The rate of a reaction becomes 4 times when temperature is raised from 293 K to 313 K. The activation energy for such reaction would be

Options

A. 50.855 kJ `" mol"^(-1)`
B. 52.849 kJ `" mol"^(-1)`
C. 54.855 kJ `" mol"^(-1)`
D. 56.855 kJ `" mol"^(-1)`

Answer

B

Explanation

From the Arrhenius equation,
`log.(k_(2))/(k_(1))=(E_(a))/(2.303R)[(T_(2)-T_(1)]/(T_(1).T_(2))]`
Hence, `log4=(E_(a))/(2.303xx8.314)[(313-293)/(293xx313)]`
`E_(a)=(11.521)/(0.000218)=52.849kJ" mol"^(-1)`