Biomedical Engineering Reference
In-Depth Information
The total molar flow rate can be computed by summing up all the component (species) flow
rates. That is
F
j0
þ n
j
X
N
S
X
N
S
X
N
S
j¼1
n
j
F
A
F
A
0
n
A
F
A
F
A
0
n
A
F ¼
F
j
¼
¼ F
0
þ
(5.15)
j¼1
j¼1
Letting
n
S
be the total stoichiometric coefficients, i.e.,
X
N
S
j¼1
n
j
n
S
¼
(5.16)
We obtain
F ¼ F
0
þ
n
S
n
A
ðF
A
F
A
0
Þ¼F
0
n
S
n
A
F
A
0
f
A
(5.17)
While the above derivation is concise, we often tabularize the stoichiometry to gain a thor-
ough understanding of the stoichiometry for every species, either be those involved in the
reaction or those that are not participating in the actual reaction. The stoichiometry is shown
in
Table 5.1
.
The concentration can be related to the molar flow rate through
F
j0
þ
n
j
F
j0
n
j
n
A
ðF
A
F
A
0
Þ
Q
n
A
F
A
0
f
A
Q
F
j
Q
¼
C
j
¼
¼
(5.18)
The volumetric flow rate
Q
can be a function of temperature and pressure (density
change). Since the mass flow rate does not change if no side inlets or outlets, we have
F
j0
þ
n
j
F
j0
n
j
n
A
ðF
A
F
A
0
Þ
Q
0
n
A
F
A
0
f
A
Q
0
C
j
¼
r
r
0
¼
r
r
0
(5.19)
For isothermal operations,
Q
is constant for reactions involving condensed matter (liquid
or solid) only. For ideal gas, the volumetric flow rate can be related to the molar flow rate
through ideal gas law
PQ¼ FRT
(5.20)
TABLE 5.1
Stoichiometry of a Reaction System with Side Inlets or Outlets
Species
Initial
Change
At
V
A
F
A0
F
A
F
A0
F
A
F
j
F
j0
¼ n
j
F
A
F
A
0
n
A
F
j
¼ F
j0
þ n
j
F
A
F
A
0
n
A
j
F
j
0
.
.
.
.
P
N
j¼1
ðF
j
F
j0
Þ¼n
S
F
A
F
A
0
n
A
P
N
F
A
F
A
0
n
A
Total
F
0
F
j
¼ F
0
þ n
S
j¼1
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