Question

A $2L$ vessel is filled with air at ${50}^{\circ }C$ and a pressure of $3atm$. The temperature is now raised to ${200}^{\circ }C$. A valve is now opened so that the pressure inside drops to one atm. What will be the fraction of the total number of moles, inside escaped on opening the valve? (Assume no change in the volume of the container).

• A. $7.7$
• B. $9.9$
• C. $8.9$
• D. $0.77$

Answer 1

The correct option is D $0.77$

Given that, $V=2L,T_1=50+273=323K,P_1=3atm$
On heating $V=2L,T_2=200+273=473,P_2=?$
Using $P-Tlaw,\frac{P_1}{T_1}=\frac{P_2}{T_2}$
$P_2=\frac{3\times 473}{323}=4.39atm$
and $n=\frac{PV}{RT}=\frac{3\times 2}{0.0821\times 323}=0.226$
Now valve is opened till the pressure is maintained at $1atm$.
Thus, at constant $V$ and $T,P\propto n$
$\therefore 4.39\propto 0.226$
$\therefore 1\propto n_{left}$
$\therefore n=\frac{0.226}{4.39}=0.052$
$\therefore$ Moles escaped out $=0.226-0.052=0.174$
$\therefore$ Fraction of moles escaped out $=\frac{0.174}{0.226}=0.77$