1Gases!Chapters 4, 14 and a bit of chapter 15Thinking like a chemist -Understanding macroscopic propertiesusing models of the particulate scalestructure and particulate behaviorProperties of Materials• Gases• Liquids• Solids• Solutions2Gases• Characteristics of gases• Pressure: causes and measurement• Gas laws:– The Volume–Pressure Lawor Boyle’s Law– The Volume–Temperature Lawor Charles’s Law– Combined Gas Law– Dalton’s Law of Partial PressuresCharacteristics of Gases• Gases may be compressed.• A fixed quantity of air (or any other gas) may bemade to occupy a smaller volume by applyingpressureOriginallychlorofluorocarbongases (CFCs)Now butane orpropaneCompressed air, ormixed gases:helium, oxygen,nitrogen3Characteristics of Gases• Gases expand to filltheir containersuniformly.• If the volume of acontainer is increased,the gas respondsimmediately, filling thelarger volume uniformly.Characteristics of Gases• All gases have low density– the volume of water expands by a factor of 1600 whenchanged from liquid to gas– The volume of the actual molecules is 0.06% of the totalvolume occupied by the sample.4Characteristics of Gases• A confined gas exerts constant pressure on the wallsof its container uniformly in all directionsParticulate modelparticles hitting the wallof the containerMacroscopic behaviorWhat creates pressure?Ideal gas model:• Gases consist of particles moving at any giveninstant in straight lines• This is why gases fill their containers. It also explainspressure: the collective effect of billions ofparticle–wall collisions is the force known as pressure• Pressure is the force exerted per unit areaP = F A5Nm2 Pa = The Mercury Barometer• The atmospheric pressure (the forceresulting from the collisions of themolecules in air with the surface ofthe mercury) is equal to the forcedue to the weight of the liquidmercury in the tube• SI unit is the Pascal (Pa)Recall: 1 N (Newton) is the force required to causea mass of 1 kg to accelerate at a rate of 1 m/s2vacuumOther units for pressure• Millimeter of mercury, mm Hg– The height of a column of mercury in abarometer• Torr– Another name for a millimeter of mercury• Atmosphere– 760 mm Hg Approximately equal toatmospheric pressure1 atm = 1.013 x 105 Pa = 760 torr = 760 mm Hgvacuum61 atm = 1.013 barOther units for pressure• Pressure is force per unit area so…• Pounds per square inch, psi– One pound (force) per square inch (area)• Bar– 1 x 105 Pa (Newtons/m2)Tire pressuresin psi1 atm = 14.69 psiAtmospheric air pressure is often given in millibarsStandard atmospheric pressure at sea-level isdefined as 1013.25 mbarOpen-end Manometer• Used to measure pressure in the laboratory• The pressure due to the gasin the flask (Pg) is equal tothe pressure due to theweight of the liquid in thetube (PHg), plus the pressuredue to the air moleculescolliding with the surface ofthe liquid (Pa)• Pg = Pa + PHg• The liquid doesn’t have to bemercury7The Volume–Pressure Lawor Boyle’s Law• The pressure of a fixed quantity of gas at constanttemperature is inversely proportional to volumeP ∝1 or P ∝ 1 volume V P = kB x 1 V“is proportional to”PV = kBP1V1 = kBP2V2 = kBP1V1 = P2V2Proportionality constantA numberNot a straight line: P α 1VBoyle’s Law8Molecular interpretation of Boyle’s LawVolume halvesPressure doubles• Pressure = Force/Area• Same force– same number of particles to collide with the container wallsper second• Smaller area– lower volume, less surface area of container walls• Greater pressure!= 729 torr x0.993 L0.720 L= 1.01 x 103 torrCheck: Volume decreases, whichleads to increased pressure.P1V1 = P2V2P2 = P1 xV1V2Example• A fixed quantity of gas in a flexible-walled container is initially at729 torr and a volume of 0.993 L. The temperature is keptconstant as the volume of the container is reduced to 0.720 L.What is the pressure at this volume?9V ∝TThe Volume–Temperature Lawor Charles’s Law• The volume of a fixed quantity of gas at constantpressure is directly proportional to absolutetemperatureDiscovered by Jacques Charles around 1787Charles’s Law• Simple experiment: Place aninflated balloon into an ice bath• The balloon collapses becausethe volume of the gas decreases• Marshmallows example? See chapter 4 in ourtext book!10Relationship between volume andtemperatureV ∝T V = kCTDividing both sides of the equation by T,kC =VTkC =V1T1 =V2T2V1T1Relationship between volume andtemperature11V1T1V2T2= V1T2 = V2T1V2 = V1 xT2T1= 3.20 L x(21 + 273) K(44 + 273) K= 2.97 LCheck: Temperature decreases, whichleads to decreased volume.Example• A fixed quantity of gas in a flexible-walled container iscooled from 44°C to 21°C. If the initial volume of thecontainer is 3.20 L, what is the final volume?V ∝Tand V1P∝Therefore,V ∝T x1PInserting a proportionality constant,V = kBC x T x1PRearranging,= kBCPVTCombining Charles’ and Boyle’slaws• When the same quantity (V) is proportional to twoother quantities (T and 1/P), it is also proportional tothe product of these two quantities12= kBCP1V1T1= kBCP2V2T2P1V1T1P2V2T2=Combined Gas Law• For a fixed quantity of a gas, the ratio PV/T is aconstantP1V1T1P2V2T2=P1V1T2 = P2V2T1V2 = V1x xP1P2T2T1= 729 mL881 mm Hg760 mm Hg(0 + 273) K(44 + 273) Kx x = 728 mLCheck: Pressure down, volume up.Temperature down, volume down.Standard temperature and pressure• STP is 0 degrees C (273 K) and 1 atm (760 torr) pressure• What is the STP volume of a sample of argon gas which had aninitial volume of 729 mL when at 44°C and 881 mm Hg?13Chalkboard example• A sample of krypton gas at a pressure of 905 torr and atemperature of 28.4 C occupies a volume of 631 mL. If the gasis allowed to expand at constant temperature until it’s pressureis 606 torr, what will be the new volume?• 1. Starting conditions– P1 = 905 torr– V1 = 631 mL– T1 = 28.4 °C• 2. Final conditions– P2 = 606 torr– V2 = ?– T2 = 28.4 °CP1V1T1P2V2T2=V2 = V1x xP1P2T2T1V2 = 942.3 mL Chalkboard examples• A sample of argon gas at a pressure of 715 mm Hg and atemperature of 26.0 ºC occupies a volume of 8.97 L. If the gas isheated at constant pressure to 71.0 ºC what will be the volume?14Chalkboard example• An experiment is designed to yield 44.5 mL oxygen at STP.What will be the actual volume if the temperature is 28 ºC andthe pressure