Question

A vessel of volume $8.0 \times 10^{-3} m ^{3}$ contains an ideal gas at $300 K$ and $200 kPa$. The gas is allowed to leak till the pressure falls to $125 kPa$. Calculate the amount of the gas (in moles) leaked assuming that the temperature remains constant.

Answer 1

SOLUTION : As the gas leaks out, the volume and the temperature of the remaining gas do not change. The number of moles of the gas in the vessel is given by $n=\frac{p V}{R T}$. The number of moles in the vessel before the leakage is

$n_{1}=\frac{p_{1} V}{R T}$

and that after the leakage is

$n_{2}=\frac{p_{2} V}{R T}.$

Thus, the amount leaked is

$n_{1}-n_{2}=\frac{\left(p_{1}-p_{2}\right) V}{R T}$

$=\frac{(200-125) \times 10^{3} N m ^{-2} \times 8.0 \times 10^{-3} m ^{3}}{\left(8.3 J K ^{-1} mol ^{-1}\right) \times(300 K )}$

$=0.24 mol ^{-1} .$