The mole fraction of Oxygen in a mixture of Methane and Oxygen containing equal masses of them is                                

${\text{m}}_{{\text{O}}_{\text{2}}}={\text{m}}_{{\text{CH}}_{\text{4}}}=x$

${\text{n}}_{{\text{O}}_{\text{2}}}=\frac{x}{32}\text{and}{\text{n}}_{{\text{CH}}_{\text{4}}}=\frac{x}{16}$

The mole fraction of oxygen gas is find as follows:

${\chi }_{{\text{O}}_{\text{2}}}=\frac{\frac{x}{32}}{\frac{x}{32}+\frac{x}{16}}=\frac{x}{32}\times \frac{32}{3x}$

       $\therefore {\chi }_{{\text{O}}_{\text{2}}}=\frac{1}{3}$