1
Four Approaches to Simplify Kinetic Analysis
In Mathematical Modeling
Reactions near equilibrium
=>
[A] = [A] - [A]
eq
<<
[A]
eq
Steady state
0
t
Steady state [A]
0
t
]
A
[
Equilibrium
A state of balance between
opposing
forces or actions
Equilibrium of a
chemical reaction
Forward rate = Reverse rate
Dimensional analysis
=>
Ignore small dimensionless terms
equilibrium
equilibrium
steady state
steady state
A
B
C
[A], [B], and [C] can be at steady state but the
reactions
cannot
be at
equilibirum
equilibirum
since they are
not reversible.
A
B
C
It is possible to have [A], [B], and [C] be at
steady state and the reactions be at
equilibirum
equilibirum.
Example 1
Example 2
]
[
]
[
]
][
[
]
[
MN
k
MN
k
N
M
k
dt
MN
d
r
f
M + N
P
k
MN
k
f
k
r
At the
steady state
of [MN],
K
k
K
k
k
k
MN
r
r
f
/
k
1
[M][N]
]
[
If the
reversible
reaction is at
equilibrium
,
K
k
k
[M][N]
]
MN
[
r
f
or
K
A

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