Equal masses of methane and oxygen are mixed in an empty container at $${25^ \circ }C.$$  The fraction of the total pressure exerted by oxygen is

Solution :
Let the mass of methane and oxygen $${\text{ = }}m{\text{ }}gm.$$
Mole fraction of $${O_2}$$
$$\eqalign{ & = \frac{{{\text{Moles of}}\,{O_2}}}{{{\text{Moles of}}\,{O_2} + {\text{Moles of}}\,C{H_4}}} \cr & = \frac{{\frac{m}{{32}}}}{{\frac{m}{{32}} + \frac{m}{{16}}}} \cr & = \frac{{\frac{m}{{32}}}}{{\frac{{3m}}{{32}}}} \cr & = \frac{1}{3} \cr} $$
Partial pressure of $${O_2} = $$  Total pressure $$ \times $$  mole fraction of $${O_2},\,{P_{{O_2}}} = P \times \frac{1}{3} = \frac{1}{3}P$$