Lecture 22 Gases 1 Read HW BLB 10 1 10 5 BLB 10 2 19a b 23 26 30 39 41 45 49 Sup 10 1 6 Know gases gas laws PV nRT partial pressures density molecular mass Exam 2 NO SCORE Not a problem Please talk with Mike Joyce in 210 Whitmore Final Exam Monday May 4 12 20 MUST register on elion for a final exam conflict or overload by March 8 See http www registrar psu edu exams exam overload cfm http www psu edu dus handbook exam html conflict Need help Get help TAs in CRC 211 Whitmore and SI hours on Chem 110 website my office hours Mon 12 30 2 Tues 10 30 12 in 324 Chem Bldg or 326 Chem Sheets Page 1 Lecture 22 It s a gas gas gas gas molecules are constantly are far apart 10 times as far as they are big occupy 0 1 of the total volume move in lines from collision to collision move at higher temperatures move at lower temperatures as a result expand in whatever volume is available have pressure collisions with walls mix completely with one another can be easily compressed when cooled will eventually condense compression may be necessary gases are described in terms of pressure P temperature T volume V moles n all gases behave similarly at low pressure gases will mix in all proportions with other gases to form mixtures Sheets Page 2 Lecture 22 Pressure pressure force unit area force kg m s 2 Newton N unit area m2 SI unit for pressure 1 N m 2 1 Pa Pascal standard atmospheric pressure 1 atm 1 013 105 Pa 1 atm 760 torr or mm Hg 1 atm 14 7 lb in2 real atmospheric pressure varies with altitude temperature and weather how big is one atm 10 tons m2 or 600 lbs head Sheets Page 3 Lecture 22 Measuring pressure barometer used to measure Patm by forces Torricelli early 1600 s measure P in terms of height of Hg 1 atm 760 torr 760 mm Hg know this conversion factoid 760 mm Hg 10 m H2O Sheets Page 4 Lecture 22 The ideal gas law state of gas described by P V T in K degrees Kelvin n STP standard temperature 273 15 K pressure 1 atm NOTE STP for gases is not the same as standard state conditions used for H more in Chap 5 absolute temperature in Kelvin K C 273 15 K Avagadro V n V n constant P T fixed proportionality constant is the same for ALL gases V n Sheets Page 5 Lecture 22 The ideal gas law cont Boyle V 1 P PV constant T n fixed V P V 1 atm 2 atm Charles V T V T constant P n fixed note T in absolute T K 1 P 4 atm V 273 15 C 0 K T C All of these laws can be described by one equation PV nRT R gas constant units of R are very very important L atm J R 0 08206 R 8 314 mol K mol K cal R 1 987 mol K Sheets Page 6 Lecture 22 Example for problems given known quantities solve for the unknown What is the volume V occupied by 1 00 mole of gas at exactly 0 C and 1 atm STP V P 1atm n 1mol T 0 273 273K 0 08206L atm R mol K Sheets PV nRT Page 7 Lecture 22 Example The gas in a 750 mL vessel at 105 atm and 27 C is expanded into a vessel of 54 5 L and 10 C What is the final pressure 1L V1 750mL 0 75L 1000mL V2 54 5L P1 105atm T2 10 273 263K T1 27 273 300K P2 PV nRT so P1V1 nRT1 n is not changing R is a constant so nR Sheets P1V1 T1 Page 8 nR P2V2 T2 Lecture 22 Density and molecular weight Example can derive d PM RT from PV nRT where d density M molar mass You should derive this on your own see BLB pp 406 407 Calculate the average molar mass of dry air if it has a density of 1 17 g L at 21 C and 740 0 d 1 17g L torr 1atm P 740 0torr 0 974atm 760torr d PM RT Sheets T 21 273 294K M Page 9 Lecture 22 Example What is the density of oxygen in grams per liter at 25 C and 0 850 atm d need g L P 0 850atm T 25 273 298K M 32g mol Sheets Page 10 Lecture 22 Dalton s law of partial pressures partial pressure the pressure a gas would have if it was the only gas in the container Dalton s law of partial pressures total pressure is equal to the sum of partial pressures Ptot P1 P2 P3 P Ptot Ptot ntot nRT V n RT n2RT n3RT 1 V V V RT n1 n2 n3 V n1 n2 n3 Ptot ntot RT V mole fraction ratio of na ntot dimensionless Xa na ntot X 1 n1 ntot n1RT P1 V n P1 1 Ptot ntot note mole fractions must sum n1 ntot RT P to 1 1 n V tot P1 X 1Ptot Sheets Page 11 Lecture 22 Example Mix 5 moles of CO2 2 moles of N2 and 1 mole of Cl2 in a 40 L container at 0 C a What is the pressure in the container b What is the partial pressure of each gas in the container c What volume does each gas occupy in the container nCO 2 5mol nN 2 2mol nCl 2 1mol Ptot ntot RT V Ptot ntot 8mol X CO 2 XN2 X Cl 2 check X 1 000 V 40L T2 0 273 273K Ptot therefore PCO 2 PN 2 PCl 2 check P P tot Sheets Page 12 4 48atm Lecture 22 Example 3 0 L of He at 5 0 atm and 25 C are combined with 4 5 L of Ne at 2 0 atm and 25 C in a 10 L vessel at constant temperature What is the partial pressure of the He in the 10 L vessel He initial VHe 3L PHe 5 0atm T 25 273 298K nHe PHeVHe RT nHe ntot nHe nNe ntot therefore X He X Ne note do not need X Ne for problem Ne initial VNe 4 5L check X 1 000 PNe 2 0atm T 25 273 298K nNe PNeVNe RT nNe Sheets on to next page Page 13 Lecture 22 Ptot in 10L vessel final Vtot 10L Ptot ntot 0 981mol T 25 273 298K Ptot ntot RT Vtot Ptot Now we need to find PHe final PHe Sheets Page 14 Lecture 22 Before next class Read HW BLB 10 6 9 BLB 10 5 8 59 61 71 75 77 82 83 84 Sup 10 7 15 Know kinetic molecular theory effusion diffusion real gases van der Waals Answers p 7 22 4 L p 8 Pfinal 1 27 atm p 9 29 0 g mol p 10 1 11 g …
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