For the following oxidation-reduction reaction, (a) write out the two half-
reactions and balance the equation, (b) calculate \(\Delta E^{\circ}\), and (c)
determine whether the reaction will proceed spontaneously as written;
\(\mathrm{Fe}^{2+}+\mathrm{MnO}^{-}{ }_{4}+\mathrm{H}^{+} \rightarrow
\mathrm{Mn}^{2+}+\mathrm{Fe}^{3+}+\mathrm{H}_{2} \mathrm{O}\)
(1) \(\mathrm{Fe}^{3+}+\mathrm{e}^{-} \leftrightarrows \mathrm{Fe}^{2+},
\mathrm{E}^{\circ}=0.77 \mathrm{eV}\)
(2) \(\mathrm{MnO}^{-}{ }_{4}+8 \mathrm{H}^{+}+6 \mathrm{e}^{-}
\leftrightarrows \mathrm{Mn}^{2+}+4 \mathrm{H}_{2} \mathrm{O},
\mathrm{E}^{\circ}=1.51 \mathrm{eV}\)