Question

A vessel has $6g$ of oxygen at pressure $P$ and temperature $400K$. A small hole is made in it so that oxygen $O_2$ leaks out. How much oxygen leaks out if the final pressure is $P/2$ and temperature $300K$?

• A. $5g$
• B. $4g$
• C. $2g$
• D. $3g$

Answer 1

The correct option is C $2g$

By ideal gas equation,

$PV=nRT$

$\therefore P_{1}V=n_{1}R{T}_1$

$P_{2}V=n_{2}R{T}_2$

$P_2=\frac{P_1}{2}$

$\frac{n_1}{n_2}=\frac{P_1\times T_2}{P_2\times T_1}=\frac{P_1\times 300}{P_2\times 400}$

$\frac{n_1}{n_2}=1.5$

Now, $n_1=\frac{mass}{molarmass}=\frac{6}{32}$

$n_2=\frac{m}{32}$

$\therefore \frac{n_1}{n_2}=1.5=\frac{\frac{6}{32}}{\frac{m}{32}}$

$m=\frac{6}{1.5}=4gm$.

$\therefore$ Mass of oxygen left$=4gm$

$\therefore$ Mass of oxygen leaked $=6-4=2gm$