$A$ violet compound of manganese $(A)$ decomposes on heating to liberate oxygen and compounds $(B)$ and $(C)$ of manganese are formed. Compound $(C)$ reacts with $KOH$ in the presence of potassium nitrate to give compound $(B)$. On heating compound $(C)$ with conc. $H_{2}SO_{4}$ and $NaCl$,chlorine gas is liberated and a compound $(D)$ of manganese along with other products is formed. Identify compounds $A$ to $D$ and also explain the reactions involved.
(A) $A: KMnO_{4}$,$B: K_{2}MnO_{4}$,$C: MnO_{2}$,$D: MnCl_{2}$
$2KMnO_{4} \rightarrow K_{2}MnO_{4} + MnO_{2} + O_{2}$
$2MnO_{2} + 4KOH + O_{2} \rightarrow 2K_{2}MnO_{4} + 2H_{2}O$
$MnO_{2} + 4NaCl + 4H_{2}SO_{4} \rightarrow MnCl_{2} + 2NaHSO_{4} + 2H_{2}O + Cl_{2}$
$2KMnO_{4} \rightarrow K_{2}MnO_{4} + MnO_{2} + O_{2}$
$2MnO_{2} + 4KOH + O_{2} \rightarrow 2K_{2}MnO_{4} + 2H_{2}O$
$MnO_{2} + 4NaCl + 4H_{2}SO_{4} \rightarrow MnCl_{2} + 2NaHSO_{4} + 2H_{2}O + Cl_{2}$
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