Question

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

• A. $2$g
• B. $3$g
• C. $4$g
• D. $1$g

Answer 1

Answer: (D)

$1$g

$PV=\frac{m}{M}RT$
Initially, $PV=\frac{6}{M}R\times 500$ $\left(i\right)$
$\frac{P}{2}V=\frac{(6-x)}{M}R\times 300$ (if x g gas leaks out) $\left(ii\right)$
Divide $\left(i\right)$ by $\left(ii\right),$ we get
$2=\frac{6}{6-x}\times \frac{5}{3}$
$\therefore x=1g.$