Question

A vessel contains $1 \, g$ of oxygen at a pressure of $10 \, atm$ and a temperature of $47 \,{}^\circ C$ . It is found that because of a leak, the pressure drops to $\frac{5}{8}^{t h}$ of its original value and the temperature falls to $27 \,{}^\circ C$ . Find the mass of oxygen that is leaked out.

• A. $\frac{\text{1}}{\text{3}} \text{ g}$
• B. $\frac{\text{1}}{\text{48}} \text{ g}$
• C. $\text{1} \text{ g}$
• D. $\frac{\text{2}}{\text{3}} \text{ g}$

Answer 1

Answer: (A)

The pressure, temperature and the number of moles of oxygen in the vessel change due to leak, while the volume remains fixed. Hence using $PV=nRT$ , we have
$\left(\frac{P_{1}}{n_{1} T_{1}}\right)=\left(\frac{P_{2}}{n_{2} T_{2}}\right)\Rightarrow n_{2}=\frac{320}{300}\times \frac{5}{8}\times \frac{1}{32}=\frac{1}{48}moles$
Mass leaking out $=1-n_{2}\left(32\right)=1-\left(2 / 3\right)=\frac{1}{3}g$