The rate constant of a reaction is 3.0x10^-4 s^-1 at 400 K and 6.0x10^-3 s^-1 at 440 K. With R=8.314 J mol^-1K^-1 and ln 20=2.996, the activation energy in kJ mol^-1 is

JEE Main levelSingle correct optionDifficulty 2 of 3ck134

The rate constant of a reaction is $3.0 \times 1 0^{- 4} s^{- 1}$ at 400 K and $6.0 \times 1 0^{- 3} s^{- 1}$ at 440 K. With $R = 8.314 J mo l^{- 1} K^{- 1}$ and $ln 20 = 2.996$ , the activation energy in $kJ mo l^{- 1}$ is

E_{a} = \frac{R l n ( k _{2} / k _{1} )}{1/ T _{1} - 1/ T _{2}} = \frac{8.314 \times 2.996}{0.0002273} J mo l^{- 1} = 109.6 kJ mo l^{- 1}