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31 Mar 2020
The enzyme carbonic anhydrase catalyzes the reaction CO2(g) + H2O(l)
HCO3- (aq) + H+(aq). In water, without the enzyme, the reaction proceeds with a rate constant of 0.039 s-1 at 25 °C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 1.0
106 s-1 at 25 °C. Assuming the collision factor is the same for both situations, calculate the difference in activation energies for the uncatalyzed versus enzyme-catalyzed reaction.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Subtracting the first and the second equation we obtain
![](data:image/png;base64,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)
![](data:image/png;base64,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)
The enzyme carbonic anhydrase catalyzes the reaction CO2(g) + H2O(l) HCO3- (aq) + H+(aq). In water, without the enzyme, the reaction proceeds with a rate constant of 0.039 s-1 at 25 °C. In the presence of the enzyme in water, the reaction proceeds with a rate constant of 1.0
106 s-1 at 25 °C. Assuming the collision factor is the same for both situations, calculate the difference in activation energies for the uncatalyzed versus enzyme-catalyzed reaction.
Subtracting the first and the second equation we obtain
Nelly StrackeLv2
27 May 2020