1. 1 Gases Chapter 5 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 5.1Substances that exist as gases 5.2Pressure of a gas 5.3The Gas Laws 5.4The Ideal Gas Equation 5.5Gas Stoichiometry 5.6Dalton’s Law of Partial Pressures 5.7The Kinetic Molecular Theory of Gases 5.8Deviation from Ideal Behavior

2. 2 5.1: Elements that exist as gases at 25 0 C and 1 atmosphere

3. 3

4. 4 Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container (infinitely miscible). Gases have much lower densities than liquids and solids. Physical Characteristics of Gases NO 2 gas Gases are thermally expandable - When a gas sample is heated, its volume increases, and when it is cooled its volume decreases. Gases have low viscosity - gases flow much easier than liquids or solids.

5. 5 Units of Pressure 1 pascal (Pa) = 1 N/m 2 1 atm = 760 mmHg = 760 torr 1 atm = 101,325 Pa Pressure = Force Area (force = mass x acceleration) 5.2: Pressure of a gas Gas molecules are constantly in motion, they exerts pressure on any surface they come in contact with.

6. A Mercury Barometer Pressure of the Atmosphere Called “atmospheric pressure,” or the force exerted upon us by the atmosphere above us. A measure of the weight of the atmosphere pressing down upon us. Measured using a barometer - a device that can weigh the atmosphere above us.

7. Sea level 1 atm 4 miles 0.5 atm 10 miles0.2 atm 5.2 The pressure exerted by a column of air extending from the earth’s surface (sea level) to the upper atmosphere is the atmospheric pressure The actual value of atm pressure depends on location, temperature and weather conditions Atmospheric pressure is measured with a barometer

8. 8 Manometers Used to Measure Gas Pressures closed-tubeopen-tube

9. A manometer – a device used to measure the pressure of gases other than the atmosphere. Type I: Closed-tube manometer (closed end manometer) is used to measure pressures below atmospheric pressures. P gas = P h

10. Type II: Open-tube manometer (open end manometer) is used to measure pressures equal to or greater than atmospheric pressures.

11. QUESTION #1: What is the pressure (in atm) in a container of gas connected to a mercury-filled, open-ended manometer if the level in the arm connected to the container is 24.7 cm higher than in the arm open to the atmosphere and atmospheric pressure is 0.975 atm? Answer:

12. QUESTION #2: What is the pressure of the gas (in mm Hg) inside the apparatus shown on the right if the external pressure is 750 mm Hg? Answer:

13. 5.3: The Gas laws Boyle’s Law P  1/V Charles’s Law Gay-Lussac’s Law V  T Avogadro’s Law V  n

14. 14 As P (h) increases V decreases Apparatus for Studying the Relationship Between Pressure and Volume of a Gas

15. 15 P  1/V P x V = constant P 1 x V 1 = P 2 x V 2 Boyle’s Law Constant temperature Constant amount of gas

16. 16 Question #3: A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?

17. 17 As T increasesV increases Variation in Gas Volume with Temperature at Constant Pressure Charles’ & Gay-Lussac’s Law

18. Variation of gas volume with temperature at constant pressure. 5.3 V  TV  T V = constant x T V 1 = V 2 T (K) = t ( 0 C) + 273.15 Temperature must be in Kelvin T1T1 T2T2 Pressure increases from P 1 to P 4

19. 19 Question #4: A sample of carbon monoxide gas occupies 3.20 L at 125 0 C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?

20. 20 Avogadro’s Law V  number of moles (n) V = constant x n V 1 / n 1 = V 2 / n 2 Constant temperature Constant pressure

21. 21 Question #5: Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure?

