Question

A metal jar has a gas of volume ${10}^{-3}m3$ at a pressure of $2\times {10}^5$ Pa and temperature 400K. The jar has small hole and hence the gas leaks into atmosphere. The pressure and temperature of atmosphere is ${10}^5$ Pa and 300 K respectively. If R is the gas constant , the number of moles of the gas that has leaked into atmosphere is

• A. $\frac{1}{5R}$
• B. $\frac{1}{6R}$
• C. $\frac{1}{7R}$
• D. $\frac{1}{8R}$

Answer 1

Answer: (B)

$\frac{1}{6R}$

Here, $P_1=2\times {10}^{5}Pa,V_1={10}^{-3}{m}^3,T_1=400K$

$P_2={10}^{5}Pa,T_2=300K,V_2={10}^{-3}{m}^3$

Using ideal gas equation , $PV=nRT$

$n_1=\frac{P_1{V}_1}{R{T}_1}and{n}_2=\frac{P_2{V}_2}{R{T}_2}$

So number of moles leaked, $n_1-n_2=\frac{P_1{V}_1}{R{T}_1}-\frac{P_2{V}_2}{R{T}_2}$

$n_1-n_2=\frac{2\times {10}^5\times {10}^{-3}}{400R}-\frac{{10}^5\times {10}^{-3}}{300R}$

On solving, we will get $\Delta n=\frac{1}{6R}$