Question

A vessel has $6\text{g}$ of hydrogen at pressure $P$ and temperature $500\text{K}$. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $P/2$ and temperature falls to $300\text{K}$ when the hole is sealed?

• A. $2\text{g}$
• B. $3\text{g}$
• C. $4\text{g}$
• D. $1\text{g}$

Answer 1

The correct option is D $1\text{g}$

Let $M$ be molar mass of gas
We know,
$PV=nRT$
$n=$ no. of mole $=\frac{m}{M}$;
where $m=$ mass of gas.
$\Rightarrow PV=\frac{m}{M}RT$
Initially,
$PV=\frac{6}{M}R\times 500$ ...(i)
Finally,
$\frac{P}{2}\times V=\frac{(6-x)}{M}R\times 300$ ...(ii)
where $x$ is the mass of gas leaked out.
$\therefore$ From eqn $\left(i\right)÷\left(ii\right)$,
$\Rightarrow 2=\frac{6}{6-x}\times \frac{5}{3}$
$\Rightarrow x=1\text{g}$