1. Gases are highly compressible and occupy the full volume of their containers. When a gas is subjected to pressure, its volume decreases. Gases always form homogeneous mixtures with other gases. Gases only occupy about 0.1 % of the volume of their containers. Characteristics of Gases

2. Pressure is the force acting on an object per unit area: SI unit of force = Newton (N) = kg*m/s 2 SI unit of area = m 2 F/A = N/m 2 = Pascal (Pa) Other common units: torr (mm Hg); atm, bar. Units: 1 atm = 760 mmHg = 760 torr = 1.01325  10 5 Pa = 101.325 kPa = 1.01325 bar. Pressure

3. Pressure

4. Atmospheric Pressure Atmospheric pressure is measured with a barometer. If a tube is inserted into a container of mercury open to the atmosphere, the mercury will rise 760 mm up the tube. Pressure

5. The pressures of gases not open to the atmosphere could be measured in liquid manometers. Nowadays other pressure sensitive devices (solid state) are more popular: capacitance manometeres, thermal gauges, etc. Pressure

6. 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 has a different energy.

7. Theory developed to explain behavior of gases. Theory of molecules in motion. 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. Kinetic Molecular Theory

8. Assumptions: –Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature. –Average kinetic energy of molecules is proportional to temperature. Kinetic molecular theory gives us an understanding of pressure and temperature on the molecular level. Pressure of a gas results from the number of collisions per unit time on the walls of container. Kinetic Molecular Theory

9. 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: Kinetic Molecular Theory

10. 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.

11. 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. Kinetic Molecular Theory

12. 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. Kinetic Molecular Theory

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

14. 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.

15. Graham’s Law of Effusion Consider two gases with molar masses M 1 and M 2, 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. Kinetic Molecular Theory

16. 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. Kinetic Molecular Theory

17. Boyle’s Law Boyle’s Law: the volume of a fixed quantity of gas is inversely proportional to its pressure. Example: Weather balloons are used as a practical consequence to the relationship between pressure and volume of a gas. The Gas Laws

19. Boyle’s Law

20. Charles’s Law Charles’s Law: the volume of a fixed quantity of gas at constant pressure increases as the temperature increases. The Gas Laws

22. Avogadro’s Law at a given temperature and pressure, the volumes of gases which react are ratios of small whole numbers. The Gas Laws

23. Avogadro’s Law Avogadro’s Hypothesis: equal volumes of gas at the same temperature and pressure will contain the same number of molecules. Avogadro’s Law: the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas. 22.4 L of any gas at 0  C contain 6.02  10 23 gas molecules or 1 mol of a gas at 0  C will occupy 22.4 L.

24. We can combine these into a general gas law: The Ideal Gas Equation Boyle’s Law: Charles’s Law: Avogadro’s Law:

25. If R is the constant of proportionality (called the gas constant), then The ideal gas equation is: R = 0.08206 L·atm/mol·K = 8.314 J/mol·K The Ideal Gas Equation

27. We define STP (standard temperature and pressure) = 0  C, 273.15 K, 1 atm. Volume of 1 mol of gas at STP is: The Ideal Gas Equation

28. Relating the Ideal-Gas Equation and the Gas Laws In general, if we have a gas under two sets of conditions, then

29. Gas Densities and Molar Mass Density has units of mass over volume. Rearranging the ideal-gas equation with the molar mass we get Other derivations of the Ideal-Gas Equation

30. Since gas molecules are so far apart, we can assume they behave independently. Dalton’s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component: Each gas obeys the ideal gas equation: Partial Pressures: Gas Mixtures

31. Combing the equations Mole Fractions Let n i be the number of moles of gas i exerting a partial pressure P i, then where  i is the mole fraction (n i /n t ). Gas Mixtures and Partial Pressures

32. 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. Real Gases: Deviations from Ideal Behavior

34. 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. Real Gases: Deviations from Ideal Behavior

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

36. 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. Real Gases: Deviations from Ideal Behavior

37. The higher the temperature, the more ideal the gas.

38. 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. Real Gases: Deviations from Ideal Behavior

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

41. Explaining Vapor Pressure on the Molecular Level Some of the molecules on the surface of a liquid have enough energy to escape the attraction of the bulk liquid. These molecules move into the gas phase. As the number of molecules in the gas phase increases, some of the gas phase molecules strike the surface and return to the liquid. After some time the pressure of the gas will be constant at the vapor pressure. Vapor Pressure

42. Explaining Vapor Pressure on the Molecular Level

43. Volatility, Vapor Pressure, and Temperature The higher the temperature, the higher the average kinetic energy, the faster the liquid evaporates.

