The correct answer is (1) \(10^{-1}\).
The Arrhenius equation relates the rate constant (\(k\)) of a reaction to the temperature (\(T\)), the Arrhenius factor (\(A\)), and the activation energy (\(E_a\)) as follows: \[k = A \cdot e^{-\frac{E_a}{RT}}\] Where: - \(k\) is the rate constant - \(A\) is the Arrhenius factor (pre-exponential factor) - \(E_a\) is the activation energy - \(R\) is the universal gas constant (8.314 J/mol·K) - \(T\) is the temperature in Kelvin In this case, you are given that the activation energy (\(E_a\)) is \(2.303RT\) J/mol. Now, let's calculate the ratio of the rate constant (\(k\)) to the Arrhenius factor (\(A\)). \[ \frac{k}{A} = e^{-\frac{E_a}{RT}} = e^{-\frac{2.303RT}{RT}} = e^{-2.303} \] Now, you can calculate this value: \[ \frac{k}{A} \approx e^{-2.303} \approx 0.1 \] So, the ratio of the rate constant to the Arrhenius factor is approximately \(0.1\), which is the same as \(10^{-1}\). Therefore, the correct option is (1) \(10^{-1}\). |