1. Gases

2. Properties of Gases  All gases have similar physical properties:  They take the shape of their container and fill it completely  Gases are compressible- Gas volume decrease as pressure increases and vice versa  Gases diffuse and they like to move spontaneously through space.  Temperature affects the volume and/or pressure of a gas. If a gas is free to expand, its volume will increase as temperature increases

3. Chapter Preparation  Review:  DensityD = m/V  PressureP = F/A  Viscosity  Mole Massn = m/M

4. Kinetic Molecular Theory  Kinetic molecular theory of gases is a model that explains the macroscopic properties of gases based on the behavior of individual particles (atoms or molecules).

5. Kinetic Molecular Theory  Molecules of an ideal gas:  are in constant motion  are point masses (an ideal particle that has no volume)  collide with walls of a container and each other with elastic collisions (kinetic energy is conserved) Which diagram represents the most likely path of travel for a gas molecule?

6. Kinetic Molecular Theory  The average kinetic energy of gas molecules is proportional to the temperature of the gas. James Clerk Maxwell equation

7. Chemical Properties of Gases All gases have different chemical properties but similar physical properties Chemical Properties: Gases are either: very unreactive (ex. F, Cl, O) slightly reactive (ex. N) or inert (ex. noble gases)

8. Gases and Pressure  Pressure: a force applied per unit area  (kPa)- kilopascals  Pressure is created by the random motion of particles  Gas particles collide with the walls of its container  The number of the force of these collisions produce gas pressure

9. Atmospheric Pressure  Pressure exerted by air on all objects  Standard Temperature and Pressure (STP) = 101.325 kPa and 0°C  But laboratory temperatures are not at 0°C  So scientists agreed on another set of conditions...  Standard Ambient Temperature and Pressure (SATP) = 100 kPa and 25°C  Much closer to lab conditions – so scientists don’t freeze

10. Q: Where did 101.325 kPa come from?  At sea level, average atmospheric pressure is about 101kPa.  Scientists used this value to define one standard atmosphere (1 atm) as 101.325kPa  Scientists have also used a mercury barometer to measure atmospheric pressure so standard pressure is also defined at 760 mm Hg  101.325 kPa = 1 atm = 760 mm Hg

11. Example  Standard ambient pressure is defined as 100 kPa. Convert this value to the corresponding values in atmospheres and millimeters of mercury.

12. Example Pressure (kPa)Pressure (atm)Pressure (mm Hg) A)96.5 B)825 C)2.50

13. When a tube filled with mercury is inverted, the weight of the column of mercury pulls it toward Earth. However, the weight of the air directly above the open dish pushes down on the surface of the mercury and prevents all of the mercury from falling out of the tube. The two opposing forces balance each other when the height of mercury is about 760 mm. If the vertical mercury filled tube is longer than 760 mm, the mercury drops to 760 mm.

15. WHY??  A student took a photo of an empty soda bottle at a rest area in the Rocky Mountains.  Their GPS helped determine the altitude.  When they returned to sea level the bottled collapsed because of the air pressure. WHY ?

16. WHY??  Marnie & Deanna are collecting air pressure readings for a class project.  Marnie is recording her data near sea level. Deanna chose to hike to the top of a nearby mountain.  Where is the air pressure greater? The picture shows how much more air is in the column above Marnie than above Deanna. The air pressure at sea level is greater than at Deanna's elevation.

17. Pressure & Volume: Boyle’s Law  Robert Boyle (1627-1691) proposed that if the temperature and amount of a gas is held constant; as the pressure on a gas increases the volume of the gas decreases. (Example: if P is multiplied by the V a constant (k) is determined.)  The constant depends on the size of the sample and the temperature.

18. Gases and Pressure  Boyle demonstrated that the volume of a given amount of gas is inversely proportional to the external pressure exerted on it when the temperature is constant. 1 atm = 760 mmHg = 101 325 Pa = 101.325 kPa = 1.01325 bar

19. Gases and Pressure Summary  As the external pressure on a gas increases, the volume begins to decrease. As the volume decreases, the molecules become closer together causing the collision frequency to increase, increasing the pressure.

