Page 70 - Modeling of Chemical Kinetics and Reactor Design

40 Modeling of Chemical Kinetics and Reactor Design

2
− ( r ) = k C C + k 2 • C CH 4 • C k C
H 2 1 CH 4 H 2 H * 3 H 2
2
net k 3 C H 2
(1-168)
= kC CH 4 C H 2 + k C C H 4 C H *
2
1
2
2
The overall rate of reaction of C is
2
CH 4
)
− ( r = k C C + k C C (1-169)
2
2
2
CH 4 net 1 CH 4 H 2 2 C H 4 H *
r − ( CH ) − k C C
2
C = 2 4 net 1 CH 4 H 2 (1-170)
H * kC CH 4
2
2
Substituting Equation 1-170 into Equation 1-168 yields
)  − ( r CH 4 ) net − k C CH 4 C H 2 


1
2
2
− ( r = k C C + k C  
H 2 1 CH 4 H 2 2 C H 4
2
2
net kC
 2 CH 4 


2
= kC C + − ( r ) − kC C
1 CH 4 H 2 C H 4 net 1 CH 4 H 2
2
2
2
− ( r ) =− ( r ) (1-171)
H 2 CH 4
2
net net
− ( r ) =− ( r ) = k C C + k C C * (1-172)
H 2 CH 4 1 CH 4 H 2 2 C H 4 H
2
2
2
net net
but
2
C * = k 3 • C CH 5 * C H 2
H k 2 C CH 4
2
)
Since (+r * net and (+r * net are zero
)
2
CH 5 H
kC C + k C C − k C C − k C C = 0 (1-173)
1 CH 4 H 2 2 C H 4 H * 3 C H 5 * H 2 4 CH 5 * H *
2
2
2
2