Question

Calculate the rate enhancement that could be accomplished by an enzyme forming one low-barrier hydrogen bond with its transition state at 25C.

Short answer

The accomplished rate enhancement will be approximately 10⁷.

Step-by-step solution

The Catalytic Effect of Enzymes

Enzymes are biological catalysts that increase the rate of biological reactions without being consumed in the reaction.

Reactants in a reaction need to reach a higher energy barrier, called the activation energy, in order for the reaction to proceed. An enzyme or a catalyst in a reaction decreases this activation energy so that the reactant can reach the energy barrier easily. Thus, the rate of the reaction increases in the presence of the enzyme or catalyst.

Calculation for the rate enhancement

It is known that a decrease of about 5.7 kJ/mol is observed in the activation free energy of the reaction when a 10 fold increase occurs in the rate of reaction at 25ºC.

The hydrogen bond has a free energy of approximately 40 kJ/mol. Now, for such a hydrogen bond, the times of a 10 fold increase that will happen is = (40 kJ/mol) / (5.7 kJ/mol) = 7.02 times = ~7 times.

Hence, the rate would show a 10 fold increase ~7 times). Thus, the enhancement in the rate will be 10⁷.