20. Pressure: Boyle’s Law  P V = k for the same gas;  P 1 V 1 = k and P 2 V 2 = k since both k's are the same a combined formula can be written P 1 V 1 = P 2 V 2

21. Boyle’s Law Example  A sample of a gas occupies 360 mL under a pressure of 0.750 atm. At a constant temperature, what volume will the sample occupy under a pressure of 1.000 atm. P 1 V 1 = P 2 V 2 => V 2 = P 1 V 1 P2P2 V 2 = 0.750 atm x 360 mL = 270 mL 1.000 atm

22. Boyle’s Law Example  If the pressure of 4.16L of gas is 120 kPa. What will the new volume of the gas be if the pressure is increased to 140kPa?

23. Boyle’s Law Example  What will the new pressure be if the volume of a gas at 130 kPa is 3.85 L and is expanded to fill a 4.55 L container?

24. Boyle’s Law Example  A 2.0L party balloon at 98 kPa is taken on top of a mountain where the pressure is 75 kPa. Assume that the temperature and chemical amount of the gas remain the same. What is the new volume of the balloon?

25. Your Task  Practice Questions page 152 # 5-10  Boyle’s Law Practice Questions

26. Quiz  The pressure exerted by a gas is 2.0 atm while it has a volume of 350 mL. What would be the volume of this sample of gas if the pressure is decreased to 1.0 atm? Assume that temperature is kept constant.  A 60 mL soap bubble is blown at standard pressure. When a thunder storm passes later in the day, the pressure becomes 700.0 mmHg. Will the bubble get bigger or smaller? What is the new volume?

27. Boyle’s Law  “As the pressure on a gas increases, the volume of the gas decreases proportionally if temperature and mass are constant”

28. Temperature  How hot or cold an object is? No, not really...  It’s the average kinetic energy of the particles of a substance  Absolute zero – the lowest temperature that can be obtained; the kinetic energy of all entities of solids, liquids or gases would become zero  Kelvin temperature scale - absolute zero is zero Kelvin ( 0 K = -273 °C )  Celsius temperature scale – zero is when water freezes (273 K = 0 °C)

29. Comparing Kelvin and Celsius Scales  To convert degrees Celsius to Kelvin, you add 273. K = °C + 273  To convert Kelvin to degrees Celsius, you subtract 273. °C = K - 273  Examples:  What is 254 K in °C ? -19°C  What is -34°C in K ? 239K

30. So do STP and SATP change?  Yes – using Kelvin you have different numbers to use: Standard Temperature and Pressure (STP) = 101 kPa and 0°C = 101.325 kPa and 273.15K (use 273K) Standard Ambient Temperature and Pressure (SATP) = 100 kPa and 25°C = 100 kPa and 298.15 K (use 298K)  Much closer to lab conditions

31. Remember  101.325 kPa =1 atm =760 mm Hg  T (K) = t (°C) + 273

32. Gas Laws  They are based on the temperature, pressure and volume relationships that all gases have in common 1. Boyle’s Law P 1 V 1 = P 2 V 2 2. Charles’ Law V 1 = V 2 T 1 = T 2 3. Combined Gas Law P 1 V 1 =P 2 V 2 T 1 = T 2

33. Charles’ Law Jacque Charles (1746- 1823) He made the first flight of a hydrogen balloon on August 27, 1783. This balloon was destroyed by terrified peasants when it landed outside of Paris.

34. Charles’ Law Shows the relationship between temperature (must be in Kelvin) and volume of gas if pressure and mass are constant This is a direct relationship: T = VT = V Charles’ Law states: “as the temperature of a gas increases, the volume increases proportionally, provided that the pressure and mass remain constant” Charles’ Equation : V 1 = V 2 T 1 = T 2

35. Charles’ Law  “As the temperature of a gas increases, the volume increases proportionally, provided that the pressure and mass remain constant”

36. Charles’ Law - Graphically When the graphs of several careful volume-temperature experiments are extrapolated, all the lines meet at absolute zero, 0K or -273° C

37. Charles’ Law - PRACTICE 1. A gas inside a cylinder with a movable piston is heated to 315°C. The initial volume of gas in the cylinder is 0.30 L at 25°C. What will be the final volume when the temperature is 315°C? * Remember temperature has to be in Kelvin

38. Charles Law Practice  A sample of neon gas has a volume of 25.0L at 25.0°C. What is the volume at 45.0° C?

39. Charles Law Practice  A sample of helium gas has a volume of 445 L at 30.0 ° C. To what temperature must the helium be heated to increase the volume to 500L?

