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A certain endothermic reaction: Ato Prod...

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.
Presence of a catalyst decreasesthe energy of activation of each path by half the value of `E_(1)`. Assuming the other factors same, the observed energy of activation would be

A

`E_(3)-(E_(2))/2`

B

`2E_(3)-E_(2)`

C

`E_(2)-(E_(3))/2`

D

`(E_(1))/2+(E_(2))/2+E_(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`E^(1)=[(2(epsilon_(3)-(epsilon_(1))/2)+(epsilon_(1)-(epsilon_(1))/2)-(epsilon_(2)-(epsilon_(1))/2))/2]=(2((2epsilon_(3)-epsilon_(1))/2)+((2epsilon_(1)-epsilon_(1))/1)-((2epsilon_(2)-epsilon_(1))/2))/2`
`=(4epsilon_(3)-2epsilon_(1)+epsilon_(1)-2epsilon_(2)+epsilon_(1))/(2xx2),epsilon^(1)=((4epsilon_(3)-2epsilon_(2)))/4,epsilon^(1)=(epsilon_(3)-(epsilon_(2))/2)`
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