The general stochiometric equation for aerobic growth considering product formation has the
following general formula:
In this practical example:
• Substrate: ethanol
CaHoo Mu 2.12 6.1 1.16 46Eno
• N-source: ammonia
NE i
• Biomass: Acetobacter aceti
12 18.105.160214 24 gota
• Product: acetic acid
Caltada Mw 2.12 4.1 216
YEjjjjjj ÉI.IE
60,1
Substituting:
Cato a0 tb NH
cCHisoosNos dCO t eHao f Ha
02
Where a, b, c, d, e, f are stochiometric coe cients
Yield coe cients are also given:
• Biomass yield from substrate
4 5 014GLIESE a activosNos
gano
• Product yield from substrate
4ps 092
siiiii EEEE
To study how the growth in this culture a ects the oxygen demand for acetic acid production, we
have to compare two di erent scenarios:
1) Oxygen demand without biomass growth
2) Oxygen demand with cell growth
Oxygen demand is de ned in this exercise as
onlythechemicalreaction CHOO 0
CHO H2O
iii
as it is indicated
This means, we have to determine the stochiometric coe cients “a” and “f” in both cases and
discuss the results. Without biomass growth, the oxygen demand is easy to calculate:
a
f
IgnotoEo Eoxygendemand 1
With cell growth, the coe cient “a” can be calculated with the degree of reduction
y (number of
equivalents of available electrons per mol of carbon in that substance) using an electron balance:
a
w8s COB
f.jp
Where:
• C
f stochiometric coe cients (unknown for now)
•
•
number of carbon atoms in the substrate
number of carbon atoms in the product
• 8s degree of reduction of ethanol relative to ammonia
• Op degree of reduction of acetic acid relative to ammonia
•8
8s 60
s 8p 4,0
degree of reduction of the biomass relative to ammonia
ya
siiiii ofEsto 3
518
216 42
The value of the stochiometric coe cients “c” and “f” can be determined form the yield coe cients
and the their respective expression :
•
Yx a
III L
En o EFJa.EE jjII c 026
a 4s MEEEE
Therefore, 0,26 gmol cells are produced per gmol ethanol consumed
Yosef EEEEE f YPs.at EEiE 092JEFEYo
jjjjjj
This means that 0,71 gmol acetic acid are produced per gmol ethanol consumed
1 071
Substituting these values into the electron balance for the theoretical oxygen demand with cell
growth gives:
9
4
2.60 026.412 0712.410
1 316gal Fo
But they ask for the oxygen demand per mol acetic acid, so:
to
1316g
071
If we compare the results obtained
gm.IE o
jjjjj
na
1
withoutbiomassgrowth
y
b
with cell growth
y 185
We can contemplate, that the e ect of growth on oxygen demand is noticeable. It is increased
from 1 gmol oxygen per gmol acetic acid to 1,85 gmol oxygen per gmol acetic acid produced.
0
