Question

A vessel has $6g$ of oxegen 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 $P/2$ and temperature is $300K$

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

Answer 1

Answer: (B)

$2g$

From ideas gas equation

$PV=nRT$

$PV=\frac{m}{M_o}RT$

$m=\frac{PV{M}_o}{RT}$

In first event

$m_1=\frac{P_{1}V{M}_o}{R{T}_1}$

$6gram=\frac{PV{M}_o}{R\times 400}$

$\frac{{\mathrm{PVM}}_o}{R}=400\times 6......\left(1\right)$

In the second event when hole is made:

$m_2=\frac{P_{2}V{M}_o}{R{T}_2}$

$m_2=\frac{\frac{P}{2}V{M}_o}{R\times 300}=\frac{1}{300\times 2}\frac{PV{M}_o}{R}$

$m_2=\frac{1}{300\times 2}\times (400\times 6)=4gram$

Leak out oxygen is $(6gram-4gram)=2gram$