Question #44755

A solution is prepared by dissolving $15.0\text{ g}$ of a salt \ce{MCl2} (Molar mass = $150\text{ g/mol}$) in $500\text{ g}$ of a solvent $L$ (Molar mass = $50\text{ g/mol}$). The vapor pressure of pure solvent $L$ at $298\text{ K}$ is $50.51\text{ torr}$, and the vapor pressure of the solution is $50.00\text{ torr}$. Assume the volume of the solution is exactly $500\text{ mL}$.

The standard reduction potential $E^\circ(\ce{M^{2+}/M})$ is $-0.75\text{ V}$. The solvent $L$ undergoes reduction at the cathode at a constant potential of $-0.82\text{ V}$ to evolve \ce{H2} gas.

If this solution is electrolyzed at $298\text{ K}$ using inert electrodes, what is the primary cathodic product and the actual reduction potential of the \ce{M^{2+}/M} couple in this solution?

(Given: $\frac{2.303 RT}{F} = 0.06\text{ V}$, $\log 2 = 0.3$)