At a certain temperature, $2{\mathrm{SO}}_2+{\mathrm{O}}_2\rightleftharpoons 2{\mathrm{SO}}_3$ reaction was allowed to take place in a vessel of one litre capacity. The equilibrium mixture contains $24.0 \mathrm{g} {\mathrm{SO}}_3, 4.8 \mathrm{g}$ ${\mathrm{O}}_2$ and $6.4 \mathrm{g} {\mathrm{SO}}_2.$ Find the value of ${\mathrm{K}}_{\mathrm{c}}.$

  $\text{ (a) }\mathrm{Wt}\text{. of }{\mathrm{SO}}_2=6.4\mathrm{g}\text{; }$

g. mol. wt. of ${\mathrm{SO}}_2=32+(2\times 16)=64\mathrm{g}$

$\therefore$ no. of mol of  ${\mathrm{SO}}_2=6.4/64=0.1$

$\left(\mathrm{b}\right)$ Wt. of ${\mathrm{O}}_2=4.8\mathrm{g};$ g. mol. wt. of ${\mathrm{O}}_2$

                    $=2\times 16=32\mathrm{g}$.

  $\therefore$ no. of mol of ${\mathrm{O}}_2=\frac{4.8}{32}=0.15$

$\left(\mathrm{c}\right)$ Wt. of ${\mathrm{SO}}_3=24\mathrm{g}$ ; g. mol. wt. of ${\mathrm{SO}}_3$

                       $=32+(3\times 16)=80\mathrm{g}$

   $\therefore$ no. of mol of ${\mathrm{SO}}_3=\frac{24}{80}=0.3$

For the following reaction at equilibrium :
           $\begin{array}{l}2{\mathrm{SO}}_2+{\mathrm{O}}_2\rightleftharpoons 2{\mathrm{SO}}_3\\ K_c=\frac{{\left[{\mathrm{SO}}_3\right]}^2}{{\left[{\mathrm{SO}}_2\right]}^2\left[{\mathrm{O}}_2\right]}\\ =\frac{0.3\times 0.3}{0.1\times 0.1\times 0.15}=60\end{array}$