5 Postulates of Kinetic Theory

1. Spherical molecules in constant, random straight-line motion • “Elastic” collisions • Point masses • No interactions • Avg. KE of gas molecules  Temperature 5 Postulates of Kinetic Theory

2. Random, straight-line motion? The gas particles move in straight lines between collisions. Recall: straight-line motion implies that no forces are acting on the particle.

3. Total KE is conserved.Total KE before collision=Total KE after collision.BUT KE may be TRANSFERRED! Elastic Collisions

4. Elastic Collisions Kinetic energy may be transferred between particles.

5. Inelastic Collision Kinetic Energy is NOT conserved!

6. Point Mass The volume of the gas molecule itself is tiny compared to the distance between gas molecules. In other words, the distance between the molecules is more important than their actual size. We say the volume of each molecule is insignificant; but they need to be a point so we can locate them in space (give them coordinates).

7. Temperature of a gas Tgas KEavg So all gases at the same T have the same average kinetic energy. Recall that KE = ½ mv2.

8. He Ne Ar Kr Xe Lightest is fastest! At the same temperature, which of the following gases diffuses most rapidly?

9. He Ne Ar Kr Xe Heaviest is slowest! At the same temperature, which of the following gases diffuses most slowly?

10. For gases at the same Temperature KE = ½ mv2 Lighter gas particles have higher average speeds than heavier gas particles at the same temperature.

11. Gas that obeys all 5 assumptions of the kinetic theory all of the time. It doesn’t exist. It’s a model. Ideal Gas

12. Most real gases obey the kinetic theory most of the time. Real Gas

13. Spherical molecules in random, straight-line motion • “Elastic” collisions Which assumptions of the kinetic theory hold up?

14. Point masses • No interactions Which assumptions of the kinetic theory break down?

15. When the gas molecules are close to each other. When do the assumptions of the kinetic theory break down?

16. At high pressure & low temperature. When are the gas molecules close to each other?

17. At low pressure & high temperature. When are the gas molecules far apart from each other?

18. Good! How do the gas molecules act when they are far apart from each other?

19. Real Gases Molecules are always attracted to one another, even if just weakly. Molecules take up space.

20. Have mass • Take the shape & volume of their container • Compressible • Flow • Diffuse • Exert Pressure What are the properties of gases?

21. Force/Area Pressure

22. Collisions of the gas molecules with the walls of the container. Pressure results from?

23. With a Barometer!P = DHggh but since DHg & g don’t change, we just report h. How do you measure air pressure?

24. How do you measure the pressure of a confined gas? Closed-ended manometer A closedended manometer: h is directly proportional to the pressure of the confined gas. Pgas = DHggh but we just say h most of the time. With a manometer! To vacuum pump Attach gas bulb here

25. How do you measure the pressure of a confined gas? A A A A 22 222222 Pgas < Patm Pgas = Patm - h An openended manometer: h tells you how far away the gas pressure is from the air pressure. So you also need a barometer to measure Patm. With a manometer! Pgas > Patm Pgas = Patm + h

26. # of impacts per unit time and force of each impact Pressure depends on? (microscopically)

27. # of gas moleculesper unit volume And temperature Pressure depends on? (macroscopically)

28. Pressure Units • 1 atm = • 760 torr = • 760 mm Hg = • 101.3 kPa = • 101,325 Pa = • 14.7 lb / in2 or psi

29. A measure of the avg. kinetic energy of the particles of a substance. Temperature

30. Temperature • Pressure • Volume • # of moles 4 variables needed to completely describe a gas-phase system?

31. Can change size:balloons orcylinders with pistons Elastic containers

32. Walls are fixed.Size does not change. Rigid Containers

33. STP Standard Temperature & Pressure 1 atm or 101.3 kPa or 760 torr 0C or 273K

34. For a fixed mass and temperature, the pressure-volume product is a constant. Boyle’s Law

35. PV = k where k = a constant Boyle’s Law Constant T, n

36. P1V1 = P2V2 Boyle’s Law

37. Hyperbola – it’s an inverse relationship! Graph of Boyle’s Law

38. Graph of Boyle’s Law, Pressure vs. Volume

39. Volume goes to ½ the original volume Double the pressure

40. Volume goes to 1/3 the original volume Triple the pressure

41. Volume goes to 2 X the original volume Halve the pressure

42. Volume goes to 1/4 of the original volume Quadruple the pressure

43. What does the graph of a direct relationship look like?

44. Kelvin: 0 K means 0 speed. Which temperature scale has a direct relationship to molecular velocity?

45. Which graph shows the relationship between average KE and Kelvin temperature? The top graph!

46. It’s a direct relationship. Graph of Volume vs. Kelvin Temperature

47. V1/T1 = V2/T2 Charles’ Law Math expression of Volume & Kelvin Temperature Constant P, n

48. The volume doubles! What happens to the volume when the Kelvin temperature is doubled?

49. The volume triples! What happens to the volume when the Kelvin temperature is tripled?

50. The volume is halved! What happens to the volume when the Kelvin temperature is halved?