BYUI CHEM 105 - Gases and the Kinetic-Molecular Theory

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Gases and the Kinetic-Molecular TheoryCommon Properties of GasesPressureSlide 4Boyle’s LawSlide 6Charles’s LawSlide 8Slide 9Slide 10Standard Temperature and PressureCombined Gas LawSlide 13Avogadro’s LawSlide 15Standard Molar VolumeSlide 17Deriving the Ideal Gas LawDeriving R in the Ideal Gas LawThe Ideal Gas LawDetermining Molecular Weights and FormulasSlide 22Slide 23Dalton’s Law of Partial PressureDalton’s Law of Partial PressuresMole Fractions and Partial PressuresSlide 27Vapor PressureProducing Gases over Water (by displacement)Producing Gases over WaterMass-Volume Relationships in Reactions Involving GasesSlide 32The Kinetic-Molecular Theory AssumptionsThe Kinetic-Molecular TheorySlide 35The Kinetic-Molecular Theory and Boyle’s LawThe Kinetic-Molecular Theory and Dalton’s LawThe Kinetic-Molecular Theory and Charles’s LawDiffusion and Effusion of GasesSlide 40Slide 41Slide 42Deviations from the Ideal Gas BehaviorFactors Contributing to Nonideal Gas BehaviorSlide 45The Van der Waals EquationSome Problems with the Van der Waals EquationGases and the Kinetic-Molecular TheoryChapter 12Common Properties of Gases•Gases can be compressed into smaller volumes by applying increased pressure•Gases exert pressure on their surroundings•Gases expand without limits–Occupy the volume of any container•Gases diffuse into one another–Gases are miscible unless they react•The amounts and properties of gases are described in terms of temperature, pressure, the volume occupied, and the number of molecules (moles) present.Pressure•Force per unit area–lb/in2 or psi•Barometer – device for measuring the pressure of the atmosphere–Measures in millimeters of Hg (mm Hg)–The Hg will rise until the pressure exerted by the atmosphere equals the pressure exerted by the column of Hg•1 atmosphere = 760 Torr = 760 mm Hg (pressure at sea level)–1 Torr = 1 mm HgNote: Pressure in Rexburg is less. Why?Pressure•A manometer measures the pressure of a gas in a sealed flask (page 437)–In this case, one side of the tube is open to the atmosphere–If the gas pressure is greater than the atmospheric pressure, thenPgas(torr) = Patm(torr) + h torr–If the gas pressure is lower than the the atmospheric pressure, thenPgas(torr)=Patm(torr) - h torrProblems: On chalkboardIllustration: Pressure apparatusBoyle’s Law•At constant temperature and mass, the volume of a gas decreases when the pressure increases–V1/P (Syringe demonstration)•Boyle illustrated that the product of pressure and volume were constant –PV = k (temperature and mass are constant)•If the amount of gas and temperature do not change, two conditions of pressure and volume will be equal–P1V1 = k and P2V2 = k, therefore, P1V1=P2V2–Demo: syringeBoyle’s Law•Let’s do some problems with Boyle’s Law–At 250C a sample of He has a volume of 400 mL under a pressure of 760 torr. What volume would it occupy under a pressure of 2.00 atm at the same T?–A sample of oxygen occupies 15.8 L under a pressure of 285 torr. At what pressure would it occupy 27.9 L?Charles’s Law•When the pressure and the mass of a gas are constant, the volume of a gas is proportional to the temperature–VT–Charles and Gay-Lussac perfomed expansion studies on different gases as a function of temperature •A quantitative relationship is not obvious on the celsius scale. The Kelvin scale was devised.Charles’s Law051015202530350 50 100 150 200 250 300 350 400Volume (L) vs Temperature (K)Gases liquefy before reaching 0KLord Kelvin noticed that the extension of the volume to 0, produced a value of –273.15C. This was defined as absolute zero on the Kelvin scale. Using this scale, a quantitative relationship was established.Charles’s Law•At constant pressure and mass, the volume occupied of a gas is directly proportional to its absolute volume–VT and V=kT (constant n and P)•V/T = k•Since V/T is constant, it can be expressed that–V1/T1 = V2/T2 (V1/T1 = k, and V2/T2 = k)–This is assuming that the pressure and amount of gas do not change upon changing the conditions (volume or temperature).Demo: Balloon with liquid nitrogenCharles’s Law•Problems with Charles’s Law–A sample of hydrogen, H2, occupies 100 mL at 250C and 1.00 atm. What volume would it occupy at 500C under the same pressure?–At 112C, a sample of O2 occupies 154 mL. What temperature would be required in C to increase the volume to 215 mL?•Remember to use the Kelvin scale with the gas laws. You will get the wrong answer if you do not.Standard Temperature and Pressure•Standard temperature and pressure–Temperature = 273.15 K (exactly 0C)–Pressure = 1 atmosphere (760. Torr)This serves as a reference point for discussing gases.Abbreviated STPCombined Gas Law•Boyle’s and Charles’ Laws combined into one statementBoyle’s Charles’sP1V1=P2V2V1/T1=V2/T2For a given sample of gas . From this relationship, . This is the combined gas law.kTPV222111TVPTVPCombined Gas Law•Problems–A sample of nitrogen gas, N2, occupies 750 mL at 750C under a pressure of 810 torr. What volume would it occupy at standard conditions?–A sample of methane, CH4, occupies 260 mL at 32oC under a pressure of 0.500 atm. At what temperature would it occupy 500 mL under a pressure of 1200 torr?Avogadro’s Law•At the same temperature and pressure, equal volumes of all gases contain the same number of molecules. Therefore, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles.–Vn or V/n = kDemo: Expanding a balloon (assume P and T constant)Avogadro’s Law•Since V/n is always equal to the same constant, at constant T and P•A balloon with a volume of 2.35 L is filled with 1.82 moles of He gas. How many more moles of He gas would have to be added to the balloon to bring the volume to 5.49 L? Assume the T and P are constant.2211nVnVStandard Molar Volume•One mole of any gas has the same V at STP.•This would be the standard molar volume –Standard molar volume = 22.4 L (this is one mole)What would be the volume of 0.25 moles of O2 gas be at STP?–Deviations from the standard molar volume (Table 12-3) indicate that the gases do not behave ideally.Standard Molar Volume•Using the standard molar volume densities at various temperatures can be converted to densities at STP•One mole of a gas occupies 36.5 L and its density is


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BYUI CHEM 105 - Gases and the Kinetic-Molecular Theory

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