2. Ideal Gas Laws

3. Law of Combining Volumes Gay Lussac At a given temperature and pressure the volumes of all gases that react with one another are in the ratio of small whole numbers. 2 Liter H 2 (g) + 1 Liter O 2 (g) → 2Liters of H 2 O (g) 3 Liters of H 2 + 1 Liter N 2 → 2 liters NH 3

4. Avogadro’s Hypothesis Explained Gay Lussac’s Law The HYPOTHESIS: The volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of the gas. Interpretation: equal volumes of different gases at the same temperature and pressure contain the same number of particles.

5. Avogadro’s Hypothesis

6. Avogadro’s Explanation

7. Avogadro's Law: the missing piece Avogadro’s At constant temperature and pressure, the volume of gas is directly related to the number of moles. V = k n (n is the number of moles) V 1 = V 2 n 1 = n 2

8. Ideal Gas Equation Boyle’s Law V = 1/P (T, n const) Charle’s Law V = kT ( P, n const.) Gay Lussac’s Law P = kT(V, n const) Avogadro’s hypothesis V = kn ( P, T const)

9. Value Of Universal Gas Constant, R Check blackboard for calculations R = 0.08306 L atm/ (mol K) R = 62.4 L mm/(mol K) R = 8.314 kPa L/(mol K)

10. Ideal Gas Law A hypothetical substance - the ideal gas Think of it as a limit. Think of it as a limit. Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature. Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature. Use the laws anyway, unless told to do otherwise. They give good estimates.

11. Ideal Gas Equation Boyle’s Law V = 1/P (T, n const) Charle’s Law V = kT ( P, n const.) Gay Lussac’s Law P = kT(V, n const) Avogadro’s hypothesis V = kn ( P, T const)

12. Value Of Universal Gas Constant, R Check blackboard for calculations R = 0.08306 L atm/ (mol K) R = 62.4 L mm/(mol K) R = 8.314 kPa L/(mol K)

13. Ideal Gas equation PV = nRT n, number of moles V, volume in liters T, temperature, K P, pressure in chosen units R, Universal Gas Constant, value depends on pressure units used

14. Ideal Gas Law: PV = nRT PV = nRT V = 22.41 L at 1 atm, 0ºC, n = 1 mole, what is R? R is the ideal gas constant. R = PV/nT Value of R depends on the units for pressure

15. The Effect of Changing # of Particles. When we blow up a balloon we are adding gas molecules. PRESSURE: Doubling the the number of gas particles __________ the pressure if the volume and temperature is kept constant. VOLUME: If the pressure and temperature are constant, the volume will ________ as we change the number of molecules.

16. 1 atm If you double the number of molecules

17. You double the pressure. 2 atm

18. As you remove molecules from a container 4 atm

19. As you remove molecules from a container the pressure decreases 2 atm

20. As you remove molecules from a container the pressure decreases Until the pressure inside equals the pressure outside Molecules naturally move from high to low pressure 1 atm

21. Ideal Gas Law A hypothetical substance - the ideal gas Think of it as a limit. Think of it as a limit. Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature. Gases only approach ideal behavior at low pressure (< 1 atm) and high temperature. Use the laws anyway, unless told to do otherwise. They give good estimates.

22. Ideal Gas Law An equation of state. Independent of how you end up where you are at. Does not depend on the path. Given 3 properties of gas you can determine the fourth. An Empirical Equation - based on experimental evidence.

23. Example #1 A 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85 atm. What is the temperature?

24. Example #2 What is the volume in liters occupied by 0.250 mol of oxygen at 20.0 ºC and 740. mm Hg pressure?

25. Example #3 Kr gas in a 18.5 L cylinder exerts a pressure of 8.61 atm at 24.8ºC What is the mass of Kr?

26. Example #4 a) What mass of chlorine gas, Cl 2, in grams, is contained in a 10.0 L tank at 27 °C and 3.5 atm pressure? B) How many molecules of Cl 2 gas?

27. Per 3: start density at STP Per 2, start density at non-STP

28. Density at STP The Molar mass of a gas can be determined by the density of the gas. d= mass = m = MM Volume V 22.4 L

29. Examples: Density at STP Calculate the density of oxygen gas, O 2, at STP. Calculate the density of methane gas,CH 4, at STP.

