Biomedical Engineering Reference
In-Depth Information
TABLE 7.9
Forward Reaction Rates,
r
, for Gas-Phase Homogeneous
Reactions
Reaction Rate
(
r
)
Heat of Formation
(m
3
/mol/s)
Reaction
References
51.8 T
1.5
exp
(
H
2
1
1
2
O
2
-
H
2
O
KC
1:5
Vilienskii and
Hezmalian (1978)
H
2
C
O
2
3420/T)
2
10
12
exp
CO
1
2
O
2
-
CO
2
KC
CO
C
0:5
O
2
C
0:5
H
2
O
2.238
Westbrook and
Dryer (1981)
1
3
(
167.47/RT)
2
CO
1
H
2
O
-
CO
2
1
H
2
KC
CO
C
H
2
O
0.2778 exp
(
Petersen and
Werther (2005)
2
12.56/RT)
Note: Here, the gas constant, R, is in kJ/mol K.
catalysts. Below 400
C, a chromium-promoted iron formulation catalyst
(Fe
2
O
3
2
Cr
2
O
3
) may be used (Littlewood, 1977).
Other gas-phase reactions include CO combustion, which provides heat
to the endothermic gasification reactions:
1
2
O
2
!
k
for
=
R6:CO
1
CO
2
2
284 kJ
mol
(7.53)
These homogeneous reactions are reversible. The rate of forward reac-
tions is given by the rate coefficients given in
Table 7.9
.
For the backward CO oxidation reaction (CO
k
back
1
2
O
2
CO
2
),
the
1
rate, k
back
, is given by Westbrook and Dryer (1981) as:
k
back
5
5
:
18
3
10
8
exp
ð
2
167
:
47
=
RT
Þ
C
CO
2
(7.54)
k
back
For the reverse of the shift reaction (CO
H
2
O
CO
2
1
H
2
), the
1
rate is given as:
m
3
k
back
5
126
:
2 exp
ð
2
47
:
29
=
RT
Þ
C
CO
2
C
H
2
mol
=
(7.55)
If the forward rate constant is known, then the backward reaction rate,
k
back
, can be determined using the equilibrium constant from the Gibbs free
energy equation:
G
0
RT
k
for
k
back
5
exp
2
Δ
K
equilibrium
5
at 1 atm pressure
(7.56)
G
0
for the shift reaction may be calculated (see Callaghan, 2006) from
a simple correlation of:
Δ
G
0
Δ
32
:
197
0
:
031T
2
ð
1774
:
7
=
T
Þ;
kJ
=
mol
(7.57)
52
1
where T is in K.
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