Page 60 - Modeling of Chemical Kinetics and Reactor Design

30 Modeling of Chemical Kinetics and Reactor Design
Adsorption Step: A + [ x (1-123)
k 1
x
1 k −1 2
Surface Reaction: x [ x (1-124)
k 2
2 k 2− 3

Desorption Step: x [ R + x (1-125)
k 3
3 k 3− 1

The rate equations are:

A: − ( r ) = k C C − k C (1-126)
A net 1 A x 1 −1 x 2

R: + ( r ) = k C − k C C (1-127)
R net 3 x 3 −3 R x 1
x : + ( r ) = + − + k )
−
A
2
1
2 x 2 k C C x 1 k C x 3 k ( − 1 2 C x 2 (1-128)
net
x : + ( r ) = + + k )
k
−
2
R
3 x 3 k C x 2 k C C − ( − 2 3 C x 3 (1-129)
3
x 1
net
Assume:
1. (+r ) and (+r ) are zero
x 2 net x 3 net
2. Number of active sites remains constant, C .
T
Thus,
C = C x 2 + C x 3 + C x 1 (1-130)
T
Usually, one of the elementary steps is rate controlling (that is, it
is very slow relative to all the other steps). Suppose that A + x →
1
x is the rate-controlling step and the reverse reaction is ignored, then
2
− ( r ) ≅ k C C (1-131)
A net 1 A x 1
Under these conditions, the desorption process and surface reactions
are in a pseudo-equilibrium state:

kC ≅ k C (1-132)
2 x 2 − 2 x 3