22. 22 Summary of Gas Laws Boyle’s Law

23. 23 Charles Law

24. 24 Avogadro’s Law

25. 5.4: The Ideal Gas Equation An ideal gas is defined as one for which both the volume of molecules and forces between the molecules are so small that they have no effect on the behavior of the gas. The ideal gas equation is: PV = nRT R = Ideal gas constant R = 8.314 J / mol K = 8.314 J mol -1 K -1 R = 0.08206 l atm mol -1 K -1

26. 26 Ideal Gas Equation Charles’ law: V  T  (at constant n and P) Avogadro’s law: V  n  (at constant P and T) Boyle’s law: P  (at constant n and T) 1 V V V  nT P V = constant x = R nT P P R is the gas constant PV = nRT

27. 27 The conditions 0 0 C and 1 atm are called standard temperature and pressure (STP). PV = nRT R = PV nT = (1 atm)(22.414L) (1 mol)(273.15 K) R = 0.082057 L atm / (mol K) Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.

28. Question #6: What volume will be occupied by 0.833 mole of fluorine (F 2 ) at 645 mmHg and 15.0 o C? Answer:

29. 29 Question #7: What is the volume (in liters) occupied by 49.8 g of HCl at STP?

30. 30 Question #8: Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0 C is heated to 85 0 C at constant volume. What is the final pressure of argon in the lightbulb (in atm)?

31. 31 Density (d) Calculations d = m V = PMPM RT m is the mass of the gas in g M is the molar mass of the gas Molar Mass ( M ) of a Gaseous Substance dRT P M = d is the density of the gas in g/L Using ideal gas equation for:

32. 32 Question #9: A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.0 0 C. What is the molar mass of the gas?

33. QUESTION #10: A sample of natural gas is collected at 25.0 o C in a 250.0 ml flask. If the sample had a mass of 0.118 g at a pressure of 550.0 Torr, what is the molecular weight of the gas? Answer:

34. 5.5: Gas Stoichiometry ReactantsProducts Molecules Moles Mass Molecular Weight g/mol Atoms (Molecules) Avogadro’s Number 6.02 x 10 23 Solutions Molarity moles / liter Gases PV = nRT

35. 35 Question #11: What is the volume of CO 2 produced at 37 0 C and 1.00 atm when 5.60 g of glucose are used up in the reaction: C 6 H 12 O 6 (s) + 6O 2 (g) 6CO 2 (g) + 6H 2 O (l)

36. Question #12: What total gas volume (in liters) at 520 o C and 880 torr would result from the decomposition of 33 g of potassium bicarbonate according to the equation: 2KHCO 3 (s) K 2 CO 3 (s) + CO 2 (g) + H 2 O(g) Answer:

37. QUESTION #13: A slide separating two containers is removed, and the gases are allowed to mix and react. The first container with a volume of 2.79 L contains ammonia gas at a pressure of 0.776 atm and a temperature of 18.7 o C. The second with a volume of 1.16 L contains HCl gas at a pressure of 0.932 atm and a temperature of 18.7 o C. What mass of solid ammonium chloride will be formed, and what will be remaining in the container, and what is the pressure? Answer:

38. For gas mixtures: gas behavior depends on the number, not the identity, of gas molecules. ideal gas equation applies to each gas individually and the mixture as a whole. all molecules in a sample of an ideal gas behave exactly the same way. Our atmosphere is a mixture of nitrogen, oxygen, argon, carbon dioxide, water vapour and small amounts of several other gases. The atmospheric pressure is actually the sum of the pressures exerted by all this individual gases. The same condition is true for every gas mixture. 5.6: Dalton’s Law of Partial Pressures

39. Definition of Dalton’s Law of Partial Pressures: To obtain a total pressure, add all of the partial pressures: P total = P 1 + P 2 + P 3 +... + P i “In a mixture of gases, each gas contributes to the total pressure the amount it would exert if the gas were present in the container by itself.”

40. 40 Dalton’s Law of Partial Pressures V and T are constant P1P1 P2P2 P total = P 1 + P 2

41. 41 Consider a case in which two gases, A and B, are in a container of volume V. P A = n A RT V P B = n B RT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B X A = nAnA n A + n B X B = nBnB n A + n B P A = X A P T P B = X B P T P i = X i P T mole fraction (X i ) = nini nTnT

42. Fig. 5.16

43. 43 Question #14: A sample of natural gas contains 8.24 moles of CH 4, 0.421 moles of C 2 H 6, and 0.116 moles of C 3 H 8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C 3 H 8 )?

