The addition of a positive chemical catalyst drops the activation energy of a specific reaction by s — Chemical Kinetics Chemistry Question
Question
The addition of a positive chemical catalyst drops the activation energy of a specific reaction by strictly $8.314 \text{ kJ mol}^{-1}$. Assuming the operating temperature is maintained identically at $300 \text{ K}$, by what exact integer multiplier will the absolute reaction rate jump? ($R=8.314 \text{ J K}^{-1}\text{mol}^{-1}$)
Answer: C
💡 Solution & Explanation
The catalyzed rate ratio evaluates exactly to $k_{cat}/k_{uncat} = e^{\Delta E_a/RT}$. Plugging in the difference (ensuring conversion to Joules): $e^{8314 / (8.314 \times 300)} = e^{8314 / 2494.2} = e^{3.33}$. Approximating the natural exponent $e^{3.33}$ mathematically yields a multiplier of approximately 28.
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