Question

A vessel contains $1g$ of oxygen at a pressure of $10atm$ and a temperature of $47{}^{\circ }C$ . It is found that because of a leak, the pressure drops to ${\frac{5}{8}}^{th}$ 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 $=1-n_2\left(32\right)=1-\left(2/3\right)=\frac{1}{3}g$