The following reaction can be best described as:
\[
3\mathrm{MnO_4^{2-}}+4\mathrm{H^+}
\rightarrow
2\mathrm{MnO_4^-}
+\mathrm{MnO_2}
+2\mathrm{H_2O}
\]
Show Hint
Whenever the same oxidation state appears on the reactant side and produces both higher and lower oxidation states on the product side, think of disproportionation.
Step 1: Determine oxidation state of Mn in manganate ion.
For
\[
\mathrm{MnO_4^{2-}}
\]
let oxidation state of Mn be \(x\).
\[
x+4(-2)=-2
\]
\[
x=+6
\]
Step 2: Determine oxidation states in the products.
For
\[
\mathrm{MnO_4^-}
\]
\[
x+4(-2)=-1
\]
\[
x=+7
\]
For
\[
\mathrm{MnO_2}
\]
\[
x+2(-2)=0
\]
\[
x=+4
\]
Step 3: Analyse oxidation and reduction.
One part of Mn(+6) is oxidised to Mn(+7).
Another part of Mn(+6) is reduced to Mn(+4).
Thus the same species undergoes both oxidation and reduction.
Step 4: Identify the reaction type.
Hence the reaction is a disproportionation reaction.
\[
{\text{Disproportionation}}
\]