(Solved): 3. Eyring Equation. An un-catalyzed reaction (SP) has a Gibb's free energy of activation of +100 ...

3. Eyring Equation. An un-catalyzed reaction $(S?P)$ has a Gibb's free energy of activation of $+100\mathrm{kJ}/\mathrm{mol}$ at $\mathrm{pH}7.0$ and $20^{?}\mathrm{C}$. An enzyme that can catalyze the conversion of $\mathrm{S}?\mathrm{P}$ (under the same conditions) binds the transition state of the reaction with a release of $40\mathrm{kJ}/\mathrm{mol}$ through formation of non-covalent interactions. Calculate the rate enhancement (fold increase over the un-catalyzed reaction) that is achieved by this enzyme at $20^{?}\mathrm{C}$.