The unbalanced chemical equation is
MnO−4(aq)+I−(aq)→MnO2(s)+I2(s)
The oxidation half reaction is
I−(aq)→I2(s)
The reduction half reaction is
MnO−4(aq)→MnO2(aq)
Balance I atoms and charges in the oxidation half reaction.
2I−(aq)→I2(s)+2e−
In the reduction half reaction, the oxidation number of Mn changes from +7 to +4. Hence, add 3 electrons to reactant side of the reaction.
MnO−4(aq)+3e−→MnO2(aq)
Balance charge in the reduction half reaction by adding 4 hydroxide
ions to product side.
MnO−4(aq)+3e−→MnO2(aq)+4OH−
To balance O atoms, add 2 water molecules to reactant side.
MnO−4(aq)+3e−+2H2O→MnO2(aq)+4OH−
To equalize the number of electrons, multiply the oxidation half reaction by 3 and multiply the reduction half reaction by 2.
6I−(aq)→3I2(s)+6e−
2MnO−4(aq)+6e−+4H2O→2MnO2(aq)+8OH−
Add two half cell reactions to obtain the balanced equation.
2MnO−4(aq)+6I−(aq)+4H2O2(l)→2MnO2(s)+3I2(s)+8OH−