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  • An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C.

Q13.4  An oxygen cylinder of volume  30 litres has an initial gauge pressure of 15 atm and a temperature of 27^{0}C . After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11  atm and its temperature drops to 17^{0}C. Estimate the mass of
oxygen taken out of the cylinder (R=8.31Jmol^{-1}K^{-1}, molecular mass of  O_{2}=32\mu).

Answers (1)

best_answer

Initial volume, V1 = Volume of Cylinder = 30 l

Initial Pressure P1 = 15 atm

Initial Temperature T1 = 27 oC = 300 K

Initial number of moles n1 inside the cylinder is

\\n_{1}=\frac{P_{1}V_{1}}{RT_{1}}\\ n_{1}=\frac{15\times 1.013\times 10^{5}\times 30\times 10^{-3}}{8.314\times 300}\\ n_{1}=18.28

Final volume, V2 = Volume of Cylinder = 30 l

Final Pressure P2 = 11 atm

Final Temperature T2 = 17 oC = 290 K

Final number of moles n2 inside the cylinder is

\\n_{2}=\frac{P_{2}V_{2}}{RT_{2}}\\ n_{2}=\frac{11\times 1.013\times 10^{5}\times 30\times 10^{-3}}{8.314\times 290}\\ n_{2}=13.86

Moles of oxygen taken out of the cylinder = n2 -n1 = 18.28 - 13.86 = 4.42

Mass of oxygen taken out of the cylinder m is

\\m=4.42\times 32\\ m=141.44g

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