Biomedical Engineering Reference
In-Depth Information
Δ G is the standard Gibbs function of reaction or free energy change
for the reaction, R is the universal gas constant, and T is the gas temperature.
Here,
Example 7.2
Find the equilibrium constant at 2000 K for the reaction
CO 2 -
CO
1
1
=
2O 2
Solution
Enthalpy change is written by taking the values for it from the NIST-JANAF ther-
mochemical tables (Chase, 1998) for 2000 K:
h f 1 Δ
h f 1 Δ
h f 1 Δ
Δ
H
5 ð
h
Þ CO 1 ð
h
Þ O 2 2 ð
h
Þ CO 2
1 mol
ð 2
110
;
527
56
;
744
Þ
J
=
mol
1
=
2 mol
ð
0
59
;
175
Þ
J
=
mol
5
1
1
1
1 mol
ð 2
393
;
522
91
;
439
Þ
J
=
mol
277
;
887 J
2
1
5
S, is written in the same way as for taking the values
of entropy change from the NIST-JANAF tables.
Δ
The change in entropy,
Δ
S
1
S CO
1
=
2
S O 2 2
1
S CO 2
5
3
1
3
3
5 ð
1 mol
3
258
:
71 J
=
mol K
Þ 1 ð
1
=
2 mol
3
268
:
74 J
=
mol K
Þ
2 ð
1 mol
309
:
29 J
=
mol K
Þ
3
K
From Eq. (7.34) , the change in the Gibbs free energy can be written as:
Δ
83
:
79 J
=
5
G
5 Δ
H
T
Δ
S
2
277
:
887 kJ
2 ð
2000 K
83
:
79 J
=
K
Þ 5
110
:
307 kJ
5
3
The equilibrium constant is calculated using Eq. (7.37) :
ð
Þ 5
e 2 ΔG
110
:
307
K 2000 K
e 2
0
:
001315
(7.38)
5
5
RT
0
:
008314
3
2000
7.4.1.3 Kinetics of Gas
Solid Reactions
The rate of gasification of char is much slower than the rate of pyrolysis of
the biomass that produces the char. Thus, the volume of a gasifier is more
dependent on the rate of char gasification than on the rate of pyrolysis. The
char gasification reaction therefore plays a major role in the design and per-
formance of a gasifier.
Typical temperatures of the gasification zone in downdraft and fluidized-
bed reactors are in the range of 700
900 C. The three most common
gas
solid reactions that occur in the char gasification zone are as follows:
ð
CO 2 -
Þ
Boudouard reaction:
R1:C
1
2CO
(7.39)
Water
gas reaction:
ð
R2:C
H 2 O
2
CO
H 2 Þ
(7.40)
1
1
Methanation reaction:
ð
R3:C
2H 2 2
CH 4 Þ
(7.41)
1
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