WOLFRAM|DEMONSTRATIONS PROJECT

Reaction Paths of Wei-Prater Complex Reaction Networks

​
k
12
1.5
k
21
1
k
13
0.5
k
31
1
k
23
1
Consider the following complex reaction network, called the Wei–Prater mechanism:
A
1
k
12
⇌
k
21
A
2
k
23
⇌
k
32
A
3
k
31
⇌
k
13
A
1
.
The relevant equations are the following:
d
C
A
1
dt
=
k
31
C
A
3
+
k
21
C
A
2
-(
k
12
+
k
13
)
C
A
1
,
d
C
A
2
dt
=
k
32
C
A
3
+
k
12
C
A
1
-(
k
21
+
k
23
)
C
A
2
,
C
A
1
+
C
A
2
+
C
A
3
=
C
Total
,
where
k
ij
is the rate constant of reaction
A
i
→
A
j
and
C
Total
is a constant equal to the total concentration of all species
A
i
for
i=1,2,3
.
The Demonstration displays parametric plots (i.e.,
C
A
1
versus
C
A
2
for different initial conditions) referred to as reaction paths. The system's steady state is shown with a blue dot; all reaction paths converge to this point. Users can set the different values of the rate constants, keeping in mind that they must obey the microscopic reversibility rule:
k
32
=
k
23
k
12
k
31
k
21
k
13
.