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.

Explanation

According to Arrhenius equation,
`log k_(2)/k_(1) = E_(a)/(2.303R)[1/T_(1)-1/T_(2)], T_(1) = 293 K, T_(2) = 313 K`
log `4/1 = E_(a)/(2.303 xx (8.314 J mol^(-1)K^(-1)))[1/293 K - 1/313K]`
`log 4 = E_(a)/(2.303 xx (8.314 J mol^(-1))) xx 20/(293 xx 313)`
`E_(a) = (0.6021 xx 2.303 xx 8.314 xx 293 xx 313 (J mol^(-1)))/(20)`
`E_(a) = 5.2863 xx 10^(4) J mol^(-1)= 52.863 kJ mol^(-1)`