HardChemistryHigh School (11–12)Organic Compounds with Functional Groups › BiomoleculesNumerical

An enzyme reaction has an activation energy of 60 kJ/mol…

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An enzyme reaction has an activation energy of $60\ \text{kJ/mol}$ . Take $R = 8.314\ \text{J/(mol K)}$ . Find the ratio of the rate constants when the temperature rises from $300\ \text{K}$ to $310\ \text{K}$ . Then take the enzyme at $330\ \text{K}$ . The Arrhenius law alone would raise the rate relative to $310\ \text{K}$ by a certain factor. But only $8\%$ of the enzyme is still folded at $330\ \text{K}$ , and unfolded enzyme has no activity. Find the factor from the Arrhenius law, and the true activity at $330\ \text{K}$ relative to $310\ \text{K}$ .

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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