Biomedical Engineering Reference
In-Depth Information
TABLE 9.3
Some Examples of LHHW Rate Expressions
Mechanism/
controlling step
Overall reaction
Rate expression
C
A
C
B
=K
eq
1) Isomerization
A
A
þ s
%
A
$s
r ¼ k
A
C
s
1
þ K
B
C
B
þ K
1
eq
K
A
C
B
B
%
C
A
C
B
=K
eq
A
$s
%
B
$s
r ¼ k
s
K
A
C
s
1
þ K
A
C
A
þ K
B
C
B
K
eq
C
A
C
B
r ¼ k
B
C
s
B
$s
%
B
þ s
1
þ K
A
C
A
þ K
eq
K
B
C
A
C
A
C
B
C
C
=K
eq
r ¼ k
A
C
s
2) Decomposition
(Double site)
A
A
þ s
%
A
$s
1
þ K
A
K
1
eq
C
B
C
C
þ K
B
C
B
þ K
C
C
C
B
þ
C
%
C
A
C
B
C
C
=K
eq
A
$s þ s
%
B
$s þ
C
$s
r ¼ k
s
K
A
C
2
s
2
ð
1
þ K
A
C
A
þ K
B
C
B
þ K
C
C
C
Þ
K
eq
C
A
C
B
C
C
K
B
K
eq
C
A
þð
B
$s
%
B
þ s
r ¼ k
B
C
s
1
þ K
A
C
A
þ K
C
C
C
ÞC
C
K
eq
C
A
C
B
C
C
K
C
K
eq
C
A
þð
C
$s
%
C
þ s
r ¼ k
C
C
s
1
þ K
A
C
A
þ K
B
C
B
ÞC
B
C
A
C
B
C
C
C
D
=K
eq
r ¼ k
A
C
s
3) Bimolecular
(single site)
A
A
þ s
%
A
$s
K
A
K
1
eq
C
C
C
D
þð
1
þ K
B
C
B
þ K
C
C
C
þ K
D
C
D
ÞC
B
þ
B
%
C
þ
D
C
A
C
B
C
C
C
D
=K
eq
r ¼ k
B
C
s
B
þ s
%
B
$s
K
B
K
1
eq
C
C
C
D
þð
1
þ K
A
C
A
þ K
C
C
C
þ K
D
C
D
ÞC
A
C
A
C
B
C
C
C
D
=K
eq
r ¼ k
s
K
A
K
B
C
2
A
$s þ
B
$s
%
C
$s þ
D
$s
s
2
ð
1
þ K
A
C
A
þ K
B
C
B
þ K
C
C
C
þ K
D
C
D
Þ
K
eq
C
A
C
B
C
C
C
D
K
eq
K
C
C
A
C
B
þð
C
$s
%
C
þ s
r ¼ k
C
C
s
1
þ K
A
C
A
þ K
B
C
B
þ K
D
C
D
ÞC
C
K
eq
C
A
C
B
C
C
C
D
K
eq
K
D
C
A
C
B
þð
r ¼ k
D
C
s
D
$s
%
D
þ s
1
þ K
A
C
A
þ K
B
C
B
þ K
C
C
C
ÞC
D
C
A
2
C
B
C
C
C
2
D
=K
eq
4) Bimolecular
(dissociative)
1
2
A
2
þ
A
2
þ
2s
%
2
A
$s
r ¼ k
A
2
C
2
s
½K
1=2
2
A
2
K
1
eq
C
C
C
D
þð
1
þ K
B
C
B
þ K
C
C
C
þ K
D
C
D
ÞC
B
B
%
C
þ
D
C
1=2
A
2
C
B
C
C
C
D
=K
eq
þ s
%
B
$s
r ¼ k
B
C
s
p
K
A
2
C
A
2
B
K
B
K
1
eq
C
C
C
D
þð
1
þ
þ K
C
C
C
þ K
D
C
D
ÞC
A
C
1=2
A
2
C
B
C
C
C
D
=K
eq
r ¼ k
s
K
1=2
A
2
K
B
C
2
p
A
$s þ
B
$s
%
C
$s þ
D
$s
K
A
2
C
A
2
s
2
ð
1
þ
þ K
B
C
B
þ K
C
C
C
þ K
D
C
D
Þ
K
eq
C
1=2
A
2
C
B
C
C
C
D
C
$s
%
C
þ s
r ¼ k
C
C
s
p
K
A
2
C
A
2
K
eq
K
C
C
1=2
A
2
C
B
þð
1
þ
þ K
B
C
B
þ K
D
C
D
ÞC
C
K
eq
C
1=2
A
2
C
B
C
C
C
D
D
$s
%
D
þ s
r ¼ k
D
C
s
p
K
A
2
C
A
2
K
eq
K
D
C
1=2
A
2
C
B
þð
1
þ
þ K
B
C
B
þ K
C
C
C
ÞC
D
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