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.
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From Arrhenius equation , we obtain `"log" (k_(2))/(k_(1)) = (E_(a))/(2.303R) ((T_(2) - T_(1))/(T_(1)T_(2)))` It is given that , `k_(2) = 4 k_(1)` `T_(1) = 293 `K `T_(2) = 313 K` Therefore , log `(4k_(1))/(k_(2)) = (E_(a))/(2.303 xx 8.314) ((313 - 293)/(293 xx 313))` `implies 0.6021 = (20 xx E_(a))/(2.303 xx 8.314 xx 293 xx 313)` `implies E_(a) = (0.6021 xx 2.303 xx 8.314 xx 293 xx 313)/(20)` = `52863.33 J mol^(-1)` = ` 52. 86 kJ mol^(-1)` Hence , the required energy of activation is `52.86 kJmol^(-1)`
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