Page 71 - Modeling of Chemical Kinetics and Reactor Design

Reaction Mechanisms and Rate Expressions 41

kC C − k C C + k C C − k C C = 0 (1-174)
1 CH 4 H 2 2 C H 4 H * 3 C H 5 * H 2 4 CH 5 * H *
2
2
2
2
Adding Equations 1-173 and 1-174 gives
2kC 2 4 C H 2 − 2k C CH * 5 C H * = 0 (1-175)
1 CH
4
2
Subtracting Equations 1-173 from Equation 1-174 yields

2kC C − 2k C C = 0
2 CH 4 H * 3 C 2 H * 5 H 2 (1-176)
2
kC CH 4 C H 2 = k C CH 5 * C H * (1-177)
4
1
2
2
and
kC C = k C C
2 CH 4 H * 3 C H 5 * H 2 (1-178)
2
2
From Equation 1-177

kC C
1
2
C * = CH 4 H 2 (1-179)
2
CH 5 kC H *
4
Substituting Equation 1-179 into Equation 1-178 gives
kC C
1
2
kC CH 4 C H * = k • C H 2 • CH 4 H 2
2
3
2
kC
4 H *
Therefore,
C 2 * = k 3 • k 1 C 2
H k k H 2
2 4

where

K = k 3 • k 1
k k
2 4