Question

A closed vessel has $6g$ of hydrogen at pressure P and temperature $500K$. A small hole is made in it so that hydrogen leaks out. How much hydrogen (in gm) leaks out if the final pressure is $P/2$ and temperature falls to $300K$.

• A. $1g$
• B. $2g$
• C. $4g$
• D. $5g$
• E. None

Answer 1

Answer: (A)

$1g$

Given, $V_1=V$ $V_2=V$

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

$T_1=500$ $T_2=300$

$m_1=6g$ $m_2=?$

So, by ideal gas equation

$\Rightarrow P_1{V}_1=n_{1}R{T}_1$ $P_2{V}_2=n_{2}R{T}_2$

Equating $V_1=V_2=V$

$\Rightarrow \frac{n_{1}R{T}_1}{P_1}=\frac{n_{2}R{T}_2}{P_2}$

$\Rightarrow \frac{m_{1}R500K}{MP}=\frac{m_{2}R300\times 2}{P}$

$\Rightarrow \frac{6\times 500}{2\times 300}=m_2$

$\Rightarrow m_2=5gm$

Hydrogen leaks out $=6-5=1gm$

Hence, the answer is $1gm.$