44. Liquids boil when the external pressure equals the vapor pressure. Temperature of boiling point increases as pressure increases.

45. Prentice Hall © 2003 David Cedeno © 2003 Pressure Effects Factors Affecting Solubility

46. Prentice Hall © 2003 David Cedeno © 2003 Pressure Effects The higher the pressure, the more molecules of gas are close to the solvent and the greater the chance of a gas molecule striking the surface and entering the solution. –Therefore, the higher the pressure, the greater the solubility. –The lower the pressure, the fewer molecules of gas are close to the solvent and the lower the solubility. If S g is the solubility of a gas, k is a constant, and P g is the partial pressure of a gas, then Henry’s Law gives: Factors Affecting Solubility

47. Prentice Hall © 2003 David Cedeno © 2003 Pressure Effects Carbonated beverages are bottled with a partial pressure of CO 2 > 1 atm. As the bottle is opened, the partial pressure of CO 2 decreases and the solubility of CO 2 decreases. Therefore, bubbles of CO 2 escape from solution. Factors Affecting Solubility

48. Prentice Hall © 2003 David Cedeno © 2003 Mass Percentage, ppm, and ppb Mole Fraction, Molarity, and Molality Recall mass can be converted to moles using the molar mass. Ways of Expressing Concentration

49. Prentice Hall © 2003 David Cedeno © 2003 Mole Fraction, Molarity, and Molality We define Converting between molarity (M) and molality (m) requires density. Ways of Expressing Concentration

50. Prentice Hall © 2003 David Cedeno © 2003 Colligative properties depend on quantity of solute molecules. (E.g. freezing point depression and melting point elevation.) Lowering Vapor Pressure Non-volatile solvents reduce the ability of the surface solvent molecules to escape the liquid. Therefore, vapor pressure is lowered. The amount of vapor pressure lowering depends on the amount of solute. Colligative Properties

51. Prentice Hall © 2003 David Cedeno © 2003 Lowering Vapor Pressure Colligative Properties

52. Prentice Hall © 2003 David Cedeno © 2003 Lowering Vapor Pressure Raoult’s Law: P A is the vapor pressure with solute, P A  is the vapor pressure without solvent, and  A is the mole fraction of A, then Recall Dalton’s Law: Colligative Properties

53. Prentice Hall © 2003 David Cedeno © 2003 Lowering Vapor Pressure Ideal solution: one that obeys Raoult’s law. Raoult’s law breaks down when the solvent-solvent and solute-solute intermolecular forces are greater than solute-solvent intermolecular forces. Boiling-Point Elevation Goal: interpret the phase diagram for a solution. Non-volatile solute lowers the vapor pressure. Therefore the triple point - critical point curve is lowered. Colligative Properties

54. Prentice Hall © 2003 David Cedeno © 2003

55. Prentice Hall © 2003 David Cedeno © 2003 Boiling-Point Elevation At 1 atm (normal boiling point of pure liquid) there is a lower vapor pressure of the solution. Therefore, a higher temperature is required to teach a vapor pressure of 1 atm for the solution (  T b ). Molal boiling-point-elevation constant, K b, expresses how much  T b changes with molality, m: Colligative Properties

56. Prentice Hall © 2003 David Cedeno © 2003 Freezing Point Depression At 1 atm (normal boiling point of pure liquid) there is no depression by definition When a solution freezes, almost pure solvent is formed first. –Therefore, the sublimation curve for the pure solvent is the same as for the solution. –Therefore, the triple point occurs at a lower temperature because of the lower vapor pressure for the solution. Colligative Properties

57. Prentice Hall © 2003 David Cedeno © 2003 Freezing Point Depression The melting-point (freezing-point) curve is a vertical line from the triple point. The solution freezes at a lower temperature (  T f ) than the pure solvent. Decrease in freezing point (  T f ) is directly proportional to molality (K f is the molal freezing-point-depression constant): Colligative Properties

58. Prentice Hall © 2003 David Cedeno © 2003 Freezing Point Depression Colligative Properties