30. Density Equations: non STP See derivation of the equations on the blackboard: PV = (m/MM) RT d = P(MM) /(RT) P(MM) = dRT

31. Molar Mass Equations Molar Mass = m (PV/RT) Molar mass = m RT V P Molar mass = dRT P Best to remember P(MM) = dRT

32. Example #1 What is the density of ammonia gas, NH 3, at 23ºC and 735 torr? At 28 °C and 740 mm Hg, 1.00 L of an unidentified gas has a mass of 5.16 g. What is the molar mass of this gas?

33. Example #3 A compound has the empirical formula CHCl. A 256 mL flask at 100.ºC and 750 torr contains.80 g of the gaseous compound. What is the molecular formula? A sample of gas with a mass of 0.225 g occupies a volume of 183 cm 3 at 22 °C and 102.5 kPa, what is its density at STP?

34. You might need to review Chapter 3

35. Stoichiometry and Gas laws 1. How many liters of O 2 at STP are required to produce 20.3 g of H 2 O using hydrogen and oxygen gas? (12.6 L) 2. How many liters of O 2 at 1.24 atm and 255ºC are required to produce 20.3 g of H 2 O using hydrogen and oxygen gas? (19.7 L)

36. At STP At STP determining the amount of gas required or produced is easy. 22.4 L = 1 mole

37. Not At STP Chemical reactions happen in MOLES. If you know how much gas - change it to moles Use the Ideal Gas Law n = PV/RT If you want to find how much gas - use moles to figure out volume V = nRT/P

38. Example #1 HCl(g) can be formed by the following reaction 2NaCl(aq) + H 2 SO 4 (aq) 2HCl(g) + Na 2 SO 4 (aq) What mass of NaCl is needed to produce 340 mL of HCl at 1.51 atm at 20ºC? (1.25 g)

39. Example #2 2NaCl(aq) + H 2 SO 4 (aq) 2HCl(g) + Na 2 SO 4 (aq) What volume of HCl gas at 25ºC and 715 mm Hg will be generated if 10.2 g of NaCl react? (4.53 L Of HCl)

40. Dalton’s law of Partial Pressures Review

41. Dalton’s Law of Partial Pressure P total = P 1 + P 2 + …….. P total = (n 1 /n total )P total + (n 2 /n total )P total + … P total = (n 1 +n 2 +..)/n tota ( l P total ) Law: The total pressure of a gas mixture is the sum of the partial pressures of the components of the mixture. Pa = (n 1 /n total ) P total, where n total = sum of all the moles of all the gases

42. Example #1 A mixture of gases contains 4.46 mol of Ne, 0.74 mol of Ar, and 2.15 mol of Xe. Calculate the partial pressures of these gases if the total pressure is 2.0 atm at certain temperature.

43. Example #2 A 428 mL sample of hydrogen was collected by water displacement in Salt Lake City at 25 °C on a day when the atmospheric pressure was 753 mm Hg. The vapor pressure of water at 25 °C is 23.8 mm Hg. Calculate A) the partial pressure of hydrogen gas B) the number of moles of hydrogen collected. The molar volume of hydrogen gas at STP.

44. Kinetic Molecular Theory of Gases

45. Kinetic Theory are evidence of this. u uKinetic theory says that molecules are in constant motion. u uPerfume molecules moving across the room

46. Kinetic Theory Of Gases Theory developed by James Maxwell, Clausius, and Boltzman – mid 19 th Century Physical properties of gases can be explained in terms of motion of individual molecules. This motion is a form of energy. Therefore: gas molecules have the capacity to do work.

47. Ê A Gas is composed of particles H usually molecules or atoms H Considered to be hard spheres far enough apart that we can ignore their volume. H Between the molecules is empty space. Considered point masses. H The particles do not attract each other The Kinetic Theory of Gases Makes three assumptions about gases

48. Ë The particles are in constant random motion. HMove in straight lines until they bounce off each other or the walls. Ì All collisions are perfectly elastic

49. The Average speed of an oxygen molecule is 1656 km/hr at 20ºC The molecules don’t travel very far without hitting each other so they move in random directions.

