For two chemical reactions $A$ and $B$, if the difference between their activation energy is 20 kJ at $300 \mathrm{~K}\left(\mathrm{R}=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$. Determine $\ln \frac{\mathrm{k}_2}{\mathrm{k}_1}$.
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