Biomedical Engineering Reference
In-Depth Information
and the reaction kinetics is given by
d A
[
]
= -
k A k A
[
]
+
¢
([
]
-
[
A
])
= - +
(
k k A k A
¢
)[
]
+
¢
[
]
(7.13)
0
0
d t
This type of kinetics is classic and its mathematical structure will be investi-
gated more closely later in the section dedicated to the Langmuir model.
7.3.1.7 Consecutive Reactions
Some reactions proceed through the formation of an intermediate. Consider for
example the consecutive reactions
A
® ®
I
P
with
d A
[
]
v
=
=
k A
[
]
A
d t
d I
[ ]
v
¢
=
=
k I
[ ]
I
d t
Let us consider the concentration in the intermediate product [
I
]
d I
[ ]
=
k A k I
[
]
-
[ ]
(7.14)
A
I
d t
The concentration [
P
] is given by the differential equation
dP
=
k I
[ ]
(7.15)
I
d t
The first of the rate laws is an ordinary first order decay and, from (7.11), we
can write
-
k t
[
A
]
=
[
A e
]
(7.16)
0
Substitution of (7.16) in (7.14) yields
d I
[ ]
-
k t
=
k A e
[
]
-
k I
[ ]
A
0
I
d t
and upon integration, assuming that [
I
]
0
= 0
k
A
-
k t
-
k t
[ ]
I
=
(
e
-
e
)[
A
]
A
I
(7.17)
0
k
-
k
I
A
If we notice that, at all times,
[
A
]
+
[ ]
I
=
[
P
]
