Reactant (A) forms two products :
`A overset(k_1)(rarr)B` Activation energy,`E_(a_1)`
`Aoverset(k_2)(rarr) C` Activation energy,`E_(a_2)`
If `E_(a_2)=2E_(a_1)`, then ky and ky are related as

Options

A. `k_2=k_1e^(E_(a_(1))//RT)`
B. `k_2=k_1e^(E_(a_(2))//RT)`
C. `k_1=Ak_2e^(E_(a_(1))//RT)`
D. `k_1=2k_2e^(E_(a_(2))//RT)`

Answer

C

Explanation

`k_1=A_1e^(-E_(a_1)//RT),k_2=A_2e^(-E_(a_2)//RT)`
`(k_1)/(k_2)=((A_1)/(A_2))e^(-E_(a_1)+E_(a_2))/(RT)`
Now,`(A_1)/(A_2)`=constant and `E_(a_2)=2E_(a_1)`
`(k_1)/(k_2)=Ae^(-E_(a_1)+2E_(a_1))/(RT)implies (k_1)/(k_2)=Ae^(E_(a_1)//RT)` or `k_1=Ak_2e^(E_(a_1)//RT)`