Air is pumped into the tubes of a cycle rickshaw at a pressure of 2 atm . At this pressure, the volume of each tube is 0.002 m ^3 . One of the tubes suffers a puncture, causing its volume to reduce to 0.0005 m ^3 . Determine the number of moles of air that have leaked out. Assume the air behaves as an ideal gas and the temperature remains constant at 300 K .

Step-by-step solution

Initial number of moles of air in the tube is given by the ideal gas equation n₁ = P₁ V₁ R T . Using P₁ = 2 atm = 2 10^5 Pa , V₁ = 0.002 m ^3 , T = 300 K , and R = 25 3 J mol ⁻¹ K ⁻¹ : n₁ = 2 10^5 0.002 25 3 300 = 400 2500 = 0.16 mol After the puncture, the pressure inside the tube drops to atmospheric pressure, so P₂ = 1 atm = 10^5 Pa . The final volume is given as V₂ = 0.0005 m ^3 . Final number of moles of air remaining in the tube: n₂ = P₂ V₂ R T = 10^5 0.0005 25 3 300 = 50 2500 = 0.02 mol Number of moles of ai