Question

A vessel of volume $30\, m ^{3}$ contains an ideal gas at temperature $27^{\circ} C$ and pressure $5.16$ bar. The gas is allowed to leak till its pressure falls to atmospheric pressure. Assuming that the temperature remains constant during leakage, the number of moles of the gas that have leaked are _________$\times 10^{4}$. (Consider, $R =8.32\, J\, mol ^{-1}\, K ^{-1}$, Atmospheric pressure $=1$ bar $=10^{5} Pa$ )

Answer 1

Before leakage,
$PV = n _{1} RT$ ...(i)
After leakage,
$P'V = n _{2} RT$ ...(ii)
Number of moles of gas leaked is given by,
$\left( n _{1}- n _{2}\right)$
Subtracting equation (ii) from equation (i),
$n _{1}- n _{2} =\frac{ PV }{ RT }-\frac{ P 'V }{ RT }$
$\therefore n _{1}- n _{2} =\frac{ V }{ RT }\left( P - P'\right)$
$=\frac{30}{8.32 \times(27+273)} \times(5.16-1) \times 10^{5}$
$=\frac{30 \times 4.16 \times 10^{5}}{8.32 \times 300}$
$\therefore n _{1}- n _{2} =0.5 \times 10^{4}$