Biomedical Engineering Reference
In-Depth Information
From Eqn
(E3-3.1)
, we obtain
v
X
¼ 1 0:52 0:21 2 0:006 4 ¼ 0:036
(E3-3.5)
Using Eqn
(E3-3.4)
, we have
v
X
O
2
v
H
2
O
¼
0:21 4 þ 0:006 8 þ 1:8
¼0:4764
(E3-3.6)
Equation
(E3-3.3)
leads to
v
X
O
2
¼0:0036
v
N
2
¼ 0:2
(E3-3.7)
Equation
(E3-3.2)
can be rearranged to yield
v
O
2
¼
1
v
X
2 ¼0:0068
v
H
2
O
0:52 2 0:21 2 0:006 2 0:5
(E3-3.8)
This concludes the determination. The final stoichiometry is given by
CO
þ 0:0068
O
2
þ 0:0036
N
2
þ 0:476
H
2
O
/
0:52
CO
2
þ 0:21
CH
COOH
þ 0:006
CH
CH
CH
COOH
þ 0:036
CH
O
0
:
5
NO
3
3
2
2
1:8
0:2
3.7. YIELD AND YIELD FACTOR
In the previous section, we found that for each (independent) reaction, there is one inde-
pendent concentration related variable in the stoichiometry. We have defined the numbers of
mole extent and fractional conversion. The fractional conversion is a visual quantity that
examines the fraction of a key reactant being converted by the reaction. In this section, we
will define new parameters that describe the product formed.
With many chemical and biochemical processes, we would like to know the ratio of a reac-
tant that is converted to a particular product. This leads to the concept of yield. We know that
the fractional conversion has a value between 0 and 1, which is easy to visualize and concep-
tually accepted. For the yield, we would like to retain the same range. It is easy for anyone to
understand that a yield between 0 and 100%. However, in order for us to restrict the number
range and make sense, we would need to have the right basis. For example, when two
different molecules (species) combine to form a third molecule (species), it would be delicate
to restrict the yield to be within unity. The yield is thus commonly defined based on given
element of group of elements as
#-moles of R in all the P formed
#-moles of R in all the A in the raw materials
Y
P
=
A
=
R
¼
(3.67)
Here R is the basis or element or groups of elements that is fully contained in both P and A.
In bioreactions, the natural reference (R) is carbon (C) as in most cases we use a carbon
source and carbon is the key component of interest. In this case, Eqn
(3.67)
can be rewritten as
#-C-moles of P formed
#-C-moles of A initially
Y
P
=
A
=
C
¼
(3.68a)
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