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

Let the rate constant at `293K=k_(1)`
the rate constant at 313K `=k_(2)=4k_(1)` (rate quadruples)
According to Arrhenius equation,
`E_(a)=2.303R[(T_(1)T_(2))/(T_(2)-T_(1))]log.(k_(2))/(k_(1))`
or, `log.(4k_(1))/(k_(1))=(E_(a))/(2.303xx8.314)[(313-293)/(293xx313)]`
or, `0.6021=(E_(a)xx20)/(2.303xx8.314xx293xx313)`
`thereforeE_(a)=52.86"kJ.mol"^(-1)`