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_(a2)//RT)`
B. `k_(1) = k_(2) e^(E_(a1)//RT)`
C. `k_(2) = k_(1) e^(E_(a2)//RT)`
D. `k_(1) = Ak_(2) e^(E_(a1)//RT)`

Answer

B

Explanation

`A overset(k_(1))(rarr) B, A overset(k_(2))(rarr) C`
By Arrhenius equation,
`k_(1) = A'e^(-E_(a_(2))//RT)`
and `k_(2) = A'e^(-2E_(a_(1))//RT)`
[A' is Arrhenius constant]
`because 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)`