The enzyme carbonic anhydrase catalyzes the reactionCO2( g )+H2O( l )HCO3( a q )

Question

The enzyme carbonic anhydrase catalyzes the reactionCO2(g)+H2O(l)HCO3(aq)+H+(aq).
In water, without the enzyme, the reaction proceeds with a rate constant of 0.039 s1 at 28 C . In the presence of the enzyme in water, the reaction proceeds with a rate constant of 1.0 ×106s1 at 28 C .

Assuming the collision factor is the same for both situations, calculate the difference in activation energies for the uncatalyzed versus enzyme-catalyzed reaction.

The enzyme carbonic anhydrase catalyzes the reactionCO2(g)+H2O(l)HCO3(aq)+H+(aq).
In water, without the enzyme, the reaction proceeds with a rate constant of 0.039 s1 at 28 C . In the presence of the enzyme in water, the reaction proceeds with a rate constant of 1.0 ×106s1 at 28 C .

Assuming the collision factor is the same for both situations, calculate the difference in activation energies for the uncatalyzed versus enzyme-catalyzed reaction.

Explanation / Answer

Use the equation

ln k = - Ea/ RT

1) For catalysed reaction,

ln 1 x 106 = -Ea/ 8.314 x 301

13.81 = -Ea/ 5202.50

Ea =71846 j / mol

2) For uncatalysed reaction

ln 0.039= -Ea/ 8.314 x 301

-3.2441 = -Ea/ 5202.50

Ea = 16877 j / mol

Energy difference = 71846 - 16877

= 54969 j / mol

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