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(D) According to the Arrhenius equation,$k = A e^{-E_a / RT}$.For reactions $R_1$ and $R_2$ with identical pre-exponential factors $A$:$k_1 = A e^{-E_

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$4$

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(D) According to the Arrhenius equation,$k = A e^{-E_a / RT}$.For reactions $R_1$ and $R_2$ with identical pre-exponential factors $A$:$k_1 = A e^{-E_{a1} / RT}$$k_2 = A e^{-E_{a2} / RT}$Dividing $k_2$ by $k_1$:$\frac{k_2}{k_1} = \frac{A e^{-E_{a2} / RT}}{A e^{-E_{a1} / RT}} = e^{(E_{a1} - E_{a2}) / RT}$Taking the natural logarithm on both sides:$\ln(k_2/k_1) = \frac{E_{a1} - E_{a2}}{RT}$Given $E_{a1} - E_{a2} = 10 \, kJ \, mol^{-1} = 10,000 \, J \, mol^{-1}$,$R = 8.314 \, J \, mol^{-1} \, K^{-1}$,and $T = 300 \, K$:$\ln(k_2/k_1) = \frac{10,000}{8.314 	imes 300} \approx \frac{10,000}{2494.2} \approx 4.009 \approx 4$.

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