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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