A rigid storage tank of volume 0.0831 ~m ³ contains 1.4 ~kg of Nitrogen gas ( N₂ ) at a temperature of 300 ~K . A valve is accidentally left open, and some gas escapes. When the valve is closed, the gauge pressure of the tank is found to be 5 ~atm . Assuming the temperature of the gas remains constant, the mass of Nitrogen that escaped from the tank is : [Given: R = 8.31 ~J ~mol ⁻¹ ~K ⁻¹ , molecular mass of N₂ = 28 ~

Step-by-step solution

The final absolute pressure of the gas in the tank is the sum of the gauge pressure and the atmospheric pressure. P = P_ gauge + P_ atm = 5 ~atm + 1 ~atm = 6 ~atm = 6 10⁵ ~N ~m ⁻² Using the ideal gas equation, the final number of moles of Nitrogen in the tank is: n_ f = PV RT Substituting the given values: n_ f = 6 10⁵ 0.0831 8.31 300 = 20 ~mol The final mass of Nitrogen remaining in the tank is: m_ f = n_ f M = 20 ~mol 28 ~g ~mol ⁻¹ = 560 ~g = 0.56 ~kg The mass of Nitrogen that escaped from the tank is the differe