Question #44324

Consider the Latimer diagram for Manganese in aqueous acidic medium (pH = 0) at 298 K: $\ce{MnO4^- \xrightarrow{E_1^\circ} MnO2 \xrightarrow{0.95 \text{ V}} Mn^{3+} \xrightarrow{1.51 \text{ V}} Mn^{2+} \xrightarrow{-1.18 \text{ V}} Mn}$ The standard reduction potential for the overall half-reaction $\ce{MnO4^- \rightarrow Mn^{2+}}$ is $+1.51 \text{ V}$. The $\ce{Mn^{3+}}$ ion is unstable in aqueous solution and undergoes spontaneous disproportionation. Calculate the standard reduction potential $E_1^\circ$, the equilibrium constant ($K_{eq}$) for the disproportionation of $\ce{Mn^{3+}}$ (based on the simplest integer stoichiometric coefficients), and the spin-only magnetic moment ($\mu_s$) of the most stable aqueous cation formed in this disproportionation. (Given: $\frac{2.303 RT}{F} = 0.059 \text{ V}$ at 298 K)