Biomedical Engineering Reference
In-Depth Information
The key phrase in the proceeding paragraph is “apparently involved in reaction.” While
one may find true first-order reactions, such as nuclear decay reactions, past experience
has shown that most apparent first-order reactions can behave differently at different concen-
trations. The main reason lies here that molecules need to be activated for reaction to occur.
Lindemann (1922) was the first to treat the apparent unimolecular reactions through the colli-
sional activation concept. In order for the reaction to occur, one A molecule needs to be acti-
vated by colliding with another molecule, i.e.
A
þ
A
þ
U
/
U
r
1
¼
k
C
A
C
U
(6.48)
1
A
þ
W
/
A
þ
W
r
2
¼
k
C
A
C
W
(6.49)
2
A
/
products
r
3
¼
k
C
A
(6.50)
3
The first step involves the activation of the A molecule by collision with another molecule U,
in the system to give A*. A second step involves the deactivation of A* by collision with
a third molecule W. One can postulate that the activated A* is unstable as it possesses higher
energy than normal A molecule. Therefore, a PSS can be applied to A*, i.e. the net formation
rate of A* is zero. This gives
r
A
¼ 1
r
1
þð1Þ
r
2
þð1Þ
r
3
¼
k
C
C
U
k
C
A
C
W
k
C
A
(6.51)
0 ¼
1
2
3
A
from which we obtain,
k
C
C
1
A
U
C
A
¼
(6.52)
k
C
W
þ
k
2
3
Thus, for the overall reaction
A
/
products
(6.53)
The reaction rate is given by
k
k
C
U
1
3
r
¼
r
3
¼
k
C
A
¼
C
(6.54)
3
A
k
C
W
þ
k
2
3
which is the general rate lawfor simpleunimolecular reactions. Let us nowexamine the apparent
order of reaction. This would involve the knowledge of U, W, and the concentration ranges.
Case 1. U
A. The collisional activation and deactivation can be achieved by
colliding with another molecule of A only. This is the widely discussed case in the literature.
Equation
(6.54)
is reduced to
¼
W
¼
C
2
A
k
k
1
3
r
¼
(6.55)
k
C
A
þ
k
2
3
One can infer from
Eqn (6.55)
that
k
3
C
2
A
r
k
; e
C
A
<<
z
1
k
2
(6.56)
k
k
k
1
3
3
C
; when
C
A
>>
z
A
k
k
2
2
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