1. Gases Chem II Chapter 10

2. Characteristics of Gases

3. 1. Substances that are typically solids or liquids at room temperature are referred to as vapors. (mercury vapor, water vapor, etc.)

4. Characteristics of Gases a.Low molar mass b.Expand spontaneously to fill its container c. Form homogenous mixtures with each other regardless of the identities or relative proportions of the component gases.

5. Pressure Pressure is defined as _________ per unit __________.

6. Pressure 2.Pressure is defined as force per unit _area. Formula : P = F/A

8. Pressure 3.Gas particles exert pressure when they collide with themselves or with their container.

9. Pressure 4. B/c the particles in air move in every direction, they exert pressure in all directions.

10. Figure 10.01

11. Pressure 5. This type of pressure is called atmospheric pressure.

12. Measuring Pressure 6.Italian physicist Evangelista Torricelli (1608 – 1647) was the first to demonstrate that air exerted pressure.

13. Measuring Pressure 7. The device that Toricelli developed was called the barometer.

14. Figure 10.02

15. Measuring Pressure 8. A barometer is an instrument used to measure atmospheric pressure.

16. Measuring Pressure 9.Gravity pulls down on the column of mercury.

17. Measuring Pressure 10. A manometer is an instrument used to measure gas pressure in a closed container.

18. Figure 10.03

19. Measuring Pressure When the valve between the flask and the u tube is open, gas particles diffuse out of the flask and push the mercury in the tube.

20. Measuring Pressure 11. The different heights of the mercury in the two arms is used to calculate the pressure of gas in the flask.

22. Units of Pressure 12.The SI unit for pressure is the Pascal - one newton of force per one square meter. ( 1N/m 2 )

23. Units of Pressure 13. More traditional units include: a. psi - pounds per square inch b.mmHg- millimeters of mercury c. torr = 1 mmHg 1atm = 1 atmosphere = 760 mmHg = 760 torr d.barr - 1 x 10 5 pascal

24. 1 atm = 760 torr= 760 mmHg=101.3 Kpa=1.013 barr 14. Standard atmospheric pressure ( typical pressure at sea level) is 760 torr or 1.01325 x 10 5 Pa.

25. Practice conversion A.).357 atmospheres to torr B.) 6.6 x 10 -2 torr to atmospheres C.) 147.2 KPa to torr D.) 745 torr to KPa E.).975 atmosphere to Pa and then to KPa

27. On a certain day the barometer in a laboratory indicates that the atmospheric pressure is764.7 torr. A sample of gas is placed in a vessel attached to an open-end mercury manometer. The level of the mercury in the open end arm of the manometer has a measured height of 136.4 mm and that in the arm that is in contact with the gas a height of 103.8 mm. What is the pressure of the gas in amospheres and in KPa?

28. The Gas Laws Boyles Law: 4 variables define the condition (state ) of a gas. * Temperature (T) * Pressure ( P) * amount of gas ( n) * volume (V)

29. The Gas Laws 15. The equations that relate these variables are known as the gas laws: * Boyles * Charles * Gay Lussac * Combined * Ideal

30. Boyles Law : Pressure - Volume Relationship 16. The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure.

31. Boyles Law : Pressure - Volume Relationship The volume of a fixed quantity of gas maintained at constant temperature is inversely proportional to the pressure

32. Boyles Law : Pressure - Volume Relationship 17. V = constant x 1/P or PV = constant Boyles Law: P 1 V 1 = P 2 V 2

33. Boyles Law : Pressure - Volume Relationship Robert Boyles made very careful measurements at constant temperature and proved that increasing the pressure by two reduces the volume by ½ : decreasing the pressure by ½ increases the volume by 2.

34. Boyles Law : Pressure - Volume Relationship PV = constant at constant temperature.

35. Example: A sample of helium gas in a balloon is compressed from 4L to 2.5 L at a constant temperature. If the pressure of the gas in the 4L volume is 210 kPa, what will be the pressure at 2.5L?

