The first scheduled quiz will be given next Tuesday during Lecture. It will last 15 minutes.

1. The first scheduled quiz will be given next Tuesday during Lecture. It will last 15 minutes. Bring pencil, calculator, and your book. The coverage will be pp 364-424, i.e. Sections 10.0 through 11.4.

2. 10.7 Kinetic Molecular Theory • Theory developed to explain gas behavior. • Theory based on properties at the molecular level. • Kinetic molecular theory gives us a model for understanding pressure and temperature at the molecular level. • Pressure of a gas results from the number of collisions per unit time on the walls of container.

3. Kinetic Molecular Theory • There is a spread of individual energies of gas molecules in any sample of gas. • As the temperature increases, the average kinetic energy of the gas molecules increases.

4. 10.7 Kinetic Molecular Theory • Assumptions: • Gases consist of a large number of molecules in constant random motion. • Volume of individual molecules negligible compared to volume of container. • Intermolecular forces (forces between gas molecules) negligible. • Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature. • Average kinetic energy of molecules is proportional to temperature.

5. Kinetic Molecular Theory • Magnitude of pressure given by how often and how hard the molecules strike. • Gas molecules have an average kinetic energy. • Each molecule may have a different energy.

6. Kinetic Molecular Theory • As kinetic energy increases, the velocity of the gas molecules increases. • Root mean square speed, u, is the speed of a gas molecule having average kinetic energy. • Average kinetic energy, , is related to root mean square speed:

7. Do you remember how to calculate vxy from vx and vy ? And how about v from all three components? Remember these equations!! They’ll pop up again in Chap. 11.

10. ump <u> urms

11. Be careful of speed versus velocity. The former is the magnitude • of the latter. • The momentum of a molecule is p = mv. During a collision, the • change of momentum is Δpwall = pfinal – pinitial = (-mvx) – (mvx) = 2mvx . • Δt = 2ℓ / vx Δpx / Δt = . . . = mvx2 / ℓ, where ℓ is length of the box • force = f = ma = m(Δv / Δt) = Δp / Δt = mvx2 / ℓ = force along x • And for N molecules, F = N(m(vx2 )avg / ℓ ) • But • And

12. But N = nN0 , so we can divide both sides by n to obtain

14. Kinetic Molecular Theory • Application to Gas Laws • As volume increases at constant temperature, the average kinetic of the gas remains constant. Therefore, u is constant. However, volume increases so the gas molecules have to travel further to hit the walls of the container. Therefore, pressure decreases. • If temperature increases at constant volume, the average kinetic energy of the gas molecules increases. Therefore, there are more collisions with the container walls and the pressure increases.

15. Kinetic Molecular Theory • Molecular Effusion and Diffusion • As kinetic energy increases, the velocity of the gas molecules increases. • Average kinetic energy of a gas is related to its mass: • Consider two gases at the same temperature: the lighter gas has a higher rms than the heavier gas. • Mathematically:

16. Kinetic Molecular Theory • Molecular Effusion and Diffusion • The lower the molar mass, M, the higher the rms.

17. Kinetic Molecular Theory • Graham’s Law of Effusion • As kinetic energy increases, the velocity of the gas molecules increases. • Effusion is the escape of a gas through a tiny hole (a balloon will deflate over time due to effusion). • The rate of effusion can be quantified.

18. Kinetic Molecular Theory • Graham’s Law of Effusion • Consider two gases with molar masses M1 and M2, the relative rate of effusion is given by: • Only those molecules that hit the small hole will escape through it. • Therefore, the higher the rms the more likelihood of a gas molecule hitting the hole.

19. Kinetic Molecular Theory • Graham’s Law of Effusion • Consider two gases with molar masses M1 and M2, the relative rate of effusion is given by: • Only those molecules that hit the small hole will escape through it. • Therefore, the higher the rms the more likelihood of a gas molecule hitting the hole.

20. Kinetic Molecular Theory • Diffusion and Mean Free Path • Diffusion of a gas is the spread of the gas through space. • Diffusion is faster for light gas molecules. • Diffusion is significantly slower than rms speed (consider someone opening a perfume bottle: it takes while to detect the odor but rms speed at 25C is about 1150 mi/hr). • Diffusion is slowed by gas molecules colliding with each other.

