Page 86 - Modeling of Chemical Kinetics and Reactor Design

56 Modeling of Chemical Kinetics and Reactor Design

− ( r ) =+ ( r )
CH 6 CH 4
2
2
dC dC  kk k  05 .
− CH 6 = CH 4 = kC * =  13 4  C
2
2
3
2
dt dt CH 5  k 5  CH 6
2
05 .
= KC (1-244)
2
CH 6
This mechanism explains the first order dependence of the reaction.
(2) Develop now another mechanism accounting for the formation
of both methane and butane.
If other possible termination steps are considered, then it can be
inferred that recombination or disproportionation of ethyl radicals,
C * is more likely than recombination of C * and C * . Step 5
2
CH 5 H CH 5
2
should then be replaced by
*
*
5a. CH + CH → C H 10
2
2
4
5
5
and
*
*
5b. CH + CH → CH + CH 6
2
5
5
4
2
2
2
This also accounts for the production of the small amount of butane.
If the reaction mechanism were steps 1, 2, 3, 4, 5a, and 5b, then
applying the steady state approximations would give the overall order
of reaction as 1/2.
Assuming that the initiation reaction is second order, then step
1 becomes
*
1a. CH + CH → 2 CH + CH 6
6
3
2
2
2
6
The reaction mechanism now becomes
Initiation
*
1a. CH + CH  → 2 CH + CH (1-245)
k a1
2 6 2 6 3 2 6

*
2. CH + C H  → CH + C H * 5 (1-246)
k 2
6
2
3
2
4