A quantity of \(25.0 \mathrm{~mL}\) of a solution containing both
\(\mathrm{Fe}^{2+}\) and \(\mathrm{Fe}^{3+}\) ions is titrated with \(23.0
\mathrm{~mL}\) of \(0.0200 M \mathrm{KMnO}_{4}\) (in dilute sulfuric acid). As a
result, all of the \(\mathrm{Fe}^{2+}\) ions are oxidized to \(\mathrm{Fe}^{3+}\)
ions. Next, the solution is treated with Zn metal to convert all of the
\(\mathrm{Fe}^{3+}\) ions to \(\mathrm{Fe}^{2+}\) ions. Finally, the solution
containing only the \(\mathrm{Fe}^{2+}\) ions requires \(40.0 \mathrm{~mL}\) of
the same \(\mathrm{KMnO}_{4}\) solution for oxidation to \(\mathrm{Fe}^{3+}\).
Calculate the molar concentrations of \(\mathrm{Fe}^{2+}\) and
\(\mathrm{Fe}^{3+}\) in the original solution. The net ionic equation is
\(\mathrm{MnO}_{4}^{-}+5 \mathrm{Fe}^{2+}+8 \mathrm{H}^{+} \longrightarrow\)
\(\mathrm{Mn}^{2+}+5 \mathrm{Fe}^{3+}+4 \mathrm{H}_{2} \mathrm{O}\)