A reactant `(A)` forms two products
`A overset (k_(1))rarr B`, Activation energy `E_(a1)`
`A overset (k_(2))rarr C`, Activation energy `E_(a2)`
If `E_(a_(2)) = 2E_(a_(1))` then `k_(1)` and `k_(2)` are related as

Options

A. `K_(1)=2k_(2)e^(Ea2,1//RT)`
B. `k_(1)=k_(2)e^(2Ea1//RT)`
C. `k_(2)=k_(1)e^(Ea2,1R//T)`
D. `k_(1)=Ak_(2)e^(Ea2,1//RT)`

Answer

B

Explanation

`Aoverset(k_(1))rarrB,Aoverset(k_(2))rarrC,`
By Arrhenius equation
`k_(1)="A "e^(-Ea1//RT)`
`and k_(2)=A_(e)^(-Ea2//RT)` (A is Arrhenius constant)
`k_(2)=A_(e)^(-2E1//RT)`
`k_(1)/(k_(2))=(Ae^(-Ea1//RT))/(Ae^(-2Ea1RT))=e^(2Ea1//RT)`
`thereforek_(1)=k_(2)e^(2Ea1//RT)`