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.

• A. 0.24
• B. 0.45
• C. 0.58
• D. 0.28

Answer 1

The correct option is A 0.24

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 $n=\frac{PV}{RT}$. The number of moles in the vessel before the leakage is,
$n_1=\frac{P_{1}V}{RT}$
and that after the leakage is,
$n_2=\frac{P_{2}V}{RT}$
Thus, the amount leaked is,
$n_1-n_2=\frac{(P_1-P_2)V}{RT}$
$=\frac{(200-125)\times {10}^{3}N/m^3\times 8.0\times {10}^{-3}{m}^3}{(8.3J/mol-K)\times \left(300K\right)}$
= 0.24 mol