106
Chapter 4
It should finally be remarked that similar to the relation
Qci=
115 K * there exists an approximate
relation between - AGd and *:*, that holds for any compound with a positive
(i.e. not C 0 2
and H20).
- A
Gci =
94.4
k *
+
86.6 kJ (C-mole)'1
1
(4.16)
This relation may be used in approximate calculations of the free energy change in a given (bio-)
chemical reaction. For the compounds listed in Table 4.3 the standard deviation o f the average
(4.16) is also about 6 kJ (C-mole)'1.
Example 4.5 Heat of reaction for aerobic growth of yeast
Consider the stoichiometry for aerobic yeast fermentation at
D =
0.3 h'1
derived in Example 3.5
- (CH20 + 0.279 • 0 .17NH3 + 0.167O2) +
(0.279CH j ,83 O 0 №
N o 17 + 0.366CO2 +0,355C H 3O 1/2 + 0.275H20 ) = 0
We now calculate the heat of reaction using eqs. (4.11), (4.12), (4.13) and (4.15) respectively:
Eq. (
4
.
1 1
):
Q
= 467 + 0.0474 *383 —
0.279* 560 —
0.355 • 683 = 86.4 kJ (C-mole glucose
)’1
Eq. (4.12):
Q
= (4 + 3 *
0.0474 - 4.71 *
0.279 -
6
0.355) *115 = 80.3 kJ (C-mole glucose
)*1
Eq. (4.13):
Q
= (4-4.20 *0.279-6-0.355) *115 = 80.3
kJ (C-mole glucose
) 1
Eq. (4.15):
Q
= 460 *0.167 = 76.8
kJ (C-mole glucose
)'1
The last result is not equal to the two previous results. The reason is that T*, was determined by an
independent measurement of the rate of oxygen uptake, and not from a degree of reduction balance. As
shown in Example 3.5 the redox balance based on the measured yield coefficients closes only to within
98%. More than this cannot be expected except in very high quality experiments, and the difference
between the calculated
Q
values reflects the uncertainty which must be expected when « are used rather
than the tabulated values of £?ci.
Using eq. (4.16) the free energy change accompanying reaction (1) can also be calculated, at least
approximately:
- AG = 94.4 (4*1+3* 0.0474 - 4.71 ■
0.279 -
6
- 0.355)
+
8 6.6
(1 + 0.0474 - 0.279 - 0.355) = 101.5 kJ (C - mole
)'1
Using thermodynamic tables one obtains the result -AG = 107.8 kJ (C-mole)'1
. The approximate result is
certainly good enough for engineering calculations - first of all it shows that the reaction is strongly
thermodynamically favored.