- #1

phyalan

- 22

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I have a question on the rate constant of a kinetic model(like the one we use in describing chemical reaction). Suppose we have the following model between two states A and B:

A--(a)-->B

A<--(b)--B

where a, b are the rate constant for the transition. So the corresponding differential equation will be

[itex]\frac{dA}{dt}=-aA+bB[/itex]

[itex]\frac{dB}{dt}=-bB+aA[/itex]

If now I add an intermediate state C, so that if we just measure the amount of A and B, the two models gives basically the same description (i.e. the overall rate constant from A to C then to B is equivalent to a and the same for reverse direction)

A--(a1)-->C--(a2)-->B

A<--(b1)--C<--(b2)--B

What is the functional relationship between the rate constant a1,a2 and a and similarly for b1, b2 and b? I am confused on how to find out the functional form. Is it just simply

[itex]\frac{1}{a}=\frac{1}{a1}+\frac{1}{a2}[/itex]?