Biomedical Engineering Reference
In-Depth Information
which leads to
d
f
A
d
f
A
kC
A
F
A
0
r
A
¼
d
V ¼ F
A
0
(E5-2.2)
The concentration of A at any where in the reactor can be calculated through
F
A
1 f
A
Q
C
A
¼
Q
¼ F
A
0
(E5-2.3)
The volumetric flow rate changes in the reactor as the number of moles of the reaction
mixture changes. The volumetric flow rate is proportional to the total molar flow rate change.
Stoichiometry is needed to find the total molar flow rate. Table E5-2 shows a summary of
stoichiometry.
TABLE E5-2
Stoichiometry of the Reaction System
Species
Initial
Change
At
V
A
F
A0
F
A0
f
A
F
A0
(1
f
A
)
B
0
F
A
0
f
A
F
A0
f
A
C
0
F
A0
f
A
F
A0
f
A
Total
F
A0
F
A0
f
A
F
A0
(1
þ
f
A
)
Based on ideal gas
PQ ¼ FRT
(E5-2.4)
Since the pressure is constant, we have
Q
Q
0
¼
F
F
0
¼ 1 þ f
A
(E5-2.5)
Substituting
Eqn (E5-2.5)
into
Eqn (E5-2.3)
, we obtain
F
A
0
Q
0
1
f
A
1 f
A
1 þ f
A
C
A
¼
1 þ f
A
¼ C
A
0
(E5-2.6)
Substituting
Eqn (E5-2.6)
into
Eqn (E5-2.2)
, we obtain
F
A
0
kC
A
F
A
0
kC
A
0
1
þ
f
A
1 f
A
Q
0
k
1
þ
f
A
1 f
A
d
V ¼
d
f
A
¼
d
f
A
¼
d
f
A
(E5-2.7)
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