(i) ${\mathrm{MnO}}_{2 }$reacts with the four moles of hydrochloric acid and formed one mole of the ${\mathrm{MnCl}}_2$ and one mole of chlorine and two mole of water.

Reaction :-

${\mathrm{MnO}}_2 + 4\mathrm{HCl}\to {\mathrm{MnCl}}_2 +{\mathrm{Cl}}_2+2{\mathrm{H}}_2\mathrm{O}$

(ii) Two mole of potassium permagnate reacts with the sixteen mole of hydrochloric acid and formed the two mole of ${\mathrm{MnCl}}_2$ and two moles of potassium chloride and five moles of chlorine gas and eight moles of water.

$2{\mathrm{KMnO}}_4 + 16\mathrm{HCl}\to 2{\mathrm{MnCl}}_2 +5{\mathrm{Cl}}_2+8{\mathrm{H}}_2\mathrm{O}+2\mathrm{KCl}$

Hence, the number of moles of chlorine gas released respectively are $1\&5$.