Question

Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm. The volume of each tube at this pressure is 0.002 m³. One of the tubes gets punctured and the volume of the tube reduces to 0.0005 m³. How many moles of air have leaked out? Assume that the temperature remains constant at 300 K and that the air behaves as an ideal gas.

Answer 1

$\begin{array}{l}\text{Here,}\\ P_1=2\times {10}^{5}pa\\ V_1=0.002{\text{m}}^{\text{3}}\\ V_2=0.0005m^3\\ T_1=T_2=300K\\ \\ \mathrm{Number\; of\; moles\; initially},n_1=\frac{P_1{V}_1}{R{T}_1}\\ \Rightarrow n_1=\frac{2\times {10}^5\times 0.002}{8.3\times 300}\\ \Rightarrow n_1=0.16\\ \text{Applying equation of state, we get}\\ P_2{V}_2=n_{2}RT\\ \text{Assuming the final pressure becomes equal to the atmospheric pressure, we get}\\ P_2=1.0\times {10}^{5}pa\\ \Rightarrow n_2=\frac{P_2{V}_2}{RT}\\ \Rightarrow n_2=\frac{1.0\times {10}^5\times 0.0005}{8.3\times 300}\\ \Rightarrow n_2=0.02\\ \text{Number of leaked moles =}{n}_2-n_1\\ =0.16-0.02\\ =0.14\end{array}$