Biomedical Engineering Reference
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Noting that at thermodynamic equilibrium the reaction rate becomes zero, we can combine
the constant terms together for
Eqn (9.135)
to give
p
3
H
2
p
2
NH
3
!
m
p
2
NH
3
p
3
H
2
!
1m
k
K
P
r ¼ kp
N
2
(9.136)
and
k ¼ k
N
2
K
P
K
N
2
RT
m
E
a
E
max
E
max
e
where
m ¼
. Eqn
(9.136)
is known as the Temkin equation.
This illustrates that the linear energy distribution with Temkin simplification also leads to
power-law kinetic expressions. The power-law appearance after Temkin simplification has it
attractive as it is analogous to homogenous reactions. Because of the approximation made in
the Temkin model that the coverage be in the intermediate region and the variation of the
TABLE 9.4
Comparison of LHHW Rate Expressions with Power-Law Expressions
Reaction and data source
LHHW
Power-law
SO
2
oxidation
kðp
SO
2
p
1=2
r ¼ kðp
SO
2
p
1=2
SO
3
p
1=2
SO
3
p
1=2
O
2
p
SO
3
=K
P
Þ
=K
P
Þ
O
2
r ¼
1
=
2
2
13.3% deviations over 12
experiments on variation of
partial pressures of SO
2
and SO
3
.
1
2
O
2
%
½
1
þðK
O
2
p
O
2
Þ
þ K
SO
2
p
SO
2
SO
2
þ
SO
3
15.4% deviations over 12
experiments on variation of
partial pressures of SO
2
and SO
3
.
W.K. Lewis and E.D. Ries,
Ind.
Eng. Chem
., 19, 830, 1937
O.A. Uyehara and K.M. Watson,
Ind. Eng. Chem.
35, 541, 1943.
Hydrogenation of codimer (C)
kp
H
2
p
C
1
=
2
r ¼ kðp
H
2
p
C
Þ
r ¼
2
ð
1
þ K
H
2
p
H
2
þ K
C
p
C
þ K
P
p
P
Þ
H
2
þ
C
P
%
19.6% deviation at 200
C
32.9% deviation at 275
C
21.4% deviation at 325
C
20.9% deviation at 200
C
19.6% deviation at 275
C
19.4% deviation at 325
C
J.L. Tschernitz et al.
Trans. Amer.
Inst. Chem. Eng.
, 42, 883, 1946
Phosgene synthesis
kp
CO
p
Cl
2
r ¼ kp
CO
p
1=2
Cl
2
13.0% deviation at 30.6
C
9.1% deviation at 42.7
C
13.9% deviation at 52.5
C
3.0% deviation at 64.0
C
r ¼
2
ð
1
þ K
Cl
2
p
Cl
2
þ K
COCl
2
p
COCl
2
Þ
CO
þ
Cl
2
%
COCl
2
3.4% deviation at 30.6
C
5.6% deviation at 42.7
C
2.6% deviation at 52.5
C
7.0% deviation at 64.0
C
C. Potter and S. Baron,
Chem. Eng.
Progr.
47, 473, 1951.
Toluene alkylation by methanol
k
ð
P
M
P
T
P
X
p
W
=
K
P
Þ
P
W
þ K
M
p
M
þ K
X
p
X
2.07% deviation
Eley
e
Rideal model
(Fraenkel D. “Role of External
Surface Sites in Shape Selective
Catalysis over Zeolites.”
Ind. Eng.
Chem. Res.
1990,29, 1814
e
1821)
r ¼
r ¼ kp
T
p
M
4.65% deviation
T
þ
M
%
X
þ
W
J.L. Sotelo et al., “Kinetics of
Toluene Alkylation with
Methanol over Mg-Modified
ZSM-5”,
Ind. Eng. Chem. Res.
1993, 32, 2548
e
2554.
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