Derive a balanced equation for the reaction occurring in the cell:
$$\mathrm{Fe}(\mathrm{s})\left|\mathrm{Fe}^{2+}(\mathrm{aq}) \|
\mathrm{Fe}^{3+}(\mathrm{aq}), \mathrm{Fe}^{2+}(\mathrm{aq})\right|
\mathrm{Pt}(\mathrm{s})$$
(a) If \(E_{\text {cell }}^{\circ}=1.21 \mathrm{V},\) calculate \(\Delta
G^{\circ}\) and the equilibrium constant for the reaction.
(b) Use the Nernst equation to determine the potential for the cell:
$$\begin{array}{r}
\mathrm{Fe}(\mathrm{s}) | \mathrm{Fe}^{2+}\left(\mathrm{aq}, 1.0 \times
10^{-3} \mathrm{M}\right) \| \mathrm{Fe}^{3+}\left(\mathrm{aq}, 1.0 \times
10^{-3} \mathrm{M}\right) \\
\mathrm{Fe}^{2+}(\mathrm{aq}, 0.10 \mathrm{M}) | \mathrm{Pt}(\mathrm{s})
\end{array}$$
(c) In light of (a) and (b), what is the likelihood of being able to observe
the disproportionation of \(\mathrm{Fe}^{2+}\) into \(\mathrm{Fe}^{3+}\) and Fe
under standard conditions?