First Step :
\(\mathrm{MnO}_2+4 \mathrm{HCl} \rightarrow \mathrm{MnCl}_2+\mathrm{Cl}_2+2 \mathrm{H}_2 \mathrm{O}\)
Here \(1 \mathrm{~mol}\) of \(\mathrm{MnO}_2\) produce \(1 \mathrm{~mol}\) of \(\mathrm{Cl}_2\)
\(\therefore\) Mole ratio of \(\mathrm{n}_{\mathrm{M}_{\mathrm{nO}_2}}: \mathrm{n}_{\mathrm{Cl}_2}=1: 1\)
Second Step :
\(\mathrm{Cl}_2+2 \mathrm{Kl} \rightarrow 2 \mathrm{KCl}+\mathrm{I}_2\)
Here, \(1 \mathrm{~mol}\) of \(\mathrm{Cl}_2\) produce \(1 \mathrm{~mol}\) of \(\mathrm{I}_2\)
Mole ratio of \(\mathrm{n}_{\mathrm{Cl}_2}: \mathrm{n}_{\mathrm{I}_2}=1: 1\)
Third Step :
\(\mathrm{I}_2+2 \mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3 \rightarrow 2 \mathrm{Nal}+\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3\)
\(1 \mathrm{~mol}\) of \(\mathrm{I}_2\) react with \(2 \mathrm{~mol}\) of \(\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3\)
Mole ratio of \(\mathrm{n}_{\mathrm{I}_2}: \mathrm{n}_{\mathrm{N}_2 \mathrm{~S}_2 \mathrm{O}_3}=1: 2\)
Given \(\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3\) is \(60 \mathrm{~mL}\) of \(0.1 \mathrm{M}\)
\(\therefore\) Number of moles of \(\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3\)
\(=\mathrm{V}(\) in \(\mathrm{L}) \times \mathrm{M}\) (Molarity)
\(=\frac{60}{1000} \times 0.1\)
\(=0.006 \mathrm{~mol}\)
\(\therefore\) Number of moles of \(\mathrm{I}_2\)
\(=\frac{1}{2}(0.006) \)
\(=0.003\)
\(\therefore\) Moles of \(\mathrm{MnO}_2=0.003\) (as mole ratio of \(\mathrm{MnO}_2\) and \(\mathrm{Cl}_2=1: 1\) )
Molar mass of \(\mathrm{MnO}_2=55+32=87\)
\(\therefore\) Mass of \(\mathrm{MnO}_2=0.003 \times 87=0.261 \mathrm{gm}\)
Given \(\mathrm{MnO}_2=2 \mathrm{~g}\)
\(\therefore \%\) of \(\mathrm{MnO}_2=\frac{0.261}{2} \times 100=13 \%\)