a
      Reduction Half      Oxidation Half

      \(2 \mathrm{MnO}_4^{-} \rightarrow 2 \mathrm{MnO}_2\)       \(2 \mathrm{I}^{-} \rightarrow \mathrm{I}_2+2 \mathrm{e}^{-}\)

\(2 \mathrm{MnO}_4^{-}+4 \mathrm{H}_2 \mathrm{O}+6 \mathrm{e}^{-} \rightarrow 2 \mathrm{MnO}_2+8 \mathrm{OH}^{-}\)     \(6 \mathrm{I}^{-} \rightarrow 3 \mathrm{I}_2+6 \mathrm{e}^{-}\)

Adding oxidation half and reduction half, net reaction is

\(2 \mathrm{MnO}_4^{-}+6 \mathrm{I}^{-}+4 \mathrm{H}_2 \mathrm{O} \rightarrow 3 \mathrm{I}_2+2 \mathrm{MnO}_2+8 \mathrm{OH}^{-}\)

\({z}=8\)

\({ Ans. }8\)