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Ch. 11 Properties of Gases

Ch. 11 Properties of Gases. Brady & Senese, 5th Ed. Index. 10.1. Familiar properties of gases can be explained at the molecular level 10.2. Pressure is a measured property of gases 10.3. The gas laws summarize experimental observations

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Ch. 11 Properties of Gases

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  1. Ch. 11 Properties of Gases Brady & Senese, 5th Ed

  2. Index • 10.1. Familiar properties of gases can be explained at the molecular level • 10.2. Pressure is a measured property of gases • 10.3. The gas laws summarize experimental observations • 10.4. Gas volumes are used in solving stoichiometry problems • 10.5. The ideal gas law relates P, V, T, and the number of moles of gas, n • 10.6. In a mixture each gas exerts its own partial pressure • 10.7. Effusion and diffusion in gases leads to Graham's law • 10.8. The kinetic molecular theory explains the gas laws • 10.9. Real gases don't obey the ideal gas law perfectly 10.1 Familiar properties of gases can be explained at the molecular level

  3. Properties of Gases • What is the shape of the air in a balloon? • Gases have anindefinite shape • What is the volume of the gas in the balloon? • They have anindefinite volume 10.1 Familiar properties of gases can be explained at the molecular level

  4. How Does a Molecular Model Explain This? • gases completely fill their containers: • Gases are in constant random motion • gases have low density and are easy to compress • gas molecules are very far apart • gases are easy to expand • gas molecules don’t attract one another strongly 10.1 Familiar properties of gases can be explained at the molecular level

  5. What Is Pressure? • The force of the collisions of the gas distributed over the surface area of the container walls; P=force/area • units : 1 atmosphere (atm) = 760 mm Hg (torr) = 1.01325(105) Pascal (Pa) = 14.7 psi=1013 millibar (mb) • measured with a barometer* • P=g×d×h • d=density of the liquid • g= gravitational acceleration • h=height of the column supported • Why use Mercury? 10.2 Pressure is a measured property of gases

  6. Learning Check: Pressure Units Convert 675 mm Hg to atm. Known: 675mmHg Unknown: atm Conversion factor? 760 mmHg = 1 atm 10.2 Pressure is a measured property of gases

  7. Learning Check: What happens to gas pressure when you raise the temperature? Pressure increases because the faster moving molecules hit the walls of the container with greater force No change in pressure is observed because the area increased. 10.3 The gas laws summarize experimental observations

  8. Learning Check What happens to gas pressure when you increase the number of molecules in the container? pressure increases because more molecules hit the walls of the container, thus exert a greater force on the container No pressure change is observed. 10.3 The gas laws summarize experimental observations

  9. Absolute Zero Temperature at which there is zero molecular motion 10.3 The gas laws summarize experimental observations

  10. Ideal Gases • Their behavior is predicted by the gas laws • There are NO ideal gases • However, most gases behave ideally at atmospheric P or lower and room T or higher • You need to know when they are not useful 10.3 The gas laws summarize experimental observations

  11. Combined Gas Law: • Boyle’s Law • Charles’ Law • Gay-Lussac’s Law • Thus combining this information • And therefore, for any 2 conditions: 10.3 The gas laws summarize experimental observations

  12. Used for calculating the effects of changing conditions works if the Temperature is in Kelvin, but P and V can be any units so long as the units cancel Learning Check: If a sample of air occupies 500. mL at STP*, what is the volume at 85 °C and 560 torr? Combined Gas Law 890 mL *Standard Temperature (273.15K) and Pressure (1 atm) 10.3 The gas laws summarize experimental observations

  13. Learning Check A sample of oxygen gas occupies 500.0 mL at 722 torr and –25 ºC. Calculate the temperature in ºC if the gas has a volume of 2.53 L at 491 mm Hg. . T2=853.90 K T2=581 °C 10.3 The gas laws summarize experimental observations

  14. Learning Check A sample of helium gas occupies 500.0 mL at 1.21 atm Calculate the volume of the gas if the pressure is reduced to 491 torr 936 mL 10.3 The gas laws summarize experimental observations

  15. Your Turn! 22.4 L of He at 25 ºC are heated to 200.ºC. What is the resulting volume? • 22.4 L • 179 L • 43.1 L • not enough information given 10.3 The gas laws summarize experimental observations

  16. Molar Volume • The volume of one mole of any gas at STP is 22.4 L. • Identity of the gas doesn’t matter • Molar mass of the gas doesn’t matter • Corollary: equal volumes of any gas contain the same number of particles as long as the T and P are the same 10.4 Gas volumes can be used in solving stoichiometry problems

  17. Learning Check: How many liters of N2(g) at 1.00 atm and 25.0 °C are produced by the decomposition of 150. g of NaN3?2NaN3(s)  2Na(s) + 3N2(g) 10.4 Gas volumes can be used in solving stoichiometry problems

  18. Bringing It Together • Avogadro: n directly proportional to V • Boyle: P indirectly proportional to V • Charles: T directly proportional to V • Gay-Lussac: T directly proportional to P • Combining these variables into one equation results in the Ideal Gas Law. • R is the constant of proportionality (the “ideal” or “universal” gas constant) its value is 0.082057 L•atm/mol•K 10.5 The ideal gas law relates P, V, T, and the number of moles of gas, n

