Question

Equal weights of methane and oxygen are mixed in an empty container at $25{}^\circ C$. The fraction of the total pressure exerted by oxygen is
(A) $\dfrac{1}{3}$
(B) $\dfrac{1}{2}$
(C) $\dfrac{2}{3}$
(D) $\dfrac{1}{3}\times \dfrac{273}{298}$

Answer 1

Hint: In a mixture of gases, each constituent gas has a partial pressure which is the pressure that gas would exert if it occupied the same volume as the mixture at the same temperature.

Complete step by step answer:
-According to the question, equal masses of methane and oxygen are mixed in an empty container at the same temperature that is $25{}^\circ C$.

-One mole of oxygen = molar mass of oxygen $({{O}_{2}})$ = $16\times 2=$32 g
One mole of methane = molar mass of methane $(C{{H}_{4}})$= $12+(1\times 4)$= 16 g

To make the equal masses, one mole of oxygen must be mixed with 2 moles of methane. So the total number of moles in the mixture will be 3 moles.
-Now calculating the mole fraction of oxygen in the mixture,
The number of molecules of a particular component in a mixture divided by the total number of moles in the given mixture is known as a mole fraction.
Mole fraction of solute $=\dfrac{\text{Moles of solute}}{\text{Moles of solute + Moles of solvent}}$
The mole fraction of oxygen $=\dfrac{1}{1+2}=\dfrac{1}{3}$

-The mole fraction is proportional to the fraction of the total pressure exerted.
Hence, the partial pressure exerted by oxygen in the mixture $=\dfrac{1}{3}\times \text{Total pressure}$
So, the correct answer is “Option D”.

Note: Methane gas is one of the most abundant gas present on earth. Methane is known by many names such as marsh gas, natural gas, carbon tetrachloride, and hydrogen carbide. Methane clathrates under the seafloor in the largest reservoir of methane. With the changing conditions on earth due to the consequences of human activities, the concentration of methane has increased $150%$ since 1750. Methane is used as fuel for ovens, water heaters, turbines, and many automobiles. Refined liquid methane when combined with liquid oxygen is used as a rocket fuel which offers the advantage of it over kerosene. Methane gas is also used for the commercial production of hydrogen gas mostly by Steam Methane Reforming (SMR).