Page 67 - Modeling of Chemical Kinetics and Reactor Design

Reaction Mechanisms and Rate Expressions 37

This agrees with experimental results.
The activation energy that is expected according to a relevant chain
reaction mechanism can be determined if each elementary rate con-
stant is expressed with a temperature dependence according to the
Arrhenius equation,

K = A exp  − E  (1-154)
i
RT 

i
i
Substituting Equation 1-154 into the predicted rate law allows the
temperature dependence of the overall reaction to be predicted. In the
decomposition of acetaldehyde, it follows that

 − E   k  . 05
1
a
K obs = A obs exp  RT  = k 2  k  
 2
4
(1-155)
− (
. 05

E RT) 
E 
= A exp  − RT  2 A exp − ( E RT) 
1
1
2


2

A exp
4
4
Separating the variables gives
1
E − )
E = E + ( 1 E 4 and A obs = A 2   A   05 . (1-156)
1
2
a
2  2 A 
4
The activation energy for an overall chain reaction can be smaller than
E , the activation energy for the initiation step.
1
CHAIN LENGTH
The efficiency of a chain reaction depends on the number of
recycles of the active center for each initiation. The chain length can
be defined as:
Chain length = the rate of the overall chain reaction
the rate of the initiation reaction