The vanadium in a sample of ore is converted to \(\mathrm{VO}^{2+}\). The
\(\mathrm{VO}^{2+}\) ion is subsequently titrated with \(\mathrm{MnO}_{4}^{-}\) in
acidic solution to form \(\mathrm{V}(\mathrm{OH})_{4}{ }^{+}\) and manganese(II)
ion. The unbalanced titration reaction is
\(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{VO}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}(t)
\longrightarrow\)
\(\mathrm{V}(\mathrm{OH})_{4}^{+}(a q)+\mathrm{Mn}^{2+}(a q)+\mathrm{H}^{+}(a
q)\)
To titrate the solution, \(26.45 \mathrm{~mL}\) of \(0.02250 \mathrm{M}
\mathrm{MnO}_{4}^{-}\) was required. If the mass percent of vanadium in the ore
was \(58.1 \%\), what was the mass of the ore sample? Hint: Balance the
titration reaction by the oxidation states method.