Question

To an evacuated vessel with movable piston under external pressure of $1atm,0.1mole$ of $He$ and $1.0mole$ of unknown compound (vapour pressure $0.68atm$ at $0^{\circ }C$) are introduced. Considering the ideal gas behaviour, the total volume (in litre) of the gases at $0^{\circ }C$ is close to

Answer 1

Let volume of vessel $=VL$
In the vapour of compound,
$PV=n_{g}RT$
$0.68\times V=n_g\times 0.082\times 273$
Total pressure $=$ External pressure,
$1\times V=(n_g+n_{He})\times 0.082\times 273$
Dividing eqn. (ii) by eqn. (i),
$\frac{1}{0.68}=\frac{n_g+n_{He}}{n_g}$
$n_g=0.68n_g+0.68n_{He}$
$=0.68n_g+0.68\times 0.1$
$0.32n_g=0.068$
$n_g=0.2125$
From eqn. (ii),
$V=(0.2125+0.1)\times 0.082\times 273$
$=6.99=7L$.