50. Kinetic Energy and Temperature Temperature is a measure of the Average kinetic energy of the molecules of a substance. Higher temperature faster molecules. At absolute zero (0 K) all molecular motion would stop. http://intro.chem.okstate.edu/1314F00/Laborator y/GLP.htm http://intro.chem.okstate.edu/1314F00/Laborator y/GLP.htm http://www2.biglobe.ne.jp/~norimari/science/Jav aApp/Mole/e-gas.htmlhttp://www2.biglobe.ne.jp/~norimari/science/Jav aApp/Mole/e-gas.html (restricted access) http://www2.biglobe.ne.jp/~norimari/science/Jav aApp/Mole/e-gas.html

51. Kinetic Energy and Temperature Temperature is a measure of the Average Kinetic Energy of the molecules of a substance. Higher temperature faster molecules. At absolute zero (0 K) all molecular motion would stop. KE = ½ mu 2, u, velocity of molecule KE = cT, c is a constant, T, Kelvin temperature The average kinetic energy is directly proportional to the temperature in Kelvin If you double the temperature (in Kelvin) you double the average kinetic energy. If you change the temperature from 300 K to 600 K the kinetic energy doubles.

52. Maxwell Speed Distributions Plots of Car Velocities and Molecular Speed Distribution Plots of Car Velocities and Molecular Speed Distribution Gas Laws Marymount Gas Laws Marymount Ohio State Ohio State

53. Maxwell’s Distribution Curves

54. Maxwell- Boltzmann Velocity (energy) Distribution KE = ½ m(u rms )2 Plot of Probability (fraction of molecules with given speed) versus velocity of the molecules.

55. 5.7 Maxwell’s Distribution Curves Molecules in a gas move at many different speeds. The Maxwell distribution shows the fraction of the molecules that are moving at a particular speed. The distribution shifts to higher speeds at higher temperatures. http://jersey.uoregon.edu/vlab/Balloon/index.html http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.ht m

56. Fig. 12-15, p.569

57. Graham’s Law of Diffusion http://chem.salve.edu/chemistry/diffusion.a sp http://chem.salve.edu/chemistry/diffusion.a sp

58. Graham’s Law of Effusion/Diffusion Effusion: flow of particles through tiny pores or pinholes. Diffusion: tendency of molecules (ions in solution) to move toward areas of low concentration. Depend on the speed of molecules Check blackboard for equations.

59. Graham's Law of Diffusion Graham's Law of Diffusion

60. Graham’s Law The Law: The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. Kinetic energy = 1/2 mv 2 m is the mass v is the velocity. Chem Express

61. bigger molecules move slower at the same temp. (by Square root) Bigger molecules effuse and diffuse slower Bigger molecules effuse and diffuse slower Helium effuses and diffuses faster than air - escapes from balloon faster. Graham’s Law

62. Graham’s Law of Diffusion We have two balloons, He filled and air (MM = 28 amu) filled. Which one will deflate faster? Calculate the average velocity of an H 2 molecule at 0 ºC if the average velocity of an O 2 molecule at this temperature is 5.00 x 10 2 m/s.

63. Example #1 In an effusion experiment, 45 sec were required for a certain number of moles of an unknown gas to pass through a small opening into a vacuum. Under the same conditions it took 28 sec for the same # of moles of Ar to effuse. Find the molecular mass of the gas.

65. Ideal Gases don’t exist Molecules do take up space There are attractive forces otherwise there would be no liquids

66. Real Gases behave like Ideal Gases When the molecules are far apart The molecules do not take up as big a percentage of the space We can ignore their volume. This is at low pressure

67. Real Gases behave like Ideal gases when When molecules are moving fast. Collisions are harder and faster. Molecules are not next to each other very long. Attractive forces can’t play a role.

68. Real Gases Real molecules do take up space and they do interact with each other (especially polar molecules). Need to add correction factors to the ideal gas law to account for these.

69. Volume Correction The actual volume (container volume) free to move in is less because of particle size. More molecules will have more effect. Corrected volume V’ = V - nb b is a constant that differs for each gas. P = nRT/V for is=deal gases For real gases P’ = nRT (V-nb)

70. Attractive Forces in Real Gases

71. Pressure correction n Because the molecules are attracted to each other, the pressure on the container will be less than ideal n depends on the number of molecules per liter. n since two molecules interact, the effect must be squared. P observed = P’ - a 2 () V n

72. Altogether Called Van der Waals Equation When rearranged, we obtain Corrected pressure Corrected volume

73. Where does it come from a and b are determined by experiment. Different for each gas. Bigger molecules have larger b. a depends on both size and polarity. once given, plug and chug.

76. Kinetic Energy % ofMolecules% ofMolecules High temp. Low temp. Av.temp Av. temp

77. Kinetic Energy % ofMolecules% ofMolecules High temp. Low temp. Few molecules have very high kinetic energy

78. Kinetic Energy % ofMolecules% ofMolecules High temp. Low temp. Average kinetic energies are temperatures

79. Fig. 12-14, p.568