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

`MnO_(4(aq))^(-)+1_((aq))^(-)to MnO_(2(s))+1_(2(s))`(Basic medium )
Reduction half cell
`MnO_(4)^(-)to MnO_(2)`
`MnO_(4)^(-)to MnO_(2)+ 2 H_(2)O` (Oxygens balanced )
`MnO_(4)^(-) + 4H_(2)O to MnO_(2)+2H_(2)O+4 OH^(-)`
(Hydrogens balanced)
`MnO_(4)^(-)+2H_(2)O to MnO_(2)+4OH^(-)`
`MnO_(4)^(-)+2H_(2)O+3e^(-)to MnO_(2)+OH^(-)`
(Charge balanced)
2 `[MnO_(4)^(-)+2HO_(2)+3e^(-)to MnO_(2)+4 OH^(-)]`
3 xx `[ 2I^(-)to I_(2)+2e^(-)]`
Oxidation half cell
`I^(-)to I_(2)`
`2 I^(-)to I_(2)` (Iodines balanced )
`2 I^(-)to I_(2)+2e^(-)` (Charge balanced )
`overset(2 MnO_(4)^(-)+4H_(2)O+6e^(-)to 2 MnO_(2)+8OH^(-))(6I^(-)to 3 I_(2)+6 e^(-))/(2 MnO_(4)^(-)+4 H_(2)O+61^(-)to2 MnO_(2)+8OH^(-))`
The above equation is balanced equation .