Question

A mixture of $N{O}_2$ and $N_2{O}_4$ has a vapour density of 38.3 at 300 K. What is the number of moles of $N{O}_2$ in 100 g of the mixture ?

• A. 0.043
• B. 4.4
• C. 3.4
• D. 0.437

Answer 1

Answer: (D)

Average mol. mass of mixture $=2\times V.D$
$=2\times 38.3=76.6$
Let mixture contains $a$ moles of $N{O}_2$ and $b$ moles of $N_2{O}_4$
$\therefore \frac{a\times 46+b\times 92}{a+b}=76.6$
(Molar mass of $N{O}_2=46gmo{l}^{-1}$ molar mass of $N_2{O}_4=92gmo{l}^{-1})$
Let mass of $N{O}_2=x$ and mass of $N_2{O}_4=100-x$
$\therefore a=\frac{x}{46}$ and $b=\frac{100-x}{92}$
$\therefore \frac{x+100-x}{\frac{x}{46}+\frac{100-x}{92}}=76.6$
$\frac{x}{46}+\frac{100-x}{92}=\frac{100}{76.6}$
$x=\frac{100\times 15.4}{76.6}$
No. of moles of $N{O}_{2}a=\frac{x}{46}$
$=\frac{100\times 15.4}{46\times 76.6}=0.437$