44. QUESTION #15: A 2.00 L flask contains 3.00 g of CO 2 and 0.10 g of helium at a temperature of 17.0 o C. What are the partial pressures of each gas, and the total pressure? Answer:

45. 45 2KClO 3 (s) 2KCl (s) + 3O 2 (g) P T = P O + P H O 22 Collecting a Gas over Water: Application of Dalton’s Law

46. Fig. 5.12

47. 47 Vapor of Water and Temperature

48. Question #16: Hydrogen gas generated when calcium metal reacts with water is collected over water. The volume of gas collected at 30 o C and pressure of 988 mmHg is 641 mL. Calculate the mass in grams of the hydrogen gas obtained? The pressure of water vapor at 30 o C is 31.82 mmHg.

49. QUESTION #17: Calculate the mass of hydrogen gas collected over water if 156 ml of gas is collected at 20 o C and 769 mm Hg. The vapor pressure of water at 20 o C is 17.54 mm Hg. Answer:

50. QUESTION #18: A sample of hydrogen gas collected by displacement of water occupied 30.0 mL at 24 o C on a day when the barometric pressure was 736 torr. What volume would the hydrogen occupy if it were dry and at STP? The vapor pressure of water at 24.0 o C is 22.4 torr. Answer:

51. 5.7: Kinetic Molecular Theory of Gases 5.7 The nanoscale behaviour of gas molecules can be used to explain why gases behave as they do – i.e. understanding the macroscopic properties of the gas in terms of the behavior the microscopic molecules making up the gas. There are 5 (five) postulates that describe the behavior of molecules in a gas. These postulates are based upon some simple, basic scientific notions, but they also involve some assumptions that simplify the calculations.

52. The 5 postulates are: 1.The gas consists of tiny particles of negligible volume. A gas is composed of molecules whose size is much smaller than the distances between them. The molecules can be considered to be points; that is, they possess mass but have negligible volume. 2.Gas molecules move randomly at various speed and in every possible directions. The gas molecules are in constant motion. They frequently collide with one another or with the walls of the container. 5.7

53. 3.Collisions among molecules are perfectly elastic. The collisions of the gas molecules, either with other molecules or with the walls of the container, are elastic. There is no loss of energy. If the collisions are inelastic, the motion of the gas molecules would become slower and slower, and finally the molecules would remain at the bottom of the container – this situation has never occurred! Therefore the molecular collision must be elastic. 4.Gas molecules exert neither attractive nor repulsive forces on one another. Intermolecular forces of attraction do not exist between gas molecules, hence, the gas molecules travel in a straight line and are not influenced by other gas molecules. 5.7

54. 5.The average kinetic energy of the molecules is proportional to the temperature of the gas in Kelvins. Any two gases at the same temperature will have the same average kinetic energy. 5.7 The average kinetic energy of a molecules is given by: whereby: m = mass u = speed N = number of molecules Since whereby: C = proportionality constant T = absolute temperature

55. 55 Kinetic theory of gases and … Compressibility of Gases Boyle’s Law P  collision rate with wall Collision rate  number density Number density  1/V P  1/V Charles’ Law P  collision rate with wall Collision rate  average kinetic energy of gas molecules Average kinetic energy  T P  T

56. 56 Kinetic theory of gases and … Avogadro’s Law P  collision rate with wall Collision rate  number density Number density  n P  n Dalton’s Law of Partial Pressures Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas P total =  P i

57. Distribution of Molecular Speed At any given time, what fraction of the molecules in a particular sample have a given speed? Some of the molecules will be moving more slowly than average, and some will be moving faster than average, but how many? Apparatus for studying molecular speed distribution:

58. Maxwell Boltzmann solved the problem mathematically. He used statistical analysis to obtain an equation that describes the distribution of molecular speed at a given temperature. 5.7 The distribution of speeds for nitrogen gas molecules at three different temperatures. At the higher temperature, more molecules are moving at faster speed. u rms = 3RT M 

59. 5.7 At a given temperature, the lighter molecules are moving faster, on the average. The distribution of speeds of three different gases at the same temperature.

