Chapter 10 What is pressure? • Gases Pressure and Boyleʼs Law Temperature and Charlesʼ Law Avogadroʼs Law Ideal gas equation of state PV=nRT Density and Molecular Weight Ideal Gas Law and Chemical Reactions Stoichiometry Partial Pressures Daltonʼs Law dPRT=MM =dRTPor 1PRESSURE Pressure: force/area F(newtons)/A(m2) SI Units: 1N/m2 = 1Pa Pascal Standard atmospheric pressure**: 1 atm ≡ 1.013x105 Pa 1 atm = 760 torr (mm Hg) 1 atm = 14.7 lb/in2 **real atmospheric pressure varies with altitude and weather What causes atmospheric pressure? 2Pressure at any altitude depends on weight of gas above it. • Pressure decreases exponentially with altitude.What is pressure? Altitude P collision frequency (km) (atm) (sec-1) 0 1 1010 50 10-3 107 100 10-6 103 200 10-13 1 What is pressure? Force on a surface exerted by colliding gas molecules More gas molecules & faster gas molecules è Higher pressure 4Measuring Pressure where g = gravitational constant d = density of liquid è Patm = constant x h è Patm ∝ height of liquid column measure P in terms of Hg column height 1 atm ≡ 760 torr “=” 760 mmHg Barometer to measure Patm Pressure balance Patm Patm = F/A F/A F/A = gdh (= g x dAh / A) 5Manometer Used to measure gas pressure P = 0 6What is the pressure in the flask? Patm = 742 torr Patm = 756 torr 7What is the pressure of the gas in the bulb? 1. Pgas = Ph 2. Pgas = Patm 3. Pgas = Ph + Patm 4. Pgas = Ph - Patm 5. Pgas = Patm - Ph 1. Pgas = Ph 2. Pgas = Patm 3. Pgas = Ph + Patm 4. Pgas = Ph - Patm 5. Pgas = Patm - Ph 1. Pgas = Ph 2. Pgas = Patm 3. Pgas = Ph + Patm 4. Pgas = Ph - Patm 5. Pgas = Patm - PhPVT relationships State of gas described by (n,P,V,T) n – # moles P – pressure V – volume T – (absolute) temperature (K) Avogadroʼs Law: V of gas at constant T and P is proportional* to the number of moles of gas: V∝n (P, T fixed) *constant of proportionality is the same for ALL gases. 22.4L / 1 mol at STP è V/n = constant T – (absolute) temperature (K) (add 273 to oC) Think about collision of gas molecules inside a balloon: higher n = more gas molecules to collide on the balloon è more inflation = larger volume STP : 0°C (273K) and 1 atm Standard Temperature and PressurePVT relationships Boylesʼ Law: V of a fixed amount of gas at constant T is inversely proportional to P V∝1/P (n,T fixed) è PV = constant 10PVT relationships Charleʼs Law: V of fixed amount of gas at constant P is proportional to the absolute temperature V∝T (n,P fixed) è V/T = constant Think about collision of gas molecules inside a balloon: higher temperature = more frequent collision of molecules è more inflation = larger volume 11PVT relationships So far: V ∝ 1/P (Boyleʼs law) V ∝ T (Charlesʼs law) V ∝ n (Avogadroʼs law) V !nTP= const.nTPCombining these: PVnT= const. = RThink about collision of gas molecules inside a balloon: • Higher outer pressure to compact the balloon è smaller volume • Higher temperature = faster moving gas molecules = more frequent collisions è more inflation = larger volume • More gas molecules = more frequent collisions è more inflation = larger volume PV = nRT12Sample problems What is the volume of a gas at 30oC if the gas has a volume of 2.0L at 50oC? What is the pressure of a gas at 30oC if the gas has a pressure of 2.0atm at 50oC? What is the pressure of a gas in a 2.0L flask if the gas has 1.0atm pressure in a 1.0L flask?Ideal Gas Law PV = nRT T units= K R gas constant • Units of R are important ! R= 0.08206L atmmol K! R= 8.314Jmol KExample: What is the volume (V) occupied by 1.00 mole of gas at exactly 0° C and 1 atm? STP Standard Temperature and Pressure 0°C (273K) and 1 atm VSTP = 22.4L/mol Note STP for gases is not the same as standard state conditions used for ΔH V = nRT/P = 1.00 mol x 0.08206 Latm/molK x 273K / 1atm = 22.4 L PV/(nT) = constant = R Typically, For pressure or volume, use R in Latm/molK. For speed or energy, use R in J/molK. When we deal with ideal gas behavior (PVT relationship), identity of molecules does not matter!!!Density and Molecular Weight mass = nM n : # of moles M : molecular weight densitymassvolume= ! gL=massvolumenV=PRT ! d =nMVdensity= d = PMRTMolecular weight= M = dRTPFrom Ideal Gas Law Units: ! =PMRT15Density and Molecular Weight • What is the density of CO2 at 2.50 atm and 30.0oC? • What is the molecular weight of a gas that has a density of 2.00 x 10-3 g/mL at 1.50 atm and 20oC? 16Mixture of gases Mix 5 moles of CO2 V = 40L 2 moles of N2 T = 0°C 1 mole of Cl2 What is the total P ? ! PTOT = nTOTRTV ! PTOT = nCO2RTV + nN2RTV+ nCl2RTV ! PTOT = PCO2 + PN2 + PCl2Or, the total pressure can be calculated by summing up the partial pressures by individual components Partial pressures When we deal with ideal gas behavior, Identity of molecules does not matter è 17Partial Pressure Partial pressure: the pressure a gas would have if it was the only gas in the container. Daltonʼs Law of Partial Pressures Total pressure is equal to the sum of partial pressures. ! PTOT = nCO2RTV + nN2RTV+ nCl2RTVThe fraction of the total pressure contributed by each gas is equal to its mole fraction: Χi = ni/ntotal ! "i=PiPTOT=ninTOTFor Example: what is the mole fraction of CO2 in a 5L container if its partial pressure is 2.8atm and the total pressure is 4.5atm? ! Pi= XiPTOT=ninTOTPTOTè 18Sample Problems 3.0L of He at 5.0 atm and 25°C is combined with 4.5 L of Ne at 2.0 atm and 25°C at constant T into a 10L vessel. What is the partial pressure of the He in the 10L vessel? What is the total pressure in the 10L vessel? What is the partial pressure of O2 in the vessel? PTOT = 756 TORR GAS MOLE FRACTION T = 300.0°C Ar 0.320 VTOT=5.00 L N2 0.270 CO2 0.150 Ne 0.160 O2 ? 1. 75.6 torr 2. 378 torr 3. 680 torr 4. 756 torr 5. There is not enough data. PV/T = constant = nR 19Collecting Gas over water Example: During a reaction, N2 is collected over H2O. Pbar = 742 torr (= PTOT) V = 55.7 ml T = 23°C How much N2 (moles) was collected? vapor pressure of water at 23oC (= 21 torr) 20More practice questions 21Composition of the atmosphere Eg. Neon xNe = 0.00001818 = 0.001818% Ne concentration in ppm = 18.18 ppm