If the ratio of masses of ${\mathrm{SO}}_3$  and $O_2$  gases confined in a vessel is 1 : 1 then the ratio of their partial pressures would be

Let ‘m’ be the mass of SO₃ and O₂ enclosed in the vessel

No. of moles of . ${\mathrm{SO}}_3=\frac{\mathrm{m}}{80}$

No. of moles of  ${\mathrm{O}}_2=\frac{\mathrm{m}}{32}$

Partial pressure of  $\left({\mathrm{SO}}_3\right){\mathrm{P}}_{\mathrm{A}}=\frac{\mathrm{m}}{80}\times \frac{\mathrm{R}\times \mathrm{T}}{\mathrm{V}}$

Partial pressure of   $\left({\mathrm{O}}_2\right){\mathrm{P}}_{\mathrm{B}}=\frac{\mathrm{m}}{32}\times \frac{\mathrm{R}\times \mathrm{T}}{\mathrm{V}}$

Now   $\frac{{\mathrm{P}}_{\mathrm{A}}}{{\mathrm{P}}_{\mathrm{B}}}=\frac{\mathrm{m}}{80}\times \frac{32}{\mathrm{m}}=\frac{2}{5}$