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The decomposition of A into product has ...

The decomposition of A into product has value of `k` as `4.5 x10^(3) (s)^(-1)` at `10^oC` and energy of activation'60 kj mol^(-1)`.At what temperature would K be `1.5 x10^(4) (s)^-1 ?`

A

`12^(@)C`

B

`24^(@)C`

C

`48^(@)C`

D

`36^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that `k_(10) = k_(283) = 4.5 xx 10^(3)s^(-1), k_(T) = 1.5 xx 10^(4) s^(-1), T = ?` Also
`E_(a) = 60 kJ mol^(-1) = 60000 J mol^(-1)`. Using Arrhenius equation, we can write
`log""(k_(T))/(k_(283)) = (E_(a))/(2.303 R)[(1)/(283) - (1)/(T)], log""(1.5 xx 10^(4)s^(-1))/(4.5 xx 10^(3)s^(-1)) = (60000 J mol^(-1))/(2.303 xx 8.3 J K^(-1)mol^(-1))[(T-283)/(283 xx T)]`
On solving , we get ` = 297 K = 24^(@)C`.
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