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Recently, I built a galvanic cell in the lab with iron (III) nitrate, magnesium sulfate, and carbon and magnesium electrodes.
My question is:
When the iron $3+$ ions are reduced, do they reduce to iron $2+$ ions or to solid iron?
I know the reduction potential for iron $3+$ to iron $2+$ is greater, indicating that it is more likely to occur.
$$\begin{align} \ce {Fe^{2+} {(aq)} + 2e^{-} &<=> Fe {(s)}} &E^⦵= \pu{-0.44V}\\ \ce {Fe^{3+} {(aq)} + e^{-} &<=> Fe^{2+} {(aq)}} &E^⦵= \pu{+0.77V}\\ \ce {Mg^{2+} {(aq)} + 2e^{-} &<=> Mg {(s)}} &E^⦵= \pu{-2.37V}\\ \end{align}$$
Thus
$$ \begin{align} \ce {Mg {(s)} + 2Fe^{3+} {(aq)} &<=> Mg^{2+} {(aq)} +2Fe^{2+} {(aq)}}&&E^⦵_{\text{cell}}= 0.77--2.37=\pu{+3.14V}\\ \ce {Mg {(s)} + Fe^{2+} {(aq)} &<=> Mg^{2+} {(aq)} +Fe {(s)}}&&E^⦵_{\text{cell}}= -0.44--2.37=\pu{+1.93V}\\ \end{align}$$
Both reactions are feasible, and I'd imagine the first would proceed until the concentration of $\ce {Fe^{3+} {(aq)}}$ is very low, and then the second would start at a noticeable rate. This assumes, of course, the iron solid is able to deposit on the carbon cathode, and I don't see why not.
Hope this was helpful.
(Thank you Dr. J for pointing out my typo)
