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Kinetic Theory (Gas Laws)

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  1. Kinetic Theory (Gas Laws) Chapter 16

  2. Atomic Mass Unit • Uses Carbon-12 as standard • 1 atom of 12C masses 12.000 u 1 u = 1.66 X 10-27 kg

  3. Review of Moles • 1 mole = 6.022 X 1023 atoms/molecules • GMA • GMMA • What is the molar mass of nitrogen, N2? • What is the molar mass of BaCl2? • How many moles are in 132 grams of CO2? • How many atoms are in a 200 gram sample of iron?

  4. States of Matter They wander in random patterns quite close to one another. Can “wiggle” in place (these are the wiggle lines)

  5. Plasma • 4th state of matter • Ionized gases • Electrons are removed from the atoms • Positive ions remain • Present in: • Stars • Lightning • Arc welding • Most common state of matter in the universe

  6. Plasma A hydrogen and helium plasma such as you would find in the sun e He+ e He+ e H+ H+ e He+ e He+ e e H+ H+ e

  7. Temperature • Measure of the average molecular motion of a group of atoms/molecules Conversion Formulas F = 1.8 (oC) + 32 K = C + 273 C = K – 273

  8. Temperature

  9. Absolute Zero • All atomic and molecular motion stops • Coldest possible temperature • Never reached absolute zero • Liquid Nitrogen = 77 K (-196 oC) • Dry Ice = 216 K (-56.6 oC)

  10. 102 oF  oC -10.0 oC  oF 25 oC  K 177 K  oC 310 oC  K

  11. 102 oF  39oC -10.0 oC  14.0 oF 25 oC  298 K 177 K  -96 oC 310 oC  583 K

  12. Kinetic Molecular Theory • A gas is composed of small particles (molecules) that are spaced widely apart. • Compressible • Low density - about a 1000 times less dense than a liquid • The molecules of a gas are in rapid, constant motion • Pressure – the force of the molecules hitting the side of a container

  13. All collisions are elastic • Molecules don’t lose any energy when they collide. • Gas molecules have little/no attractive force on one another. • Too far apart • Mix thoroughly – unlike oil and water (too far apart for polar/non-polar forces to matter)

  14. The temperature of a gas is directly proportional to average kinetic energy of the molecules. KE = 3kT 2 k = Boltzmann’s constant = 1.38 X 10-23 J/K

  15. Kinetic Molecular Theory: Ex 1 What is the average KE of molecules in a gas at 37oC? T = 273 + 37 = 310 K KE = 3kT 2 KE = (3/2)(1.38 X 10-23 J/K)(310 K)= 6.42 X 10-21J (this is per molecule)

  16. Kinetic Molecular Theory: Ex 2 What is the average KE of molecules in a gas at 100 oC? ANS: 7.72 X 10-21J

  17. P1V1 = n1RT1 P2V2 = n2RT2 Solve both equations for R R = P1V1 R = P2V2 n1T1 n2T2 P1V1 = P2V2 n1T1 n2T2

  18. See what you can cross out (what you are not told) • Remember to convert to Kelvin and moles if needed.

  19. Boyle’s Law • Boyle’s Law – The pressure and volume of a gas are inversely related • Bicycle pump example • Piston down – low volume, high pressure • Piston up – high volume, low pressure

  20. Example: The volume of a car’s cylinder is 475 mL at 1.05 atm. What is the volume when the cylinder is compressed and the pressure is 5.65 atm? P1V1 = P2V2 n1T1 n2T2

  21. Collapses to: P1V1 = P2V2 (Answer: 88.3 mL)

  22. Example: • A weather balloon has a volume of 40.0 liters on the surface of the earth at 1.00 atm. What will be the volume at 0.400 atm as it rises? P1V1 = P2V2 n1T1 n2T2

  23. Barometer • Torricelli (1643) • Height of column stayed about 760 mm (760 torr) • The higher the elevation, the lower the mercury • Weather • Rising pressure – calm weather • Dropping pressure – storm (fast moving air)

  24. Charles Law • Charles Law – The temperature and volume of a gas are directly related • “HOTTER = BIGGER” • Can be used to find absolute zero • Temperature must be in Kelvin

  25. A basketball has a volume of 12.0 L when blown up at 25.00 oC. What will be the volume if it is taken outside on a day when it is only 5.00 oC? P1V1 = P2V2 n1T1 n2T2

  26. Collapses to: V1 = V2 T1 T2

  27. 2. If a tire contains 30.0 L of air at 10.0 oC, what volume will it occupy when it is driven and warms up to 50.0 oC?

