A closed metal jar of volume 1.0 10⁻³ m ^3 is filled with oxygen at a pressure of 1.5 10^5 Pa and a temperature of 400 K . A small leak is present in the jar. The atmospheric pressure is 1.0 10^5 Pa and the atmospheric temperature is 300 K . Determine the mass of the gas that escapes by the time the pressure and temperature inside the jar become equal to those of the surroundings.

Step-by-step solution

The initial number of moles of oxygen gas in the jar is given by the ideal gas equation: n₁ = P₁ V R T₁ The final number of moles of oxygen gas in the jar is: n₂ = P₂ V R T₂ The number of moles of gas that escaped is: n = n₁ - n₂ = V R ( P₁ T₁ - P₂ T₂ ) Substituting the given values V = 1.0 10⁻³ m ^3 , P₁ = 1.5 10^5 Pa , T₁ = 400 K , P₂ = 1.0 10^5 Pa , T₂ = 300 K , and R 25 3 J mol ⁻¹ K ⁻¹ : n = 1.0 10⁻³ 25/3 ( 1.5 10^5 400 - 1.0 10^5 300 ) n = 3 10⁻³ 25 ( 375 - 1000 3 ) n = 3 10⁻³ 25 ( 1125 - 1000 3 ) n = 3 10⁻³ 2