Biomedical Engineering Reference
In-Depth Information
Thus,
ln C
A
ln C
A0
¼kt
(E4-1.10)
Equation
(E4-1.10)
can be rearranged to yield
C
A
¼ C
A0
expðktÞ
(E4-1.11)
That is, the concentration of A decreases exponentially in a batch reactor for a first-order
reaction.
If
O
RA
s
1, Eqn
(E4-1.7)
is integrated to yield
C
A
C
A0
¼ktj
t
0
C
1O
RA
A
1 O
RA
(E4-1.12)
Thus,
C
1O
RA
A
C
1O
RA
A0
¼ð1 O
RA
Þkt
(E4-1.13)
Equation
(E4-1.13)
can be rearranged to yield
h
C
1O
RA
i
1
1O
RA
C
A
¼
A0
ð1 O
RA
Þkt
(E4-1.14)
That is, the concentration of A decreases following a hyperbolic path for an
O
RA
th-order
reaction.
Fig. E4-1.2
shows the plots for the concentration of A as a function of time. One can
observe that the concentration drops down quicker for a lower order reaction than a higher
order reaction. This is due to the fact that at low concentrations, higher order reactions are
slower than lower order reactions.
Example 4-2. Variable Volume Batch Reactor. A gaseous reaction
r ¼ kC
2
A
;
A ! B þ C
0.1 mol
1
·L·s
1
with
k
¼
C
A0
C
A
O
RA
> 1
O
RA
= 1
O
RA
< 1
0
0
O
RA
-1
k
C
A0
t
FIGURE E4-1.2
Concentration of A as a function time
t
for an O
RA
th-order reaction in a constant volume batch
reactor.
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