Balance the following redox reaction in basic medium by ion-electron method :
`MnO_(4(aq))^(-)+1_((aq))^(-) rarr MnO_(2(s))+1_(2(s))`

Explanation

`R.H.R" "O.H.R`
`MnO_(4)^(-)toMnO_(2)" "I^(-)toI_(2)`
`MnO_(4)^(-)toMnO_(2)+2H_(2)O" "2I^(-)toI_(2)`
`underset((-1))(MnO_(4)^(-))+underset((+4))(4H^(+))tounderset((0))(MnO_(2))+underset((0))(2H_(2)O)" "-2+x=0`
`-1+4+x=0" "x=+2`
`x=-3" ""Hence 2 electrons are to be subtracted")`
Hence 3 electrns are to be added `" "2I^(-)-2etoI_(2)`
`MnO_(4)^(-)+4H^(+)+3etoMnO_(2)+2H_(2)O("or")2I^(-)toI_(2)+2e`
`R.H.Rxx2," "2MnO_(4)(-)+8H^(+)+cancel(6e)to2MnO_(2)+4H_(2)O`
`O.H.Rxx3,ul(" "6I^(-)to3I_(2)+cancel(6e))`
`" "2MnO_(4)^(-)+6I^(-)+8H^(+)to2MnO_(2)+3I_(2)+4H_(2)O`
`" "("Acidic medium")`
Adding `8OH^(-)` both sides
`2MnO_(4)^(-)+6I^(-)+8H^(+)+8OH^(-)to2MnO_(2)+3I_(2)+4H_(2)O+8OH^(-)`
`2MnO_(4)^(-)+6I^(-)+8H_(2)Oto2MnO_(2)+3I_(2)+4H_(2)O+8OH^(-)`
`2MnO_(4)^(-)+6I^(-)+4H_(2)Oto2MnO_(2)+K3I_(2)+8OH^(-)` (Basic medium)