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

Answer

B

Explanation

`A overset(k_(1))to B,A overset(k_(2))to C`
By Arrhenius equation,
`k_(1)=A.e^(-E_(a_(1))//RT) and k_(2)=A.e^(-E_(a_(2))//RT)" "`[A. is Arrhenius constant]
`:.E_(a_(2)) =2E_(a_(1))`
`:.k_(2)=A.e^(-2E_(a_(1))//RT) " " :. (k_(1))/(k_(2)) =(A.e^(-E_(a_(1))//RT))/(A.e^(-2E_(a_(1))//RT))=e^(E_(a_(1))//RT) :.k_(1)=k_(2)e^(E_(a_(1))//RT)`