Question

A certain endothermic reaction: `Ararr` Product, `DeltaH=+ve` proceeds in a sequence of three elementary steps with the rate constants `K_(1), K_(2)` and `K_(3)` and each one having energy of activation `E_(a), E_(2)` and `E_(3)` respectively at `25^(@)C`. The observed rate constant for the reaction is equal to `K_(3) sqrt(K_(1)/K_(2)). A_(1), A_(2)` and `A_(3)` are Arrhenius parameters respectively.
Presence of a catalyst decreases the energy of activation of each path by half the value of `E_(1)`. Assuming the order actors same, the observed energy of activation would be:
A. (a) `E_(3)-E_(2)/2`
B. (b) `2E_(3)-E_(2)`
C. (c ) `E_(2)-E_(3)/2`
D. (d) `E_(1)/2+E_(2)/2+E_(3)`

Answer 1

Correct Answer - a
`E_(obs)=(E_(1)-E_(2)+2E_(3))/(2)`
if each is lowered by `E_(1)//2`, then
`E_(obs)=(E_(1)-E_(1)/2-(E_(2)-E_(1)/2)+2(E_(3)-E_(1)/2))/(2)`
`=E_(3)-E_(2)/2`