40. The Combined Gas Law Combined Gas Law You can get Boyle’s Law back by assuming temperature is constant. You can get Charles’ Law back by assuming pressure is constant

41. The Combined Gas Law  When Boyle’s and Charles’ laws are combined, the resulting combined gas law produces a relationship among the volume, temperature, and pressure of any fixed mass of gas.  The combined gas law is a useful starting point for all cases with gases, even if one of the variables is a constant.  A variable that is constant can easily be eliminated from the combined gas law equation, reducing it back to Boyle’s or Charles’ Law

42. Combined Gas Law - Practice 1. A gas cylinder with a fixed volume contains a gas at a pressure of 652 kPa and a temperature of 25°C. If the cylinder is heated to 150°C, use the combined gas law to calculate the new pressure.

43. Combined Gas Law - Practice 2. A balloon containing helium gas at 20 °C and a pressure of 100 kPa has a volume of 7.50 L. Calculate the volume of the balloon after it rises 10 km into the upper atmosphere, where the temperature is –36 °C and the outside air pressure is 28 kPa. (Assume that no gas escapes and that the balloon is free to expand so that the gas pressure within it remains equal to the air pressure outside.)

44. Combined Gas Law Example  A sample of ethane gas has a volume of 35.0L at 25.0°C and 100.0 kPa. The temperature is increased to 35.0°C while the pressure drops to 85.0 kPa. What is the volume of the gas?

45. Combined Gas Law Practice  A sample of neon gas has a volume of 145mL at -10.0°C and 755mmHg. The temperature is increased to 45.0°C and the pressure is increased to 805mmHg. What is the new volume of the neon gas?

46. SUMMARY STP: 0 °C and 101.325 kPa (exact values) SATP: 25 °C and 100 kPa (exact values) 101.325 kPa = 1 atm = 760 mm Hg (exact values) absolute zero = 0 K or –273.15 °C K = (°C) + 273 (for calculation) Boyle’s Law P 1 V 1 = P 2 V 2 Charles’ Law V 1 = V 2 T 1 = T 2 Combined Gas Law P 1 V 1 = P 2 V 2 T 1 = T 2

47. Your Task  Complete the questions in your notes.

48. Kinetic Molecular Theory  According to the Kinetic Molecular Theory, the motion of molecules is different in solids, liquids and gases.  Solids- primarily vibrational motion.  Liquids- vibrational, rotational and some translational motion  Gases- the most important form of motion is translational

49. Kinetic Molecular Theory  Kinetic Molecular Theory explains: 1. Gases are compressible (due to most of a sample of gas being unoccupied space, thus particles can be forced closer together) 2. Gas pressure (due to pressure being the result of particle collisions distributed over walls of a container causing a force per unit area) 3. Boyle’s Law (due to reduced volume, there is a shorter distance between walls thus more frequent collisions, causing increased pressure) 4. Charles’ Law (due to increase in temperature, there is an increase in particle speed causing more collisions with the wall. The wall moves outward, thus volume increases)

50. The Law of Combining Volumes Joseph Gay-Lussac Amedeo Avogadro

51. Law of Combining Volumes  The kinetic molecular theory explains many physical properties of gases. But what about their chemical properties?  In 1809, Joseph Gay-Lussac, a colleague of Jacques Charles, measured the relative volumes of gases involved in chemical reactions.  His observations led to the Law of Combining Volumes, which states that:  “When measured at the same temperature and pressure, volumes of gaseous reactants and products of chemical reactions are always in simple ratios of whole numbers”  This is also known as the Gay-Lussac’s Law

53. The Law of Combining Volumes If two volumes of one gas react with one volume of another gas (at the same temp. and press.) the theory indicates that two molecules of the first react with one molecule of the second.

54. Gay-Lussac’s Law of Combining Volumes  A simple example of this is the decomposition of liquid water, in which the volumes of hydrogen and oxygen gas are always produced in a 2:1 ratio  Which side is Hydrogen? 2H 2 O (l)  2H 2(g) + O 2(g)

55. Law of Combining Volumes Example 1 Hydrogen and chlorine react to produce hydrogen chloride gas. What volume of hydrogen chloride gas will be produced from 10 L of chlorine and 10 L of hydrogen at a fixed temperature and pressure? H 2(g) + Cl 2(g) -> 2 HCl (g) thus: 20 L of HCl gas are produced

