Chapter 10: Gases Part 2: Kinetic Molecular TheoryChapter 10: Gases Part 2: Kinetic Molecular TheoryDensity is Proportional to Molar MassPartial PressurePractice ProblemMole Fraction and Partial PressurePractice ProblemCollecting Gases Over WaterPractice ProblemKinetic Molecular TheoryTemperature and Molecular SpeedRMS Speed, Molecular Mass, and TemperatureKMT: The “Why” Behind the Gas LawsPractice ProblemPractice ProblemWhat You Should KnowChapter 10: GasesPart 2: Kinetic Molecular TheoryCH110 FA11 SAS 1Prepare for Recitation October 20thALEKS Objective 8 due October 18thANGEL Quiz 8, October 20thLecture 22: October 12thLecture 23: October 14thLecture 24: October 17thRead: Ch. 10.1-10.9Additional Preparation: BLB 10: 5,23,30,45,71,75,82-84; Packet 10: 1-15BLB 25: 11,12,25CH110 FA11 SAS 2By the end of Today’s Lecture you should know:Kinetic-molecular theoryPartial pressureEffusion and diffusionKEY QUESTIONS: THE BIG PICTUREChapter 10: GasesPart 2: Kinetic Molecular TheoryWhat does partial pressure mean?What type of mixtures do gasses form?What state equation can we use to describe mixtures of gasses?Remember: macroscopic properties come from microscopic originsHow does the energy of a molecule in a gas compare with intermolecular forces?How can we describe mixtures of gasses?How do real gasses differ from ideal gasses?Density is Proportional to Molar MassCH110 FA11 SAS 3Example: Air is approximately 80% N2and 20% O2. What is its average molar mass?The contents of a 1.00 L bulb of air are measured to weigh 1.20 g. What is the average molar mass of air? (Assume T = 294 K, P = 1 atm)Partial PressureCH110 FA11 SAS 4On the previous slide, I assumed mixtures of gases obey the ideal gas law!Since all ideal gases behave the same, n can represent ANY gas – including mixturesDalton’s Law:ntotal= n1+ n2+ …Since n ∝P, then…Ptotal∝ ntotalPtotal= P1+ P2+ P3 +…Practice ProblemCH110 FA11 SAS 5If 5 mole CO2, 2 mole N2, 1 mole Cl2 are mixed in a 40 L vessel at 0 oC, what is the total pressure in the vessel?What is the partial pressure of CO2?Mole Fraction and Partial PressureCH110 FA11 SAS 6Dalton’s law of partial pressure says that:Ptotal= ntotalRT/VP1+P2+P3+… = (n1+n2+n3+…)RT/VDalton’s law can be re-written as:Pi= Ptotalnintotalni= ntotalPi Ptotal-or-The fraction of the total pressure contributed by each gas is equal to its mole fraction: XiWhat was the mole fraction of CO2on the previous page?Practice ProblemCH110 FA11 SAS 7What is the partial pressure of O2in the vessel below?A. 75.6 torrB. 378 torrC. 680 torrD. 756 torrE. There is not enough data.PTOT= 756 TORR GAS MOLE FRACTIONT = 300.0°C Ar 0.320VTOT=5.00 L N20.270CO20.150Ne 0.160O2?Collecting Gases Over WaterCH110 FA11 SAS 8If you know the barometric pressure, you can determine the partial pressure of a gas collected over water at a given temperature:Ptotal= PH2O+ P1+ P2+ P3+ …Example: at 23oC, PH2O= 21 torr(Appendix B, Pvapof H2O)Vapor Pressure:Practice ProblemCH110 FA11 SAS 9A reaction produced nitrogen gas, which was collected over water. The measured barometric pressure of the collected gas was 742 torr in a volume of 55.7 mL at 23oC. How many grams of N2were collected?A. 0.0022 gB. 0.031 gC. 0.062 gD. 0.39 gE. 0.78 gKinetic Molecular TheoryCH110 FA11 SAS 10• PV = nRTexplains HOW gases behave• Need more to explain whyLook at gases on the molecular levelFive key postulates of KMT:1)Molecules move in straight-lines…2) Molecules are small –3) Molecules are not sticky –4) Molecules experience elastic collisions5) Mean kinetic energy ∝ T (in K)Ek= ½ mv2Kinetic Molecular Theory (KMT)Ideal Gas Law:Temperature and Molecular SpeedCH110 FA11 SAS 11Distribution of speeds:Some molecules move more slowlySome move fasterRoot-Mean-Square (RMS) speed (u)The speed of a molecule possessing the average kinetic energyEntire curve (and u) shifts to ______ speed with __________ temperatureRMS Speed, Molecular Mass, and TemperatureCH110 FA11 SAS 12According to KMT:ε = ½ m u2root mean square speedmassε = ½ m u2 = 3 RT2 NAvogadro’s numberAverage kinetic energyu = 3RTM√The _____ a gas is, the _____ its RMS speed will be at a given temperature.KMT: The “Why” Behind the Gas LawsCH110 FA11 SAS 13At constant V, P increases as T increasesTPAt constant T, P decreases as V increasesPVPractice ProblemCH110 FA11 SAS 14What is the average speed of N2at 20oC (293K) [M = 0.028 kg/mol]?Practice ProblemCH110 FA11 SAS 15You have three flasks of gas under the conditions below:Ar T = 25oC P = 1 atmN2T = 50oC P = 2 atmO2T = 50oC P = 1 atmWhich of the following statements is TRUE?(A) Ar has the greatest average kinetic energy of the 3 gases(B) N2has the lowest average kinetic energy of the 3 gases(C) O2has no kinetic energy(D) Ar and O2have the same kinetic energy(E) N2and O2have the same kinetic energyWhat You Should Know CH110 FA11 SAS 16Gas Mixtures• What is partial pressure hand how does Dalton’s Law help us to use it?• What is the mole fraction of a gas?Kinetic Molecular Theory• How does KMT help us to describe ideal gases? What are the postulates of KMT?• At a given temperature, what do we know about the kinetic energy of any given gas based on KMT?• What is the root mean square speed of a gas at a given temperature and how is it related to the mass of the gas particles?• What are diffusion and effusion and how does the speed at which a gas will do either relate to its molar mass?• What is the mean free path and how is it related to
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