Question

A gas is enclosed in a vessel at a constant temperature at a pressure of 2.5 atmospheres and a volume of 4 litres. Due to leak in the vessel, after some time the pressure is reduced to 2 atmospheres. As a result :

• A. 20% of the gas remains in the vessel
• B. 20% of the gas escapes out
• C. 25% of the gas escapes out
• D. 25% of the gas remains in the vessel

Answer 1

The correct option is B 20% of the gas escapes out

$P=2.5atm$ $P^1=2atm$
$V>4l$
$2.5\times 4=nRT$ , $2\times 4=n^{1}RT$
$\frac{2.5\times 4}{20\times 4}=\frac{n}{n^1}$
$\frac{n}{n^1}=\frac{5}{4}$
$n^1=\frac{4}{5}n\Rightarrow \Delta n=\frac{n}{5}$
i.e. 20% gas escaped out.