Question

A gaseous mixture of helium and oxygen is found to have a density of $0.518gd{m}^{-3}$ at ${25}^{\circ }C$ and $720torr$. What is the per cent by mass of helium in this mixture?

Answer 1

We know that, $Pm=dRT$
$\frac{720}{760}\times m=0.518\times 0.0821\times 298$
$m=13.37g/mol$
Let mole fraction of $He$ in mixture be $\alpha$.
$\therefore x_{He}=\alpha ,x_{O_2}=(1-\alpha )$
Average molecular weight $=\alpha \times M_{He}+(1-\alpha )M_{O_2}$
$13.37=\alpha \times 4+(1-\alpha )32$
$\alpha =0.666$
% by mass of $He=0.666\times \frac{4}{0.666\times 4+0.334\times 32}\times 100$
$=19.95$%