36. Charles Law Temperature and Volume Relationship

37. 18.The French physicist Jacques Charles (1746- 1823) studied the relationship between volume and pressure.

38. Charles Law Temperature and Volume Relationship 19. When the temperature increases the molecules move fast and hit the walls of the container more often and with more force. If pressure remains constant, the volume must increase.

39. Charles Law Temperature and Volume Relationship 20.Charles Law states: The volume of a given mass of a gas is directly proportional to its Kelvin temperature at constant pressure. V 1 = V 2 T 1 T 2

40. Charles Law Temperature and Volume Relationship The temperature must be expressed in __________________ Tk = 273 + Tc

41. Charles Law Temperature and Volume Relationship 21.The temperature must be expressed in Kelvin. Tk = 273 + Tc

42. Charles Law example A gas sample at 40º C occupies a volume of 2.32 L. If the temperature is raised to 75º C, What will the volume be, assuming pressure is constant?

43. Gay – Lussac’s Law : Temperature and pressure 22. The pressure of a given mass of gas varies directly with Kelvin temperature.

44. Gay – Lussac’s Law : Temperature and pressure When the pressure remains constant… P 1 = P 2 T 1 T 2

45. Example Gay-Lussac problem The pressure of a gas in a tank is 3.2 atm @ 22º C If the temperature raises to 60º C, What will be the gas pressure in the tank?

46. Combined gas Law : 23. The Combined gas law states the relationship among pressure, volume and temperature of a fixed amount of gas. P 1 V 1 = P 2 V 2 T 1 T 2

47. Example Combined Gas Law A gas at 110 kPa and 30 º C fills a flexible container with an initial volume of 2L. If the temperature is raised to 80 º C and the pressure increased to 440kPa, what is the new volume?

48. 24.Avogadro’s Principle : Equal volumes of gas at the same temperature and pressure contain equal numbers of particles.

49. Avogadro’s Principle : 25. The molar volume for a gas is the volume that one mole occupies at 0ºC and 1 atm. of pressure.

50. Avogadro’s Principle : 26. 1 mole of any gas at standard temperature and pressure (STP) will occupy 22.4 L.

52. Avogadro’s Principle : 22.4 L is known as the molar volume

53. Example a. Calculate the volume that.881 mol of gas at STP will occupy.

54. Example b.Calculate the volume that 2kg of methane gas (CH 4 ) will occupy at STP.

55. Ideal Gas Law 27.The laws of Avogadro, Boyle, Charles and Gay-Lussac can be combined to form the ________ ______ _______: PV = nRT P = pressure V = volume n = number of moles R = the gas constant T= temp in Kelvin

56. Ideal Gas Law 28.Each of the four variables will affect the others. These variables are all interrelated/ connected

57. R represents the gas constant UnitsNumerical value L atm /mol K 0.08206 J / mol K 8.314 cal / mol K1.987 m 3 Pa/ mol K8.314 L torr /mol K62.36

58. R represents the gas constant UnitsNumerical value L atm /mol K 0.08206 J / mol K 8.314 cal / mol K1.987 m 3 Pa/ mol K8.314 L torr /mol K62.36

59. PV = nRT The above equation is known as the ideal gas equation. This equation would work for an ideal gas which is hypothetical.

60. 29.Ideal gases have no intermolecular attractive forces and the particles take up no space. 30.No gas is truly ideal.

61. Calcium carbonate CaCO 3 (s) decomposes upon heating to give CaO (s) and CO 2(g), A sample of CaCO 3 is decomposed and the carbon dioxide is collected in a 250mL flask. After the decomposition is complete, the gas has a pressure of 1.3 atm at a temperature of 31ºC How many moles of CO 2 gas were generated? Example 10.4 ( page 376)

62. Practice Tennis balls are usually filled with air or N 2 gas to a pressure above atmospheric pressure to increase their “bounce” If a particular tennis ball has a volume of 144 cm 3 and contains 0.33 g of N 2 gas, what is the pressure inside the ball at 24 º C?

