Question #44571

A metalloenzyme features a rigid tetrahedral binding site that acts as a perfect 'lock and key' for $d^{10}$ metal ions. The standard reduction potential for the aqueous couple \ce{Cu^{2+}{(aq)} / Cu^+{(aq)}} is $+0.15 \text{ V}$ at $300 \text{ K}$.

The binding of \ce{Cu^+_{(aq)}} to the apoenzyme (E) has $\Delta H^\circ = -40 \text{ kJ mol}^{-1}$ and $\Delta S^\circ = -50 \text{ J K}^{-1} \text{ mol}^{-1}$.

The binding of \ce{Cu^{2+}_{(aq)}} to the apoenzyme has $\Delta H^\circ = -70 \text{ kJ mol}^{-1}$. However, because \ce{Cu^{2+}} is a $d^9$ ion, it undergoes Jahn-Teller distortion, forcing a conformational change in the rigid enzyme. This induced fit results in an additional conformational entropy penalty, making its total binding entropy $\Delta S^\circ$ more negative by $36 \text{ J K}^{-1} \text{ mol}^{-1}$ compared to the ideal $d^{10}$ binding.

Calculate the standard reduction potential ($E^\circ$) of the enzyme-bound copper couple (\ce{E-Cu^{2+} / E-Cu^+}) at $300 \text{ K}$. (Assume Faraday's constant $F = 96000 \text{ C mol}^{-1}$)