In the reaction $2{\mathrm{SO}}_{3( \mathrm{g})}\rightleftharpoons 2{\mathrm{SO}}_{2( \mathrm{g})}+{\mathrm{O}}_{2( \mathrm{g})} +{\mathrm{SO}}_{3( \mathrm{g})}$ is 50% dissociated at $27°\mathrm{C}$ when the equilibrium pressure is $0.5 \mathrm{atm}$. Partial pressure of ${\mathrm{SO}}_{3( \mathrm{g})}$at equilibrium is

$2{\mathrm{SO}}_{3( \mathrm{g})}\rightleftharpoons 2{\mathrm{SO}}_{2( \mathrm{g})}+{\mathrm{O}}_{2( \mathrm{g})}$

2                        0                0

2 -2x                   2x               x                  

At equilibrium, total number of moles are $2+\mathrm{x}$

50 % dissociation means out of 2 moles of ${\mathrm{SO}}_3,1$ mole dissociates. Hence $2\mathrm{x}=1$ or $\mathrm{x}=0.5$

The mole fraction of sulphur trioxide ${\mathrm{X}}_{{\mathrm{SO}}_3}=\frac{2-2\mathrm{x}}{2+\mathrm{x}}=\frac{2-1}{2+0.5}=\frac{1}{2.5}=0.4$

Partial pressure of ${\mathrm{P}}_{{\mathrm{SO}}_3}=0.5\times {\mathrm{X}}_{{\mathrm{SO}}_3}=0.2 \mathrm{atm}$

Hence the correct option is (C) $0.2 \mathrm{atm}$