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Thermal decomposition of a Mn compound (X) at 513K results in compound Y, \[Mn{O_2}\] and a gaseous product. \[Mn{O_2}\] reacts with NaCl and concentrated \[{H_2}S{O_4}\] to give a pungent gas Z. X, Y and Z respectively.
A. \[{K_2}Mn{O_4},{\text{ }}KMn{O_4}and S{O_2}\]
B. \[{K_2}Mn{O_4},{\text{ }}KMn{O_4}and{\text{ }}C{l_2}\]
C. \[{K_3}Mn{O_4},{\text{ }}{K_2}Mn{O_4}and{\text{ }}C{l_2}\]
D. \[KMn{O_{4,}}{K_2}Mn{O_4}\;and{\text{ }}C{l_2}\]

Answer
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Hint: since a compound of Mn undergoes thermal decomposition to produce \[Mn{O_2}\], a compound Y and a gaseous product. We must take into account qualitative analysis for the tests of permanganate and manganate radicals.

Complete step by step answer:
Out of various tests let us remember the heating effect of potassium permanganate.
The reaction is preceded by heating dry crystals of \[KMn{O_4}\] almost black in colour gives a black residue. Addition of little water to this residue, followed by filtration, gives green filtrate and black residue. Reaction involved is:
$2Kmn{O_4}\xrightarrow{\Delta }{K_2}Mn{O_4} + Mn{O_2} + {O_2}$
Potassium manganate is water soluble and so is leached out as green filtrate. \[Mn{O_2}\]is insoluble in water and gives black residue. The oxygen gas is released in this reaction. In the first step potassium permanganate (\[KMn{O_4}\]) the compound (X) decomposes on heating to give potassium manganate (${K_2}Mn{O_4}$) which is the compound (Y), \[Mn{O_2}\] and the gaseous product is oxygen .

In the second step \[Mn{O_2}\] further reacts with NaCl and concentrated sulfuric acid to give a pungent-smelling gas that is Chlorine gas (\[C{l_2}\]), $MnS{O_4}$ , \[N{a_2}S{O_4}\] and ${H_2}O$. The reaction is: .
$Mn{O_2} + 2NaCl + 2{H_2}S{O_4} \to MnS{O_4} + C{l_2} + N{a_2}S{O_4} + 2{H_2}O$
This a test for Chloride anion as on solid chloride on treating with magnesium oxide and concentrated sulfuric acid evolves a yellow green colour gas with a strong pungent smell that is chlorine. Always remember while finding out the compounds it evolves pungent smell it confirms chlorine in the compound.
The compound X= \[KMn{O_4}\], Y=${K_2}Mn{O_4}$, Z=\[C{l_2}\].

Hence the correct option is option D.

Note:
Potassium permanganate decomposes when heated, the oxidation state of manganese changes as the oxidation state of $KMnO_4$ is +7 decomposes to potassium manganate which oxidation state is +6 and manganese dioxide its oxidation state is +4, it is a redox reaction in which Mn which undergo both oxidation and reduction such type of a reaction is known as disproportional reaction.