Equal weights of ${\mathrm{CH}}_4 \& {\mathrm{O}}_2$ are mixed in an empty container at 25°C .The fraction of the total pressure exerted by oxygen is

${\mathrm{P}}_{{\mathrm{O}}_2}={\mathrm{X}}_{{\mathrm{O}}_2}.\mathrm{Pt}$

${\mathrm{X}}_{{\mathrm{O}}_2}=\frac{{\displaystyle \frac{\mathrm{x}}{16}}}{{\displaystyle \frac{\mathrm{x}}{16}}+{\displaystyle \frac{\mathrm{x}}{32}}}=\frac{{\displaystyle \frac{\mathrm{x}}{16}}}{{\displaystyle \frac{3\mathrm{x}}{32}}}$

 $\frac{2\times 1\mathrm{x}}{32}=\frac{3x}{32}$

$\frac{\cancel{\mathrm{x}}}{\cancel{{16}_1}}\times \frac{\cancel{{32}^2}}{\cancel{x_3}}=\frac{2}{3}{P}_T$

${\mathrm{P}}_{{\mathrm{O}}_2}=\frac{2}{3}{\mathrm{P}}_{\mathrm{T}}$

∴ The total pressure exerted by Oxygen is  $\frac{2}{3} of total pressure$