56. Law of Combining Volumes Example 2 Carbon monoxide gas is reacted with oxygen gas to produce carbon dioxide gas at a constant temperature and pressure. What is the volume ratio. 2 CO (g) + O 2(g) -> 2 CO 2(g) the volume ratio is: 2:1:2

57. Law of Combining Volumes Example 3 What volume of carbon dioxide will be produced if 4.5 mL of oxygen react? 2 CO (g) + O 2(g) -> 2 CO 2(g) Since all molecules are in the gas state we can apply the Law of Combining Volumes. - the volume ratio is: 1 O 2(g) :2 CO 2(g) so 4.5 mL of O 2(g) will produce 9 mL of CO 2(g)

58. Avogadro’s Theory  Two years after Gay-Lussac’s Law, Avogadro proposed an new explanation in terms of numbers of molecules  Avogadro proposed: “equal volumes of gases at the same temperature and pressure contain equal numbers of molecules”  This means the mole ratios provided by a balanced equation are also the volume ratios.  This in now best called Avogadro’s Theory

59. Avogadro’s Law This relationship applies only to gases

60. Avogadro’s Theory  When all gases are at the same temperature and pressure, the law of combining volumes provides an efficient way of predicting the volumes of gases in a chemical reaction. Coefficients: 132 Chemical Amounts: 1 mol 3 mol 2mol Volumes: 1 L3 L2 L Example:2 mL6 mL4 mL V H 2 : 2 ml x ( 3 ) = 6 mL 1 V NH 3 : 2 ml x ( 2 ) = 4 mL 1

61. Recall: STP & SATP  STP: 0 °C and 1 atm of pressure  SATP: 25 °C and 100 kPa of pressure.  Molar Volume of an ideal gas at:  STP is 22.4 L/mol  SATP is 24.8 L/mol

62. Example: Law of Combining Volumes Use the law of combining volumes to predict the volume of oxygen required for the complete combustion of 120 mL of butane gas from a lighter. 1) The first step is to write the balanced chemical equation, including what you are given and what you need to find: 2) From this chemical equation you can see that 13 mol of oxygen is required for every 2 mol of butane. Therefore, the volume of oxygen has to be greater than 120mL by a factor of 13/2. To make sure that the ratio is used in the correct order, you could include the chemical formula with each quantity as shown above. Note the cancellation of the units and chemical formulas

63. Example #2: Law of Combining Volumes A catalytic converter in the exhaust system of a car uses oxygen (from the air) to convert carbon monoxide to carbon dioxide, which is released through the tailpipe. If we assume the same temperature and pressure, what volume of oxygen is required to react with 125L of carbon monoxide during a 100 km trip? 1) The first step is to write the balanced chemical equation, including what you are given and what you need to find: 2) From this chemical equation you can see that 1 mol of oxygen is required for every 2 mol of carbon monoxide. Therefore, the volume of oxygen has to be less than 125L by a factor of 1/2. According to the law of combining volumes, of oxygen is required.

64. Learning Tip  This equivalence between the chemical amounts (coefficients) and the volumes only works for gases, and only if they are at the same temperature and pressure.

65.  This often involves integrating two or more concepts.  I.e. Boyle’s and Charles’ Laws were combined to create the Combined Gas Law  Similarly, Avogadro’s Theory and the Mole concept can also be combined:  Avogadro: “Equal volumes of any gases at the same temperature and pressure contain equal numbers of entities”  Therefore, for all gases at a specific temperature and pressure, there must be a certain volume, the molar volume, that contains one mole of entities  Molar Volume: the volume that one mole of a gas occupies at a specified temperature and pressure The Evolution of Scientific Knowledge

66.  Molar volume is the same for all gases at the same temperature and pressure (remember, all gases have the same physical properties)  At STP, molar volume = 22.4 L/mol (101.325 kPa and 0°C)  At SATP, molar volume = 24.8 L/mol (100 kPa and 25°C)  This can be used as a conversion factor just like molar mass! Molar Volume At STP, one mole of gas has a volume of 22.4 L, which is approximately the volume of 11 “empty” 2 L pop bottles. STP = 22.4L/mol SATP = 24.8 L/mol

67.  Chemists created the concept of molar volume to convert between volume and chemical amount Molar Volume as a Conversion Factor V n litres mol x 1 mol x L x x L 1 mol Remember the conversion factor will be different at STP and SATP!

