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

a) `MnO_(4)^(-)(aq)+I^(-)(aq)toMnO_(2)(s)+I_(2)(s)` (In basic 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)+3I_(2)+8OH^(-)` (Basic medium)
b) `MnO_(4)^(-)(aq)+SO_(2)(g)toMn^(2+)(aq)+HSO_(4)^(-)(aq)` (in acidic solution)

Adding one `OH^(-)` both sides
`2MnO_(4)^(-)+5SO_(2)+2H_(2)O+H^(+)+OH^(-)to2Mn^(2+)+5HSO_(4)^(-)+OH^(-)`
`2MnO_(4)^(-)+5SO_(2)+3H_(2)Oto2Mn^(2+)+5SO_(4)^(-)+OH^(-)` (Basic)
c) `H_(2)O_(2)(aq)+Fe^(2+)(aq)toFe^(3+)(aq)+H_(2)O(l)` (in acidic solution)