  19. Ideal Gas Law • Used to describe a sample of gas under one set of conditions • The units have to be: • P in atm or torr • V in L • n in mol • T in K • R = 0.082057 L•atm/mol•K = 62.36 L•torr/mol•K PV = nRT 10.5 The ideal gas law relates P, V, T, and the number of moles of gas, n

  20. Your Turn! 12.2 g of Ne are placed into a 5.0 L flask at 25 ºC. What is the pressure of the gas? • 3.0 atm • 60. atm • 0.25 atm • None of these 10.5 The ideal gas law relates P, V, T, and the number of moles of gas, n

  21. The number of moles may be related to both the mass (m) of the gas sample and the molar mass (MM) of the gas involved Thus we may rewrite the Ideal Gas Law as Further, since d=m/V, we can rewrite the equation in terms of density Gas Density 10.5 The ideal gas law relates P, V, T, and the number of moles of gas, n

  22. What is the molar mass of a gas with a density of 6.7 g/L at -73.ºC and a pressure of 36.7 psi? Learning Check 44 g/mol = MM 10.5 The ideal gas law relates P, V, T, and the number of moles of gas, n

  23. What is the density of NO2 at 200 ˚C and 600. torr? Learning Check 0.9 g/L 10.5 The ideal gas law relates P, V, T, and the number of moles of gas, n

  24. Your Turn! What is the density of Helium gas at 35 ºC and 1.2 atm? • 5.1 g/L • 0.20 g/L • 2.34 g/L • None of these 10.5 The ideal gas law relates P, V, T, and the number of moles of gas, n

  25. Learning Check A sample of fluorine gas occupies 275 mL at 945 torr and 72 ºC. What is the mass of the sample? PV = nRT 0.459 g = mass 10.5 The ideal gas law relates P, V, T, and the number of moles of gas, n

  26. Learning Check Determine the molecular weight of a gas if 1.053 g of the gas occupies a volume of 1.000L at 25 °C and 752 mm Hg (The Dumas Method) PV = nRT 26.0 g/mol = mass 10.5 The ideal gas law relates P, V, T, and the number of moles of gas, n

  27. Your Turn! What is the molar mass of a sample of gas if 2.22 g occupies a volume of 5.0 L a 35 ºC and 769 mm Hg? • 1.3 g/mol • 0.015 g/mol • 0.090 g/mol • None of these =11 g/mol 10.5 The ideal gas law relates P, V, T, and the number of moles of gas, n

  28. Dalton’s Law The partial pressure of a gas is the pressure that the gas would exert if it were in the container by itself 10.6 In a mixture each gas exerts its own partial pressure

  29. PTotal = P1 + P2 + P3 + …. Learning Check: Pump 520 mm Hg N2 and 250 mm Hg O2 into an empty gas cylinder. What is the overall pressure of the mixture? Pt=520 mm Hg + 250 mm Hg=770 mm Hg 10.6 In a mixture each gas exerts its own partial pressure

  30. PTotal = P1 + P2 + P3 + …. Learning Check: 32.5 mL of Hydrogen gas is collected over water at 25 ºC and 755 torr. What is the pressure of dry hydrogen gas? VP25ºC = 23.76 mmHg) • Correct Pt to find the Pdry gas: • 755-23.76 torr=731.24 torr 731 torr = Phydrogen 10.6 In a mixture each gas exerts its own partial pressure

  31. Mole Fraction, X • Each gas molecule contributes a fraction of the total pressure • Xa=the mole fraction of substance “a” • na =the moles of component “a” • nt= the total number of moles of gas in the mixture • Application: The partial pressure contributed by the component gas “a” is a fraction of the total pressure 10.6 In a mixture each gas exerts its own partial pressure

  32. Learning Check: What is the mole fraction of N2 in the atmosphere? 1.000atm Air = .7808 atm N2+ .2095 atm O2+ .0093 atm Ar + .00036 atm CO2 .7808 = Xnitrogen 10.6 In a mixture each gas exerts its own partial pressure

  33. Diffusion vs. Effusion • When the partition is removed, blue molecules diffuse to mix • The molecules effuse through a pinhole into a vacuum 10.7 Effusion and diffusion in gases leads to Graham’s Law

  34. Graham’s Law Of Effusion • At the same temperature, particles of the different gases will have the same average kinetic energy • The greater the molecular mass of the gas, the slower its velocity to achieve this kinetic energy • Gases with lower molecular masses have higher velocities and gases with higher molecular masses have lower velocities at the same temperature 10.7 Effusion and diffusion in gases leads to Graham’s Law

  35. Your Turn! The average kinetic energy of all gas molecules is the same at the same temperature. Compared to lighter atoms at the same temperature, heavier atoms on average: • move faster • move slower • move at the same average velocity 10.7 Effusion and diffusion in gases leads to Graham’s Law

  36. Your Turn! Three balloons are filled with equal volumes of the gases: CH4, H2, and He. After 5 hours the balloons look like the picture. • Which is the He balloon? C A B 10.7 Effusion and diffusion in gases leads to Graham’s Law

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