Biomedical Engineering Reference
In-Depth Information
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
(5.50)
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
(5.51)
which leads to
1 þ
n
S
n
A
Q
0
¼
1
n
S
n
A
f
A
Q
0
P
0
T
PT
0
F
F
0
P
0
T
PT
0
F
A
F
A
0
F
0
P
0
T
PT
0
F
A
0
F
0
Q ¼
Q
0
¼
(5.52)
Example 5-3. Rework example 5-1 for a CSTR. An elementary first-order reaction:
/
B
is to be carried out in a CSTR. If the rate constant
k
A
0.02/s and the volumetric flow rate is
constant at 10 L/s, calculate the reactor volume required for 50% conversion.
Solution.
Figure E5-3
shows a schematic diagram of the constant density CSTR.
Mole balance for species A over the entire CSTR volume at steady state leads to
¼
ðQC
A
Þ
0
ðQC
A
Þþr
A
V ¼ 0
(E5-3.1)
which leads to
f
A
f
A
f
A
kC
A
0
1 f
A
QC
A
0
r
A
¼ V ¼ QC
A
0
kC
A
¼ QC
A
0
(E5-3.2)
Therefore
Q
k
f
A
1 f
A
V ¼
(E5-3.3)
Q
A B
C
A
C
B
Q
C
A
C
B
f
Ae
FIGURE E5-3
A schematic diagram of a constant density CSTR.
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