Biomedical Engineering Reference
In-Depth Information
TABLE 4.2
Reaction Residence Time Requirement and Concentration Profile for Single Reactions in an
Isothermal Constant Volume Batch Reactor for Some Simple Kinetic Models
1. Zeroth order
A
products
;
r
¼
k
:
/
t ¼ð
C
A0
C
A
Þ=k
;C
A
¼
C
A0
kt
;
r
¼
k
C
A
2. First order
:
A
/
products
t ¼ lnð
C
A0
C
A
Þ=k
;C
A
¼
C
A0
expðktÞ
k
C
n
A
3. Power-law kinetics
A
products
;
r
¼
:
/
C
1n
C
1n
A
ð1 nÞk
;C
A
¼
C
1n
A
0
1 n
kt
1
A
0
t ¼
1n
4. Bimolecular
A
þ
B
products
;
r ¼ k
C
A
C
B
:
/
C
A
;C
A
¼
t ¼
1
k
C
A
0
C
A
0
1 þ k
C
B
¼
C
A
0
t
;
if C
A
0
¼
C
B
0
1
C
A
0
ð
C
A
þ
C
B
0
C
A
0
Þ
C
A
0
ð
C
B
0
C
A
0
Þ
t ¼
ln
;C
A
¼
;C
B
¼
C
B0
C
A0
þ
C
A
kð
C
B
0
C
A
0
Þ
C
A
C
B
0
C
B
0
exp½kð
C
B
0
C
A
0
Þt
C
A
0
5. Autocatalytic: A
þ
R
2 R
þ
products
;
r
¼
k
C
A
C
/
R
1
C
A
0
ð
C
A
0
þ
C
R0
C
A
Þ
C
A
0
ð
C
A
0
þ
C
R0
Þ
t ¼
ln
;
C
A
¼
;C
R
¼
C
A0
þ
C
R
0
C
A
kð
C
A
0
þ
C
R0
Þ
C
A
C
R0
C
A
0
þ
C
R0
exp½kð
C
A
0
þ
C
R0
Þt
k
C
A
K
A
þ
6. Unimolecular catalytic
A
products
;
r
¼
:
/
C
A
C
A
1
k
C
A
0
C
A
þ
t ¼
K
A
ln
C
A
0
k
C
2
A
K
A
þ
;
r
¼
7. Unimolecular catalytic
:
A
/
products
C
A
1
k
C
A
0
C
A
þ
K
A
C
A
K
A
t ¼
ln
C
A
0
8. First-order reversible
:
A
%
B
;
r
¼
k
f
C
A
k
b
C
B
k
f
C
A
0
k
b
C
B
0
exp
h
i
C
A
0
þ
C
B
0
k
f
þ k
b
t
þ k
b
k
f
C
A
0
k
b
C
B
0
1
k
f
þ k
b
ln
C
A
k
b
C
A
0
þ
C
B
0
;C
A
¼
t ¼
k
f
þ k
b
k
f
þ k
b
C
B
¼
C
A0
þ
C
B
0
C
A
k
ð
C
A
C
B
=
K
C
Þ
9. Catalytic first-order reversible
A
B
;
r ¼
:
%
1
þ
K
A
C
A
þ
K
B
C
B
K
A
K
B
C
A
0
C
A
C
A
0
þ
K
B
þ
K
A
K
B
K
C
K
C
kð1 þ K
C
Þ
ln
ð1 þ K
C
Þ
C
A
0
ð
C
A
0
þ
C
B
0
Þ
t ¼
þ
1 þ
C
B
0
ð1 þ K
C
Þ
C
A
ð
C
A
0
þ
C
B
0
Þ
C
B
¼
C
A0
þ
C
B0
C
A
(
Continued
)
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