Question

A mixture of carbon monoxide and carbon dioxide is found to have a density of $1.6\text{g/L}$ at S.T.P. The mole fraction of carbon monoxide is:

• A. $0.51$
• B. $2.81$
• C. $1.21$
• D. None of these.

Answer 1

The correct option is A $0.51$

Average molecular mass, $M=\frac{dRT}{P}$
$\therefore M_{mix}=\frac{dRT}{P}$
at STP
$M_{mix}=\frac{1.6\times 0.0821\times 273}{1}$
=$1.6\times 22.4$
=$35.84gmo{l}^{-1}$

Let $X_{CO}$ be the mole fraction of $CO$
Then mole fraction of $C{O}_2$ = $1-X_{CO}$
Since molar masses of $CO$ and $C{O}_2$ are $28gmo{l}^{-1}$ and $44gmo{l}^{-1}$

putting all values,
$M_{mix}=X_{CO}\times M_{CO}+(1-X_{CO})\times M_{C{O}_2}$
$35.84=X_{CO}\times 28+(1-X_{CO})\times 44$
$X_{CO}=0.51$