  28. Guy-Lussac’s Law Gay-Lussac’s Law = The temperature and pressure of a gas are directly related. • Temperature must be in Kelvin • Gas in a spray can has a pressure of 5.00 atm at 25.0 oC. What will be the pressure at 400.0 oC? P1V1 = P2V2 n1T1 n2T2

  29. Avagadro’s Law Avagadro’s Law = The volume of a gas is directly proportional to the moles present • “MORE = BIGGER” • A balloon has a volume of 1.00 L when 50.0 grams of N2 are in the balloon. What is the volume if an additional 25.0 grams of N2 are added?

  30. Putting it all together • Often you change more than one thing at a time. • Ex: In a car, volume, temperature, and pressure may change. 1. The volume of 0.0400 mol of a gas is 500.0 mL at 1.00 atm and 20.0 oC. What is the volume at 2.00 atm and 30.0oC?

  31. 2. The gauge pressure in a tire is 200 kPa at 10oC. After driving, the temperature rises to 40oC. What will be the new gauge pressure? (Remember to add 101.3 kPa to the gauge pressure to get absolute pressure)

  32. The Ideal Gas Law • Works very well in situations close to Earth’s pressures and temperatures • Does not work for “extreme” situations (Jupiter’s atmosphere is too cold and too dense)

  33. PV = nRT • P = pressure in atmosphere • V = volume in Liters • n = number of moles • T = Temperature in Kelvin • R = gas constant R = 8.31 J/ mol-K

  34. STP Standard Temperature & Pressure • Standard Temperature = 0oC (273 K) • Standard Pressure = 1.013 X 105 N/m2 (101.3 kPa, 1 atm)

  35. The Ideal Gas Law Examples: • What is the volume of 1.00 mole of a gas at STP? • What is the mass of oxygen in a container at STP that has a volume of 10.0 m3? • A helium balloon has a radius of 18.0 cm. How many moles and grams of helium are needed to fill the balloon at 20oC and 1.05 atm? (V = 4/3pr3)

  36. The Ideal Gas Law 4. Estimate the number of molecules you exhale in one breath at STP.

  37. Three Processes • Constant Volume (isochoric) • Vertical Line on PV diagram • No work done • Pressure cooker • Constant Pressure (isobaric) • Horizontal line on PV graph • Work done • Constant Temperature (isothermal) • Hyperbola curve on PV graph

  38. Stop here in Knight’s Text

  39. Graham’s Law of Diffusion • Gases mix to fill their volume evenly • Graham’s Law of Diffusion – the speed of a gas is inversely proportional to its molar mass • The larger the molar mass, the slower the gas molecule

  40. Graham’s Law Example At the same temperature, which moves faster, an He atom or an N2 molecule?

  41. Calculating Average Speed • Root-mean-square velocity vrms = 3kT m • Heavier molecules are slower • Temperature increases speed Molar mass

  42. Average Speed: Example 1 What is the rms speed of one O2 molecule at 20oC? First we need the mass of one O2 in kilograms (32 u)(1.67 X 10-27kg) = 5.3 X 10-26 kg vrms = (3)(1.38 X 10-23 J/K)(293 K)½ (5.3 X 10-26 kg) vrms = 480 m/s (about 1000 mph)

  43. Average Speed: Example 2 What is the rms speed of one N2 molecule at 20oC? ANS: 510 m/s (about 1100 mph)

  44. Relative Humidity • Vapor exists above all liquids • Even solids have a vapor pressure • Saturated vapor pressure depends on temperature • When saturated vapor pressure exceeds atmospheric pressure, boiling occurs