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

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$2 g$

$3 g$

$4 g$

$1 g$

answer is D.

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Detailed Solution

$P V = \frac{m}{M} R T$

Initially, $P V = \frac{6}{M} R x 500$ ……..(i)

$\frac{P}{2} V = \frac{(6 - x)}{M} R x 300$ (if $x$ gas leaks out) ………(ii)

Divide (i) by (ii), we get $2 = \frac{6}{6 - x} x \frac{5}{3}$

$∴ x = 1 g$

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