Question

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

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

Answer 1

Answer: (C)

$PV=\frac{m}{M}RT$ (for m grams of gas) $...\left(i\right)$
$P^{\prime }V=\frac{m^{\prime }}{M}R{T}^{\prime }...\left(ii\right)$
Dividing equation $\left(ii\right)$ by $\left(i\right)$ we get
$\frac{P^{\prime }}{P}=\frac{m^{\prime }}{m}\frac{T^{\prime }}{T}$
$m^{\prime }=\frac{P^{\prime }}{P}\times \frac{T}{T^{\prime }}\times m=\left(\frac{P/2}{P}\right)\times \frac{400}{300}\times 6=4g$
$\therefore$ Mass of oxygen leaked, $\Delta m=m-m^{\prime }=6-4=2g$