Question

A vessel of volume $8\times {10}^{-3}{m}^3$ contains and Ideal gas at 300k and 210 K Pa the gas is allowed to leak till the pressure falls to 135 K Pa. Calculate the amount of the gas in moles leaked assuming the temperature remains constant.

• A. 0.34 mol
• B. 0.43 mol
• C. 0.24 mol
• D. 0.04 mol

Answer 1

The correct option is C 0.24 mol

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 $n_2=\frac{P_{2}V}{RT}$
$\therefore$ The amount of Gas leaked is
$n_1-n_2=\frac{(P_1-P_2)V}{RT}=\frac{(210-135)\times 8\times {10}^{-3}}{8.3\times 300}=0.24$