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A certain endothermic reaction: Ararr Pr...

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.
If temperature coefficient of the observed reaction is `2`, the numerical value of `E_(1)-E_(2)+2E_(3)` is:

A

(a) `12.73 kcal`

B

(b) `25.46 kcal`

C

(c ) `38.19 kcal`

D

(d) Cannot be calculated

Text Solution

Verified by Experts

The correct Answer is:
b
`K_(2)=Ae^(-E_(obs)//Rxx308), K_(1)=Ae^(-E_(obs)//Rxx298)`
:. `K_(2)/K_(1)=e^(E_(obs)/R[1/298-1/308])`
`2.303log K_(2)/K_(1)=E_(obs)/Rxx10/(308xx298)`
`:. E_(obs)=(E_(1)-E_(2)+2E_(3))/(2)`
`=(308xx298xx2xx3.303log2)/(10)`
`=12.73xx10^(3) cal =12.73 kcal`
`:. E_(1)-E_(2)+2E_(3)=25.46 kcal`
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