Two reactions R_1 and R_2 have identical pre-exponential factors. Activation energy of R_1 exceeds that of R_2 by 10 kJ mol^-1. If k_1 and k_2 are…

Two reactions $\displaystyle \mathrm{R}_1$ and $\displaystyle \mathrm{R}_2$ have identical pre-exponential factors. Activation energy of $\displaystyle R_1$ exceeds that of $\displaystyle R_2$ by $\displaystyle 10 \mathrm{~kJ} \mathrm{~mol}^{-1}$. If $\displaystyle \mathrm{k}_1$ and $\displaystyle \mathrm{k}_2$ are rate constants for reactions $\displaystyle \mathrm{R}_1$ and $\displaystyle \mathrm{R}_2$ respectively at $\displaystyle 300$ K, then $\displaystyle \ln \left(\mathrm{k}_2 / \mathrm{k}_1\right)$ is equal to : $\displaystyle \left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)$