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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cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27°C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17°C. Estimate the mass of oxygen taken out of the cylinder. (R = 8.31 J mol-1 K-1, molecular mass of O2 = 32 u) |
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Answer» Under the initial conditions, V = 30 litre = 30 x 10-3 m3 p = 15 atm = 15 x 1.01 x 105 Pa T = 27°C = 273 + 27 = 300 K Also; R = 8.31 J mol-1 K-1 and molar mass, M = 32 x 10-3 kg Using the relation, pV = uRT ⇒ u = pV/RT = {15 x 1.01 x 105 x 30 x 10-3}/{8.31 x 300} = 18.23 Now, u = m/M ⇒ m = Mu = 18.23 x 32 x 10-3 kg or, m = 0.58 kg Under the final conditions: V' = 30 litre = 30 x 10-3 m3 p' = 11 atm = 11 x 1.01 x 105 Pa T' = 17°C = 17 + 273 = 290 K We have, u' = p"V'/RT' = {11 x 1.01 x 105 x 30 x 10-3}/{8.31 x 290} = 13.83 m' = u'm = 13.83 x 32 x 10-3 kg = 0.44 kg Mass of the oxygen taken out of the cylinder = m - m' = 0.58 - 0.44 = 0.14 kg |
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