The number of moles of ${\mathrm{KMnO}}_4$ that will be needed to react with one mole of sulphite ion in acidic solution is

$\begin{array}{l}2{\mathrm{KMnO}}_4+3{\mathrm{H}}_2{\mathrm{SO}}_4\to {\mathrm{K}}_2{\mathrm{SO}}_4+2{\mathrm{MnSO}}_4+3{\mathrm{H}}_2\mathrm{O}+5\left[\mathrm{O}\right]\\ \frac{\left[{\mathrm{SO}}_3^{2-}+\left[\mathrm{O}\right]\to {\mathrm{SO}}_4^{2-}\right]\times 5}{2{\mathrm{KMnO}}_4+3{\mathrm{H}}_2{\mathrm{SO}}_4+5{\mathrm{SO}}_3^{2-}\to {\mathrm{K}}_2{\mathrm{SO}}_4}\\ \mathrm{or}\frac{+2{\mathrm{MnSO}}_4+3{\mathrm{H}}_2\mathrm{O}+5{\mathrm{SO}}_4^{2-}}{2{\mathrm{MnO}}_4^{-}+6{\mathrm{H}}^{+}+5{\mathrm{SO}}_3^{2-}\to 2{\mathrm{Mn}}^{2+}}\\ +5{\mathrm{SO}}_4^{2-}+3{\mathrm{H}}_2\mathrm{O}\\ 5\mathrm{moles}\mathrm{of}{\mathrm{SO}}_3^{2-}\mathrm{required}2\mathrm{moles}\mathrm{of}{\mathrm{MnO}}_4^{-}\\ 1\mathrm{moles}\mathrm{of}{\mathrm{SO}}_3^{2-}\mathrm{will}\mathrm{be}\mathrm{required}\frac{2}{5}\mathrm{moles}\mathrm{of}{\mathrm{MnO}}_4^{-}\end{array}$