The `Mn^(3+)` ion is unstable in solution and undergoes disproportionation reaction to give `Mn^(+2), MnO_(2)`, and `H^(o+)` ion. Write a balanced ionic equation for the reaction.

Explanation

The reaction may be written as :
`Mn^(3+) (aq) rarr Mn^(2+)(aq) +MnO_2(s) +H^(+) (aq)`
This may be balanced as :
Oxidation half equation :
`overset(3+)Mn^(3+)(aq)rarroverset(4+)(Mn)O_2(s)`
Balance O.N. by adding electrons
`Mn^(3+)(aq)rarr overset(+4)(Mn)O_2(s) +e^(-)`
Balance charge by adding `H^+` ions
`Mn^(3+) (aq) rarr MnO_2(s) +4H^(+) +e^(-)`
Balance charge by adding `H_2O`
`Mn^(3+)(aq) +2H_2O(l) rarr MnO_2(s) + 4H^(+) (aq) +e^(-) " "....(i)`
Reduction half equation
`Mn ^(3+ )(aq) rarr Mn^(2+) (aq)`
Balancing O.N. by adding electrons .
`Mn^(3+)(aq) +e^(-) rarr Mn^(2+)(aq) " "...(ii)`
Adding eq. (i) and eq . (ii)
`2Mn^(3+)(aq) +2H_2O(l) rarr MnO_2(s) + Mn ^(2+) (aq) + 4H^(+) (aq)`