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_(2)=k_(1)e^(E_(a_(1))//RT)`
B. `k_(2)=k_(1)e^(E_(a_(2))//RT)`
C. `k_(2)=k_(2)e^(E_(a_(1))//RT)`
D. `k_(2)=2k_(2)e^(E_(a_(2))//RT)`

Answer

A

Explanation

`k_(2)=Ae^(-E_(a_(2))//RT)`
`k_(1)=Ae^(-E_(a_(1))//RT)`
`:.(k_(2))/(k_(1))=e^((-E_(a_(2))+E_(a_(1)))//RT)`
`:.(k_(2))/(k_(1))=e^((-E_(a_(1))//RT)" " "Since"E_(a_(2))=2E_(a_(1))`
`k_(2)=k_(1)e^(E_(a_(1))//RT)`