Balance the reaction ${\mathrm{MnO}}_4^{-}+{\mathrm{SO}}_3^{-2}\to {\mathrm{Mn}}^{+2}+{\mathrm{SO}}_4^{-2}$ in acid medium
(or)
Write the balanced equation for the oxidation of sulphite ions to sulphate ions in acid medium by permanganate ion.

Equation

Oxidation half reaction ${\mathrm{SO}}_3^{2-}\to {\mathrm{SO}}_4^{2-}$
1) Balance the atoms other than H and O
${\mathrm{SO}}_3^{2-}\to {\mathrm{SO}}_4^{2-}$
2) Balance of oxygen atoms
${\mathrm{SO}}_3^{2-}+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{SO}}_4^{2-}$
3) Balance of Hydrogen atoms
${\mathrm{SO}}_3^{2-}+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{SO}}_4^{2-}+2{\mathrm{H}}^{+}$
4) Balance of charges
${\mathrm{SO}}_3^{2-}+{\mathrm{H}}_2\mathrm{O}\to {\mathrm{SO}}_4^{2-}+2{\mathrm{H}}^{+}+2{\mathrm{e}}^{-}\dots \left(1\right)$
Reduction half reaction ${\mathrm{MnO}}_4^{-}\to {\mathrm{Mn}}^{2+}$
1) Balance the atoms other than H and O
${\mathrm{MnO}}_4^{-}\to {\mathrm{Mn}}^{2+}$
2) Balance of oxygen atoms
${\mathrm{MnO}}_4^{-}\to {\mathrm{Mn}}^{2+}+4{\mathrm{H}}_2\mathrm{O}$
3) Balance of Hydrogen atoms
${\mathrm{MnO}}_4^{-}+8{\mathrm{H}}^{+}\to {\mathrm{Mn}}^{2+}+4{\mathrm{H}}_2\mathrm{O}$
4) Balance of charges
${\mathrm{MnO}}_4^{-}+8{\mathrm{H}}^{+}+5{\mathrm{e}}^{-}\to {\mathrm{Mn}}^{2+}+4{\mathrm{H}}_2\mathrm{O} ----\left(2\right)$
Balancing of electrons in both sides
Adding the two half reaction
$1\times 5;5{\mathrm{SO}}_3^{2-}+5{\mathrm{H}}_2\mathrm{O} \to 5{\mathrm{SO}}_4^{2-}+10{\mathrm{H}}^{+}+10{\mathrm{e}}^{-}----\left(3\right)$
$2\times 2;2{\mathrm{MnO}}_4^{-}+16{\mathrm{H}}^{+}+10{\mathrm{e}}^{-}\to 2{\mathrm{Mn}}^{2+}+8{\mathrm{H}}_2\mathrm{O} ----\left(4\right)$
(3) + (4)
$2{\mathrm{MnO}}_4^{-}+5{\mathrm{SO}}_3^{2-}+16{\mathrm{H}}^{+}+5{\mathrm{H}}_2\mathrm{O}\to 2{\mathrm{Mn}}^{2+}+5{\mathrm{SO}}_4^{2-}+10{\mathrm{H}}^{+}+8{\mathrm{H}}_2\mathrm{O}$
$2{\mathrm{MnO}}_4^{-}+5{\mathrm{SO}}_3^{2-}+6{\mathrm{H}}^{+}\to 2{\mathrm{Mn}}^{2+}+5{\mathrm{SO}}_4^{2-}+3{\mathrm{H}}_2\mathrm{O}$