Biomedical Engineering Reference
In-Depth Information
7.4.1.2 Gibbs Free Energy
Gibbs free energy, G, is an important thermodynamic function. Its change in
terms of a change in entropy,
Δ
Δ
S, and enthalpy,
H, is written as:
Δ
G
5
Δ
H
T
Δ
S
(7.34)
2
The change in enthalpy or entropy for a reaction system is computed by
finding the enthalpy or entropy changes of individual gases in the system. It
is explained in Example 7.2. An alternative approach uses the empirical
equations given by Probstein and Hicks (2006). It expresses the Gibbs func-
tion (
Eq. (7.35)
) and the enthalpy of formation (
Eq. (7.36)
) in terms of tem-
perature, T, the heat of formation at the reference state at 1 atm and 298 K,
and a number of empirical coefficients, a
0
, b
0
, and so forth.
T
3
T
4
c
0
2
d
0
3
G
f
;
T
5
Δ
h
298
2
a
0
T ln
b
0
T
2
Δ
ð
T
Þ
2
2
2
1
(7.35)
e
0
2T
f
0
1
g
0
T kJ
=
mol
1
1
e
0
T
H
f
;
T
5
Δ
h
298
2
a
0
T
b
0
T
2
c
0
T
3
d
0
T
4
f
0
kJ
Δ
=
mol
(7.36)
1
1
1
1
The values of the empirical coefficients for some common gases are given
in
Table 7.5
.
The equilibrium constant of a reaction occurring at a temperature T may
be known using the value of Gibbs free energy.
2
Δ
G
RT
K
e
5
exp
(7.37)
TABLE 7.4
Equilibrium Constants and Heats of Formation for Five
Gasification Reactions
Heat of Formation
(kJ/mol)
Equilibrium Constant (log
10
K)
Reaction
298 K
1000 K
1500 K
1000 K
1500 K
C
2
O
2
-
CO
24.065
10.483
8.507
111.9
116.1
1
1
2
2
C
O
2
-
CO
2
69.134
20.677
13.801
394.5
395.0
1
2
2
C
2H
2
-
CH
4
8.906
0.999
2.590
89.5
94.0
1
2
2
2
2
2C
2H
2
-
C
2
H
4
11.940
6.189
5.551
38.7
33.2
1
2
2
2
H
2
2
O
2
-
H
2
O
40.073
10.070
5.733
247.8
250.5
1
1
2
2
Source: Data compiled from Probstein and Hicks (2006), p. 64.
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