Question

Consider the composite system, which is held at $300K$, shown in the following figure. Assuming ideal gas behavior, calculate the total pressure (in atm) if the barriers separating the compartments are removed. Assume that the volume of the barriers is negligible. (Given : $R=0.082atmL/mol.K$)

Answer 1

The number of moles of $He,Ne$ and $Xe$ is given by,
$n_{He}=\frac{PV}{RT}=\frac{3}{RT};n_{Ne}=\frac{PV}{RT}=\frac{10}{RT};n_{Xe}=\frac{PV}{RT}=\frac{1}{RT}$
$n=n_{He}+n_{Ne}+n_{Xe}=\frac{(3+10+1)}{RT}$
The total pressure is given by,
$P=\frac{(n_{He}+n_{Ne}+n_{Xe})RT}{V}$
$P_{total}=\frac{(3+10+1)}{RT}\times \frac{RT}{7}=2atm$.