Biomedical Engineering Reference
In-Depth Information
Under this form, an interpretation of the rate constant is the rate of success-
ful collisions between reacting molecules [3]. The activation energy represents the
minimum kinetic energy that reactants must have in order to form products and the
“frequency” term A corresponds to the rate at which collisions occur.
7.3.1.5 Rate Laws and Reaction Kinetics
Rate laws are differential equations and their integration is the concentration as a
function of time (i.e., the reaction kinetics). However, their integration is seldom
possible analytically. Take the example of the first-order unimolecular reaction
A
®
P
We have the following reaction rate
d A
[
]
= -
k A
[
]
d t
and the reaction kinetics is
-
kt
[
A
]
=
[
A e
]
0
(7.11)
7.3.1.6 Near Equilibrium Reactions
Very often a reaction is partly reversible, that is, the product is formed and at the
same time dissociate according to
A
®
P
P
®
A
The rate laws for the two reactions are
d A
[
]
v
=
=
k A
[
]
d t
d P
[
]
v
¢
=
=
k P
¢
[
]
d t
The concentration [ A ] is reduced by the first reaction and increases by the re-
verse reaction and the net rate of change is
d A
[
]
= -
k A k P
[
]
+ ¢
[
]
(7.12)
d t
If the initial concentration is [ A ] 0 , and if there is no initial concentration of [ P ],
then
[
A
]
+
[
P
]
=
[
A
]
0
 
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