340
(iii) Reaction of CO 2 with reduced site of the catalyst
CO 2  + O x − 1  ↔ CO + O x
Forward rate constant = k 3 and backward rate
constant = k −3
(iv) Reaction of adsorbed hydrogen atom
4H ∗  ↔ 2H 2  + 4∗
Forward rate constant = k 4 and backward rate
constant = k −4
(v) Water is produced by reverse water gas shift reaction
H 2  + O x  ↔ H 2 O + O x − 1
Forward rate constant = k 5 and backward rate
constant = k −5
Authors have assumed each of the first four reactions (i) to (iv) as rate-determining
step and have derived following rate expressions (models 1–4, respectively):
Model 1: RDS: equation (i)
r
k
E
RT
N
N N
N N
K
CH
CH
CO
CH
CO
4
4
2
4
2
01
1
2
2
1
1
1
1
=
−






−








exp
H
eq
+ +
+








K
N
N
K N
CO
CO
A
B H
2
1 2
5
2
2
/
Model 2: RDS: equation (ii)
r
k
E
RT
N
N
N N
N N
K
CH
CH
CO
CH
CO
4
4
2
2
4
2
02
2
2
2
2
1
1
1
=
−






−





exp
H
H
eq  


+
+








1
2
1 2
2
2
K
N
N
K N
CO
CO
A
B H
/
Model 3: RDS: equation (iii)
r
k
E
RT
N N
N N
N N
N N
K
CH
CH
CO
CO
CO
CH
CO
4
4
2
2
2
4
2
03
3
2
2
2
1
1
=
−






−
exp
H
H
eq q1








Model 4: RDS: equation (iv)
S. Gupta et al.