21. Kinetic Molecular Theory • Diffusion and Mean Free Path • Average distance of a gas molecule between collisions is called mean free path. • At sea level, mean free path is about 6  10-6 cm.

22. Real Gases: Deviations from Ideal Behavior • From the ideal gas equation, we have • For 1 mol of gas, PV/nRT = 1 for all pressures. • In a real gas, PV/nRT varies from 1 significantly and is called Z. • The higher the pressure the more the deviation from ideal behavior.

24. Real Gases: Deviations from Ideal Behavior • From the ideal gas equation, we have • For 1 mol of gas, PV/RT = 1 for all temperatures. • As temperature increases, the gases behave more ideally. • The assumptions in kinetic molecular theory show where ideal gas behavior breaks down: • the molecules of a gas have finite volume; • molecules of a gas do attract each other.

26. Real Gases: Deviations from Ideal Behavior • As the pressure on a gas increases, the molecules are forced closer together. • As the molecules get closer together, the volume of the container gets smaller. • The smaller the container, the more space the gas molecules begin to occupy. • Therefore, the higher the pressure, the less the gas resembles an ideal gas.

27. Real Gases: Deviations from Ideal Behavior • As the gas molecules get closer together, the smaller the intermolecular distance.

28. Real Gases: Deviations from Ideal Behavior • The smaller the distance between gas molecules, the more likely attractive forces will develop between the molecules. • Therefore, the less the gas resembles and ideal gas. • As temperature increases, the gas molecules move faster and further apart. • Also, higher temperatures mean more energy available to break intermolecular forces.

29. Real Gases: Deviations from Ideal Behavior • Therefore, the higher the temperature, the more ideal the gas.

30. The first scheduled quiz will be given next Tuesday during Lecture. It will last 15 minutes. Bring pencil, calculator, and your book. The coverage will be pp 364-424, i.e. Sections 10.0 through 11.4.

31. Real Gases: Deviations from Ideal Behavior • The van der Waals Equation • We add two terms to the ideal gas equation one to correct for volume of molecules and the other to correct for intermolecular attractions • The correction terms generate the van der Waals equation: • where a and b are empirical constants characteristic of each gas.

33. Real Gases: Deviations from Ideal Behavior • The van der Waals Equation • General form of the van der Waals equation: Corrects for molecular volume Corrects for molecular attraction

34. Chapter 11 -- Intermolecular Forces, Liquids, and Solids In many ways, this chapter is simply a continuation of our earlier discussion of ‘real’ gases.

35. Remember this nice, regular behavior described by the ideal gas equation.

36. This plot for SO2 is a more representative one of real systems!!!

37. And this is a plot for an ideal gas of the dependence of Volume on Temperature.

38. Now this one includes a realistic one for Volume as a function of Temperature!

40. Why do the boiling points vary? Is there anything systematic? London Dispersion Forces

41. Hydrogen Bonding

42. Dipole-Dipole Forces

43. Intermolecular Forces -- forces between molecules -- are now going to be considered. Note that earlier chapters concentrated on Intramolecular Forces, those within the molecule. Important ones: ion-ion similar to atomic systems ion-dipole (review definition of dipoles) dipole-dipole dipole-induced dipole London Dispersion Forces: induced dipole-induced dipole polarizability Hydrogen Bonding

44. How do you know the relative strengths of each? Virtually impossible experimentally!!! Most important though: Establish which are present. London Dispersion Forces: Always All others depend on defining property such as existing dipole for d-d. It has been possible to calculate the relative strengths in a few cases.

45. Relative Energies of Various Interactions d-d d-id disp Ar 0 0 50 N2 0 0 58 C6H6 0 0 1086 C3H8 0.0008 0.09 528 HCl 22 6 106 CH2Cl2 106 33 570 SO2 114 20 205 H2O 190 11 38 HCN 1277 46 111

47. Let’s take a closer look at these interactions: Ion-dipole interaction

49. Let’s take a closer look at dipole-dipole interactions. This is the simple one.

50. But we also have to consider other shapes. Review hybridization and molecular shapes.