A blackish brown coloured solid ‘A’, when fused with alkali hydroxide in presence of air produces a dark green coloured compound ‘B’. When electrolytic oxidation in alkaline medium gives a dark purple coloured compound. Identify A, B and C and write the reaction involved.

A balckish brown coloured solid is ${\mathrm{MnO}}_2$ when it is fused with alkali hydroxide in presence of air it produce Potassium manganate,(B) is ${\mathrm{K}}_2{\mathrm{MnO}}_4$

$$\begin{gathered} \underset{\left(\mathrm{A}\right)}{2{\mathrm{MnO}}_2}+4\mathrm{KOH}+{\mathrm{O}}_2 \to \underset{\left(\mathrm{B}\right)}{2{\mathrm{K}}_2{\mathrm{MnO}}_4} + 2{\mathrm{H}}_2\mathrm{O} \\ \mathrm{C} \mathrm{is}\hspace{0.17em}{\mathrm{KMnO}}_4 \\ \mathrm{At} \mathrm{anode}: \\ \underset{\underset{\left(\mathrm{green}\right)}{(\mathrm{Maganate} \mathrm{ion})}}{{{\mathrm{MnO}}_4}^{2-}} \to \underset{\underset{\left(\mathrm{violet}\right)}{(\mathrm{Permanganate} \mathrm{ion})}}{{{\mathrm{MnO}}_4}^{-}+{\mathrm{e}}^{-}} \end{gathered}$$

At cathode:
2H⁺ + 2e^–  → H₂

The overall reaction is
2K₂MnO₄ + H₂O + O → 2KMnO₄ + 2KOH