Chapter 10 Gases Part 2 Kinetic Molecular Theory Prepare for Recitation October 20th ALEKS Objective 8 due October 18th ANGEL Quiz 8 October 20th Lecture 22 October 12th Lecture 23 October 14th Lecture 24 October 17th Read Ch 10 1 10 9 Additional Preparation BLB 10 5 23 30 45 71 75 82 84 Packet 10 1 15 BLB 25 11 12 25 CH110 FA11 SAS 1 Chapter 10 Gases Part 2 Kinetic Molecular Theory KEY QUESTIONS THE BIG PICTURE What 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 origins How 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 By the end of Today s Lecture you should know Kinetic molecular theory Partial pressure Effusion and diffusion CH110 FA11 SAS 2 Density is Proportional to Molar Mass Example Air is approximately 80 N2 and 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 CH110 FA11 SAS 3 Partial Pressure On 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 mixtures Dalton s Law Since n P then Ptotal ntotal Ptotal P1 P2 P3 ntotal n1 n2 CH110 FA11 SAS 4 Practice Problem If 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 CH110 FA11 SAS 5 Mole Fraction and Partial Pressure Dalton s law of partial pressure says that Ptotal ntotalRT V P1 P2 P3 n1 n2 n3 RT V Dalton s law can be re written as ni Ptotal Pi ntotal or Pi ni ntotal Ptotal The fraction of the total pressure contributed by each gas is equal to its mole fraction Xi What was the mole fraction of CO2 on the previous page CH110 FA11 SAS 6 Practice Problem What is the partial pressure of O2 in the vessel below PTOT 756 TORR T 300 0 C VTOT 5 00 L A B C D E GAS Ar N2 CO2 Ne O2 MOLE FRACTION 0 320 0 270 0 150 0 160 75 6 torr 378 torr 680 torr 756 torr There is not enough data CH110 FA11 SAS 7 Collecting Gases Over Water Vapor Pressure If 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 Pvap of H2O CH110 FA11 SAS 8 Practice Problem A 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 N2 were collected A B C D E 0 0022 g 0 031 g 0 062 g 0 39 g 0 78 g CH110 FA11 SAS 9 Kinetic Molecular Theory Ideal Gas Law PV nRT explains HOW gases behave Need more to explain why Look at gases on the molecular level Kinetic Molecular Theory KMT Five key postulates of KMT 1 Molecules move in straight lines 2 Molecules are small 3 Molecules are not sticky 4 Molecules experience elastic collisions 5 Mean kinetic energy T in K Ek mv2 CH110 FA11 SAS 10 Temperature and Molecular Speed Distribution of speeds Some molecules move more slowly Some move faster Root Mean Square RMS speed u The speed of a molecule possessing the average kinetic energy Entire curve and u shifts to speed with temperature CH110 FA11 SAS 11 RMS Speed Molecular Mass and Temperature According to KMT m u2 Average kinetic energy root mean square speed mass m u2 3 RT 2 N Avogadro s number u 3RT M The a gas is the its RMS speed will be at a given temperature CH110 FA11 SAS 12 KMT The Why Behind the Gas Laws At constant V P increases as T increases P T At constant T P decreases as V increases V P CH110 FA11 SAS 13 Practice Problem What is the average speed of N2 at 20oC 293K M 0 028 kg mol CH110 FA11 SAS 14 Practice Problem You have three flasks of gas under the conditions below P 1 atm Ar T 25oC N2 T 50oC P 2 atm O2 T 50oC P 1 atm Which of the following statements is TRUE A Ar has the greatest average kinetic energy of the 3 gases B N2 has the lowest average kinetic energy of the 3 gases C O2 has no kinetic energy D Ar and O2 have the same kinetic energy E N2 and O2 have the same kinetic energy CH110 FA11 SAS 15 What You Should Know Gas 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 pressure CH110 FA11 SAS 16
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