60. Molecular Mass and Molecular Speeds Molecule H 2 CH 4 CO 2 Molecular Mass (g/mol) Kinetic Energy (J/molecule) Velocity (m/s) 2.016 16.04 44.01 6.213 x 10 - 21 6.0213 x 10 - 21 6.213 x 10 - 21 1,926 683.8 412.4

61. Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties. 5.7 Graham’s Law: Diffusion & Effusion of Gases A path traveled by a single gas molecule. Each change in direction represents a collision with another molecule. NH 3 17 g/mol HCl 36 g/mol NH 4 Cl NH 3 is lighter & diffuses faster, therefore NH 4 Cl appears nearer to HCl bottle. r1r1 r2r2 M2M2 M1M1  =

62. Graham's Law of Diffusion: The rate at which gases diffuse is inversely proportional to the square root of their densities. If the number of moles per liter at a given T and P is constant, then, the density of a gas is directly proportional to its molar mass (MM). In comparing two gases at the same T and P, the formula becomes:

63. 63 Gas effusion is the is the process by which gas under pressure escapes from one compartment of a container to another by passing through a small opening (pinhole). = r1r1 r2r2 t2t2 t1t1 M2M2 M1M1  = Thomas Graham (1805-1869) According to Graham’s Law, the rate of effusion of a gas is inversely proportionate to the square root of its mass. The lighter the molecule, the more rapidly it effuses.

64. QUESTION #19: Which gas in each of the following pairs diffuses more rapidly, and what are the relative rates of diffusion? (a) Kr & O 2 (b) N 2 & acetylene, C 2 H 2

65. 65 Question #20: Example #Nickel forms a gaseous compound of the formula Ni(CO) x What is the value of x given that under the same conditions methane (CH 4 ) effuses 3.3 times faster than the compound?

66. 5.8: Deviations from Ideal Behavior 5.8 The deviation from ideal behavior is large at high pressure and low temperature. At lower pressures and high temperatures, the deviation from ideal behavior is typically small, and the ideal gas law can be used to predict behavior with little error. Molecules are perfectly elastic (no INTERMOLECULAR FORCES). Molecules are point masses (NEGLIGIBLE volume). Molecules move at random. Remember the conditions assumed for an Ideal Gas?:

67. The first two of these assumptions is clearly WRONG for all gases, because at low temperatures all gases CONDENSE, or form a liquid phase. This must happen because of the intermolecular forces that exist between the molecules. Moreover, the liquid has measurable molar volume, and this volume is simply the size of the close- packed molecules of the liquid. At high pressures, the intermolecular distances can become quite short, and attractive forces between molecules becomes significant. Neighboring molecules exert a relatively long- ranged attractive force on one another, which will reduce the momentum in which they transfer to the container walls. The observed pressure exerted by the gas under these conditions will be less than that for an Ideal Gas.

68. 68 Deviations from Ideal Behavior 1 mole of ideal gas PV = nRT n = PV RT = 1.0 Repulsive Forces Attractive Forces

69. Dutch physicist, Johannes van der Waals modified the ideal gas law to describe the behaviour of real gases by including the effects of molecular size and intermolecular forces.

70. 70 Van der Waals equation nonideal gas P + (V – nb) = nRT an 2 V2V2 () } corrected pressure } corrected volume

71. QUESTION #21: You are in charge of the manufacture of cylinders of compressed gas at a small company. Your company president would like to offer a 4.0-L cylinder containing 500 g of chlorine in the new catalog. The cylinders you have on hand have a rupture pressure of 40 atm. Use both the ideal gas law and the van der Waals equation to calculate the pressure in a cylinder at 25 o C. Is this cylinder likely to be safe against sudden rupture (which would be disastrous because chlorine gas is highly toxic)?