CH 5 (1-238)
2
kC
1 CH 6
2