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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