Question

A vessel of volume $V$ contains an ideal gas at absolute temperature $T$ and pressure $P$. The gas is allowed to leak till its pressure falls to $P$. Assuming that the temperature remains constant during leakage, the number of moles of the gas that have leaked is

• A. $\frac{V}{RT}(P+P^{\prime })$
• B. $\frac{V}{2RT}(P+P^{\prime })$
• C. $\frac{V}{RT}(P-P^{\prime })$
• D. $\frac{V}{2RT}(P-P^{\prime })$

Answer 1

The correct option is C

$\frac{V}{RT}(P-P^{\prime })$

Number of moles present initially is $n=\frac{PV}{RT}$. Let $n^{\prime }$ be the number of moles of the gas that leaked till

the pressure falls to $P^{\prime }$. Since volume V of the vessel cannot change and temperature T remains

constant during leakage, we have

$n^{\prime }=\frac{P^{\prime }V}{RT}$

$\therefore$ Number of moles that leaked is

$\Delta n=n-n^{\prime }=\frac{PV}{RT}-\frac{P^{\prime }V}{RT}=\frac{V}{RT}(P-P^{\prime })$

So the correct choice is (C)