Question

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

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

Answer 1

The correct option is C $2$g

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