Thermal decomposition of a $Mn$ compound (X) at 513 K 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 are

• Thermal decomposition of $\mathrm{Mn}$ compound (X), i.e. ${\mathrm{KMnO}}_4$ at 513K produces compound Y (i.e. ${\mathrm{K}}_2{\mathrm{MnO}}_4$), ${\mathrm{MnO}}_2$, and a gaseous product.
  ${\mathrm{MnO}}_2$ reacts with $\mathrm{NaCl}$ and concentrated ${\mathrm{H}}_2{\mathrm{SO}}_4$ to form the pungent gas Z (i.e. $C{l}_2$ ).
  The following are the reactions:

      $2\mathrm{K}\underset{\left(\mathrm{X}\right)}{\mathrm{M}}{\mathrm{nO}}_4\underset{\mathrm{\Delta }}{\stackrel{513 \mathrm{K}}{⟶}}{\mathrm{K}}_2\underset{\left(\mathrm{Y}\right)}{\mathrm{M}}{\mathrm{nO}}_4+{\mathrm{MnO}}_2+{\mathrm{O}}_2( \mathrm{g})$

${\mathrm{MnO}}_2+4\mathrm{NaCl}+4{\mathrm{H}}_2{\mathrm{SO}}_4\to {\mathrm{MnCl}}_2+4{\mathrm{NaHSO}}_4+2{\mathrm{H}}_2\mathrm{O}+\underset{\text{ pungent gas }}{{\mathrm{Cl}}_{2( \mathrm{g}}\left(\mathrm{Z}\right)}$