The rate of a reaction quadruples when the temperature changes from `293K` to `313K`. Calculate the energy of activation of the reaction assuming that it does not change with temperature.

Options

A. `48.625kJ" mol"^(-1)`
B. `654.35kJ" mol"^(-1)`
C. `354.20kJ" mol"^(-1)`
D. `52.854kJ" mol"^(-1)`

Answer

D

Explanation

According to Arrhenius equation,
`"log"k_(2)/(k_(1))=E_(a)/(2.303R)[(1)/(T_(1))-(1)/(T_(2))]`
`"log"(4)/(1)=E_(a)/(2.303xx(8.314Jmol^(-1)k^(-1)))xx(20)/(293xx313)`
`E_(a)=52.854kJmol`