Question

A vessel has \(6\) gram 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 the temperature falls to \(300\) K?

• A. \(2\) gram
• B. \(3\) gram
• C. \(4\) gram
• D. \(1\) gram

Hint:

The vessel volume is fixed, so $n\propto P/T$.

Answer 1

The Correct Option is D

Step 1: Use moles
$6$ g of H$_2$ is $3$ mol. $n_1=\frac{PV}{R\times500}$ and $n_2=\frac{(P/2)V}{R\times300}=\frac{PV}{600R}$.
$n_2=3\times\frac{500}{600}=2.5$ mol. Lost $=0.5$ mol $=1$ g.

Final Answer:
Option (D). \[ \boxed{\text{(D)}} \]