Page 77 - Modeling of Chemical Kinetics and Reactor Design

Reaction Mechanisms and Rate Expressions 47

Solution

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*
The free radicals are C H O and CH . The net rate of disap-
3
5
2
pearance of C H ONO is:
2
5
2
− ( r ) = k C + k C * C (1-209)
2
C H ONO 2 net 1 C H ONO 2 3 CH 3 C H ONO 2
5
5
2
2
5
*
The net rates of disappearance of the free radicals, C H O and
2
5
*
CH are:
3
( −r * ) = k C * + k C 2 *
2
4
CH O
C H O
CH O
2
5
2
2
5
5
net
(1-210)
− kC − k C C = 0
1 C H ONO 2 3 CH 3 * C H ONO 2
5
5
2
2
( −r ) = k C C − k C = 0
5
2
CH 3 * 3 CH 3 * C H ONO 2 2 CH O * (1-211)
5
2
net
From Equation 1-210
kC CH O * + k C 2 C H O * − k C C H ONO 2 − k C CH 3 * C C H ONO 2 = 0 (1-212)
2
1
3
4
2
5
5
2
5
2
5
2
From Equation 1-211
kC * C − k C * = 0 (1-213)
3
2
5
2
2
5
CH 3 C H ONO 2 CH O
kC * C = k C * (1-214)
3
2
5
2
2
5
CH 3 C H ONO 2 CH O
Substituting equation 1-214 into Equation 1-212 gives
kC CH O * + k C 2 C H O * − k C C H ONO 2 − kC CH O * = 0
1
2
2
4
2
5
5
5
2
2
2
5