- #1

Saitama

- 4,243

- 93

## Homework Statement

For the two parallel reactions ##A \stackrel{k_1}{\rightarrow} B## and ##A \stackrel{k_2}{\rightarrow} C##, show that the activation energy ##E'## for the disappearance of ##A## is given in terms of activation energies ##E_1## and ##E_2## for the two paths by

[tex]E'=\frac{k_1E_1+k_2E_2}{k_1+k_2}[/tex]

## Homework Equations

## The Attempt at a Solution

I don't know what should be the way to approach this problem. I can find the concentration of A as a function of time which is

[tex]A=A_0e^{-(k_1+k_2)t}[/tex]

(I guess I can call ##k_1+k_2## as the equivalent rate constant. Is it correct to say so?)

Applying the Arrhenius equation to both the reactions

[tex]k_1=A_1e^{-E_1/(RT)}[/tex]

[tex]k_2=A_2e^{-E_2/(RT)}[/tex]

I am clueless about what to do.

Any help is appreciated. Thanks!