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

A

12.73 kcal

B

25.4 kcal

C

38.19 kcal

D

cannot be calculated

Text Solution

Verified by Experts

The correct Answer is:
B

`log((K_(2))/(K_(1)))=(E_(a))/(2.303R)(1/(T_(1))-1/(T_(2))),log(2)=(epsilon_(a))/(2.3.3R)(1/298-1/308)`
`epsilon_(a)=((0.3010xx2.303xx2xx298xx308)/10),epsilon_(a)=12.72KCal=((2epsilon_(3)+epsilon_(1)-epsilon_(2))/2)`
`12.72=((2epsilon_(3)+epsilon_(1)-epsilon_(2))/2)(2epsilon_(3)+epsilon_(1)-epsilon_(2))=12.72xx2=25.4499,(epsilon_(1)-epsilon_(2)+2epsilon_(3))~=25.4` Kcal
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