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^(Ea_(2)//RT)`
B. `k_(2)=k_(1)e^(Ea_(1)//RT)`
C. `k_(2)=k_(1)e^(Ea_(2)//RT)`
D. `k_(1)=A" k"_(2)e^(Ea_(1)//RT)`

Answer

D

Explanation

`k_1=A_1e^(-E_(a1)//RT), k_2=A_2e^(-E_(a2)//RT)`
`:." "k_1/k_2=A_1/A_2e^((E_(a_2)-E_(a1))//RT)=A_1/A_2e^((2E_(a_1)-E_(a_(1))))`
`(because E_(a2)=2E_(a_1))`
or `k_1=k_2Ae^(E_(a1)//RT)`