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A reaction in the body has an activation energy of 85 kJ/mol without a catalyst…

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A reaction in the body has an activation energy of $85\ \text{kJ/mol}$ without a catalyst. With its enzyme, the activation energy is $50\ \text{kJ/mol}$ . The temperature is $310\ \text{K}$ , and the frequency factor is the same in both cases. Take $R = 8.314\ \text{J/(mol K)}$ . Find the natural logarithm of the ratio of the rate constants, and the ratio as a power of ten.

Need a reminder? The key ideaShow

An enzyme lowers the activation energy $E_a$ . With the same frequency factor, $k_{\text{enzyme}} / k_{\text{no enzyme}} = e^{\Delta E_a / RT}$ with $R = 8.314\ \text{J/(mol K)}$ . Between two temperatures, $k_2/k_1 = \exp\left[\dfrac{E_a}{R}\left(\dfrac{1}{T_1} - \dfrac{1}{T_2}\right)\right]$ . A denatured enzyme has lost its activity.

The worked solution

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