68.  Why are we dealing with molar volume instead of molar mass ???  It’s a lot easier to measure the volume of a gas than trying to measure its mass.  You would have to trap the gas in a container and measure its mass on a balance and them make corrections for the buoyant force of the surrounding air... not easy Molar Volume

69. Molar Volume – Practice 1. Calculate the volume occupied by 0.024 mol of carbon dioxide at SATP. 2. What chemical amount of oxygen is available for a combustion reaction in a volume of 5.6 L at STP? STP = 22.4L/mol SATP = 24.8 L/mol

70. Molar Volume – Practice 3. What volume does 3.50 g of helium gas (He) occupy at SATP?  Once these calculations are clearly understood, they can be combined into a single calculation using unit analysis. All units except the final unit will cancel. STP = 22.4L/mol SATP = 24.8 L/mol

71. Molar Volume – Practice 4. A propane tank for a barbecue contains liquefied propane. IF the tank mass drops by 9.1 kg after a month’s use, what volume of propane gas at SATP was used for cooking?  What if I wanted your answer in litres? STP = 22.4L/mol SATP = 24.8 L/mol

72. Summary STP = 22.4L/mol SATP = 24.8 L/mol Molar volume : the volume that one mole of a gas occupies at a specified temperature and pressure

73. Your Task

74. Fantasy vs. Reality

75. Ideal vs. Real Gas  An ideal gas behaves perfectly under ALL conditions of pressure, temperature and volume  This means it;  Must not condense to a liquid when cooled  Their graphs of V vs. T & P vs. T must be perfectly straight lines.  Collide with perfectly elastic collisions  Have particles of zero size that have no forces of attraction between them  For example, ideal gases do not condense into liquids

76. Real Gases  Real gases deviate from most ideal gases at lower temperatures or higher pressures, when intermolecular forces and molecular size become important.  Low temperature and high pressures cause gasses to move more slowly and become more dense thus they deviate from ideal behavior.  As temperature increases and pressure decreases, real gases behave more ideally.  Small gas molecules behave more ideally than large gas molecules

77. Real vs. Ideal Gases Real GasIdeal Gas Molecules have a distinct size and are “soft”Molecules are point masses (have no size) and are “hard” Forces of attraction between molecules cause them to condense into a liquid if the temperature gets low enough Molecules do not have forces of attraction among them so there is no cause for them to condense into liquid Molecules move about randomly but because of the attraction between them, they don’t travel in straight lines- they are influenced by each other Molecules of gas move about randomly; only collisions with container walls and other molecules cause them to change direction Collisions between molecules are inelastic- kinetic energy isn’t conserved Collisions between molecules are elastic- kinetic energy is conserved

78. Ideal Gas Law  Describes the interrelationship of pressure, temperature, volume and amount (moles) of matter; the four variables that define a gas system  REMEMBER:  Boyle’s Law : Volume is inversely proportional ( α) to pressure V α 1/P  Charles ’ Law : Volume is directly proportional to temperature V α T  Avogadro’s Theory : Volume is directly proportional to chemical amount (mol) V α n

79. Ideal Gas Law  Combining the Combined Gas Law and Avogadro’s Law results in the Ideal Gas Law:

80. R = universal gas constant  Depends on STP or SATP, atm or kPa  Units: L kPa/mol Kvalue = 8.314 L kPa/mol K  Units: L atm/mol Kvalue = 0.0821 L atm/mol K Make sure you look at the unit for pressure to decide which R value to use  Any idea how we came up with the number??  You substitute SATP or STP conditions for one mole into the ideal gas law and solve for R

81. Using the Ideal Gas Law  When solving for the ideal gas law, start by listing your variables. If three are known of the four, you can solve for the last one. Example One : What mass of neon gas should be introduced into an evacuated 0.88L tube to produce a pressure of 90 kPa at 30°C?

82. Ideal Gas Law – Practice  A rigid steel cylinder with a volume of 2.00 L is filled with nitrogen gas to a final pressure of 20.0 atm at 27°C. How many moles of N2 gas does the cylinder contain?

83. Example  Predict the volume occupied by 0.78 g of hydrogen at 22°C and 125 kPa

84. Example  What is the volume of 3.35 mol of neon at 42.5°C and 96.5 kPa?

85. Example  What is the volume of 66.4g of carbon dioxide gas at 32.0 °C and 115 kPa?