Question

Calculate the rate enhancement that could be accomplished by an enzyme forming one low-barrier hydrogen bond that has a free energy of -45 kJ/mol with its transition state at

Answer 1

The enzyme forming this low-barrier hydrogen bond with its transition state achieves a rate enhancement of approximately 4224 times compared to the uncatalyzed reaction.

The free energy change (ΔG) of the hydrogen bond, which = -45 kJ/mol.

The Eyring equation

k = (k_B*T)/h * exp(-ΔG/RT)

we divide the Eyring equation for the catalyzed reaction by that for the uncatalyzed reaction:

k_cat/k_unc = exp(-(ΔG_cat - ΔG_unc)/RT)

ΔG_unc = 0 and

ΔG_cat = -45 kJ/mol.

k_cat/k_unc = exp(-(-45 kJ/mol) / (8.314 J/mol*K * 298 K))

= 4224