Answer
The mole fractions of Nitrogen and Hydrogen gas are 0.333 and 0.667 respectively.
Work Step by Step
Given information in the question,
Number of moles of $\mathrm{H}_{2}=2$ moles
Number of moles of $\mathrm{N}_{2}=1$ mole
Volume of the vessel $=22.4 \mathrm{dm}^{3}=22.4$ litres
Temperature $=\mathrm{T}=273.15 \mathrm{K}$
$\begin{aligned} \text { Total number of moles in the system } &=\text { Moles of Nitrogen }+\text { Moles of Hydrogen } \\ &=1+2 \text { moles } \\ &=3 \text { moles } \end{aligned}$
Calculating the Mole fraction
Mole fraction of an element in a combined system is defined as:
Mole fraction of an element $=\frac{\text { Number of moles of the element }}{\text { Total number of moles in the system }}$ (1)
Substituting the values and calculating mole fraction of Nitrogen and Hydrogen,
$$
\begin{aligned} \text { Mole fraction of Nitrogen } &=\frac{\text { Number of moles of Nitrogen }}{\text { Total number of moles in the system }} \\ &=\frac{1}{3} \\ &=0.333 \end{aligned}
$$
$\begin{aligned} \text { Mole fraction of Hydrogen } &=\frac{\text { Number of moles of Hydrogen }}{\text { Total number of moles in the system }} \\ &=\frac{2}{3} \\ &=0.667 \end{aligned}$
Hence the mole fractions of Nitrogen and Hydrogen gas are 0.333 and 0.667 respectively.
