Page 85 - Modeling of Chemical Kinetics and Reactor Design

Reaction Mechanisms and Rate Expressions 55

If the chain length is large, it follows that

kC * >> k C (1-239)
3
1
2
2
CH 5 CH 6
and Equation 1-236 becomes
kk C 2 − k k C 2 = 0 (1-240)
3 5 * 14 CH 6
2
2
CH 5
Thus,
 kk  05 .
C * =  14  C (1-241)
2
2
CH 5  kk  CH 6
3 5
Substituting Equation 1-241 into Equation 1-237 gives

.
dC  kk  05
2
+ ( r ) = CH 4 = k  14  C
2
CH 4 dt 3  kk  CH 6
2
3 5
 kk k  05 .
=  13 4  C (1-242)
 k 5  CH 6
2
The rate of decrease in ethane C H is:
2 6
dC
2
− ( r ) =− CH 6
2
CH 6 dt
dC
− CH 6 = kC + k C * C + k C * C − k C * C *
2
5
4
2
1
2
2
2
dt CH 6 CH 3 CH 6 H CH 6 H C H 5
2
which together with Equation 1-232 yields
dC
2
− ( r ) =− CH 6 = kC + k C * (1-243)
2
2
CH 6 dt 1 CH 6 3 CH 5
2
From Equations 1-237, 1-239, and 1-242, it follows that