The rate of a reaction quadruples when the temperature changes from 300 to 310 K. The activation energy of this reaction is `:`
( Assume Activation energy and pre-exponential factor are independent of temperature, `ln(2) = 0.693, R = 8.314J - mol^(-1) K^(-1))`

Options

A. `107.2``"kJ mol"^(-1)`
B. `53.6``"kJ mol"^(-1)`
C. `26.8``"kJ mol"^(-1)`
D. `214.4``"kJ mol"^(-1)`

Answer

A

Explanation

`"ln"(k_(2))/(k_(1)) =(E_(a))/(R ) ((1)/(T_(1)) -(1)/(T_(2)))`
ln 4`=(E_(a))/(8.314) ((1)/(300)-(1)/(310)) rArr 1.386 xx 8.314 =E_(a)(0.000107)`
`E_(a) =(1.386xx8.314)/(0.000107526) rArr E_(a)=107.2`kJ/mol