A certain endothermic reaction: `Ato` Product, `DeltaH=+ve` proceeds ina sequence of three elementary steps with the rate constant `K_(1),K_(2)` and `K_(3)` and each one having energy of activation `E_(1),E_(2)` and `E_(3)` respectively at `25^(@)C`. The observed rate constannt for the reaction is equal to `K_(3)sqrt((K_(1))/(K_(2)))`.
`A_(1),A_(2)` and `A_(3)` are Arrhenius parameters respectively.
The observed energy of activation for the reaction is

Options

A. `(2E_(1)-E_(2)+2E_(3))/2`
B. `(E_(2)-E_(1)-2E_(3))/2`
C. `sqrt((E_(1)E_(3))/(E_(2)))`
D. `(E_(1)-E_(2))/2+E_(3)`

Answer

D

Explanation

Here `K=K_(3)sqrt((K_(1))/(K_(2)))`……….1 `K_(1)=A_(1)e^(-E_(1)//RT),K_(2)=A_(2)e^(-E_(2)//RT),K_(3)=A_(3)e^(-E_(3)//RT)`…..2 from (1) (2)