Question

The vapour density of a mixture containing $N{O}_2$ and $N_2{O}_4$ is $38.3$ at $300K$. The number of moles of $N{O}_2$ in $100g$ of the mixture is approximately

• A. 0.44
• B. 4.4
• C. 33.4
• D. 3.34

Answer 1

Answer: (A)

Molecular weight of mixture $=38.3\times 2=76.6$

Let mass of $N{O}_2$ in mixture $=xg$

Then mass of $N_2{O}_4=(100-x)g$

Number of moles of $N{O}_2=x/46$

Number of moles of $N_2{O}_4=\frac{100-x}{92}$

$\frac{\text{ Weight }}{\text{ Number of moles }}=$ Molecular weight

$\frac{x+(100-x)}{\frac{x}{46}+\frac{(100-x)}{92}}=76.6$

$\Rightarrow \frac{x}{46}+\frac{(100-x)}{92}=\frac{100}{76.6}$

$\Rightarrow x=20.1$

Number of moles of $N{O}_2=\frac{20.1}{46}=0.437\approx 0.44$