Biomedical Engineering Reference
In-Depth Information
t
= 0,
C
A
=
C
A0
A
…
t
=
t
,
C
A
FIGURE E4-1.1
A schematic diagram of the batch reactor.
Since the volume is constant (constant volume batch reactor), Eqn
(E4-1.2)
is reduced to
d
C
A
d
¼ r
A
(E4-1.3)
t
Applying the rate law,
r
A
¼ v
A
r ¼kC
O
RA
(E4-1.4)
A
Substitute the rate expression, Eqn
(E4-1.4)
, into the reduced mole balance Eqn
(E4.1-3)
,
one obtains
d
C
A
d
¼ r
A
¼kC
O
RA
(E4-1.5)
A
t
Separation of variables,
d
C
A
C
O
RA
A
¼k
d
t
(E4-1.6)
And integrate:
Z
C
A
Z
t
d
C
A
C
O
RA
A
¼
k
d
t
(E4-1.7)
C
A0
0
If
O
RA
¼
1, i.e. for a first-order reaction, we have
Z
C
A
Z
t
d
C
A
C
A
¼
k
d
t
(E4-1.8)
0
C
A0
which can be integrated to yield
C
A
C
A0
¼ktj
t
0
ln C
A
j
(E4-1.9)
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