# Reaction Paths of Wei-Prater Complex Reaction Networks

Reaction Paths of Wei-Prater Complex Reaction Networks

Consider the following complex reaction network, called the Wei–Prater mechanism: .

AAAA

1

k

12

⇌

k

21

2

k

23

⇌

k

32

3

k

31

⇌

k

13

1

The relevant equations are the following:

dC

A

1

dt

31

A

3

21

A

2

12

13

A

1

dC

A

2

dt

32

A

3

12

A

1

21

23

A

2

C+C+C=C

A

1

A

2

A

3

Total

where is the rate constant of reaction → and is a constant equal to the total concentration of all species for .

k

ij

A

i

A

j

C

Total

A

i

i=1,2,3

The Demonstration displays parametric plots (i.e., versus 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: .

C

A

1

C

A

2

k=

32

kkk

23

12

31

kk

21

13