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Chapter 9 Worked Example 1 The density of water at 20 o C is 0.998 g.cm-3. What height would the column of liquid be in a water barometer at 20 oC when the atmospheric pressure corresponds to 760. mm of mercury? Solution P = dw hwg = dHg hHgg Hence hw = dHghHg dw (13.595 g cm-3)(760. mm) = (0.998 g cm-3) = 1.04 x 104 mm (10.4 m) Chapter 9 Worked Example 2 A student attaches a glass bulb containing neon gas to an open-tube manometer and calculates the pressure of the gas to be 0.890 atm. (a) If the atmospheric pressure is 762 Torr, what height difference between the two sides of the mercury in the manometer did the student find? (b) Which side is higher, the side of the manometer attached to the bulb or the side open to the atmosphere? (c) If the student mistakenly switches the numbers for the sides of the manometer when recording the data in the laboratory notebook, what would be the reported pressure in the gas bulb? Solution Chapter 9 Worked Example 3 In a petroleum refinery a 750.-L container containing ethylene gas at 1.00 bar was compressed isothermally to 5.00 bar. What was the final volume of the container? Solution Isothermally means at constant temperature, hence Boyle's law can be used. P1V1 = P2V2, V2 = 150. L (1.00 bar)(750. L) = (5.00 bar)V2 Chapter 9 Worked Example 4 A parcel of air (the technical term in metereology for a small region of the atmosphere) of volume 1.00 x 103 L at 20. oC and 1.00 atm rises up the side of a mountain range. At the summit, where the pressure is 0.750 atm, the parcel of air has cooled to -10. o C. What is the volume of the parcel of air at that point? Solution P1V1 n1T1 = P2V2 n2T2 where n1 = n2 (1.00 atm)(1.00 x 103 L) (293.15 K) V2 = 1.20 x 103 L = (0.750 atm)V2(L) (263.15 K) Chapter 9 Worked Example 5 Calculate the volume occupied by 1.0 kg of hydrogen at 25 oC and 1.0 atm. Solution We can use the ideal gas equation PV = nRT, after first finding the number of moles of H2 in 1.0 kg. n= Mass = Molar mass 1.0 x 103 g = 496 mol 2.016 g/mol (1.0 atm)V(L) = (496 mol)(8.206 x 10-2 L atm K-1mol -1)(298.15 K) V = 1.2 x 104 L Chapter 9 Worked Example 6 A sample of methane gas, CH4, was slowly heated at a constant pressure of 0.90 bar. The volume of the gas was measured at a series of different temperatures and a plot of volume vs. temperature was constructed. The slope of the line was 2.88×10-4 L K-1. What was the mass of the sample of methane? Solution Chapter 9 Worked Example 7 A baby with a severe bronchial infection is in respiratory distress. The anesthetist administers heliox, a mixture of helium and oxygen with 92.3% by mass O2. What is the partial pressure of oxygen being administered to the baby if the atmospheric pressure is 730 Torr? Solution n(He) = 0.077 g = 0.0193 mol n(O2) = 4.00 g mol -1 x(He) = 0.0193 mol 0.0481 mol 0.923 g = 0.0288 mol 32.0 g mol -1 = 0.401 x(O2) = 0.0288 mol 0.0481 mol = 0.599 [= 1.00 - 0.401 (only two components)] Chapter 9 Worked Example 8 Estimate the root mean square speed of water molecules in the vapor above boiling water at 100. oC. Solution Molar mass of water is 18.01 g mol -1 or 0.01801 kg mol-1. From vrms = (3RT/M) 1/2, 3 x (8.3145 J K-1 mol -1) x (373 K) vrms = = 0.01801 kg mol-1 719 m s-1