63. Example 10.5 The gas pressure in an aerosol can is 1.5 atm. at 25ºC. Assuming that the gas inside obeys the ideal gas equation, what would the pressure be if the can were heated to 450ºC?

64. A large natural gas storage tank is arranged so that the pressure is maintained at 2.20 atm. On a cold day in December when the temperature is -15ºC (4ºF), the volume of gas in the tank is 28,500 ft 3. What is the volume of the same quantity of gas on a warm July day when the temperature is 31ºC (88ºF)?

65. Example 10.6 An inflated balloon has a volume of 6.0 L at sea level (1 atm) and is allowed to ascend in altitude until the pressure is 0.45 atm. During ascent the temperature of the gas falls from 22ºC to -21ºC. Calculate the volume of the balloon at its final altitude.

66. Gas Densities and Molar Mass 31.Density is mass per unit volume.

67. Gas Densities and Molar Mass Rearrange the ideal gas law (Pv=nRT) n = P V RT

68. Gas Densities and Molar Mass n = P V RT n/V would have the units moles/ L If you multiply both sides by molar mass ( grams/ mole)

69. Gas Densities and Molar Mass Moles grams Liter Mole the units become grams Liter which are the units for density.

70. Gas Densities and Molar Mass Density = P M R T The density of a gas depends on its pressure, __molar mass and temperature.

71. Gas Densities and Molar Mass Density = P M R T The density of a gas depends on its pressure, __molar mass and temperature.

72. Gas Densities and Molar Mass * as pressure and molar mass increase the density increases * as temperature increases the density decreases.

73. Example 10.7 What is the density of carbon tetrachloride vapor at 714 torr and 125 ºC?

74. The mean molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6 g/mol. The surface temperature is 95K, and the pressure is 1.6 atm. Assuming ideal behavior, calculate the density to Titan’s atmosphere.

75. Example 10.8 A series of measurements are made in order to determine the molar mass of an unknown gas. Fist, a large flask is evacuated and found weigh 134.567 g. It is then filled with the gas to a pressure of 735 torr at 31º C and reweighed; its mass is now 137.456 g. Finally, the flask is filled with water at 31ºC and found to weigh 1067.9 g. ( The density of the water at this temperature is 0.997 g/mL) Assuming that the ideal gas equation applies, calculate the molar mass of the unknown gas.

76. Calculate the average molar mass of dry air if it has a density of 1.17 g/L at 21ºC and 740.0 torr.

77. Example 10.9 The safety air bags in cars are inflated by nitrogen gas generated by the rapid decomposition of sodium azide, NaN 3 ; 2NaN 3(s) → 3 N 2(g) + 2 Na (s) If an air bag has a volume of 36L and is filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26.0ºC, how many gram of NaN 3 must be decomposed?

78. Ammonia is synthesized from hydrogen and nitrogen N 2 + 3H 2 → 2NH 3 If 5L of nitrogen reacts completely by this reaction at constant temperature and pressure of 3 atm and 298K, how many grams of NH 3 are produced?

79. Gas Mixtures and Partial Pressures. Daltons Law of Partial Pressures 32.The total pressure of a mixture of gases is equal to the sum of the pressures of all of the gases in the mixture. P total = P 1 + P 2 + P 3 + …. P n

80. Gas Mixtures and Partial Pressures. A mixture of oxygen gas (O 2 ), carbon dioxide (CO 2 ) and nitrogen (N 2 ) has a total pressure of.97 atm. What is the partial pressure of O 2 if the partial pressure of CO 2 is.7 atm and the partial pressure of N 2 is.12 atm.

81. Example 10.10 A gaseous mixture made from 6.00 g O 2 and 9.00 g CH 4 is placed in a 15.0 L vessel at 0ºC What is the partial pressure of each gas and what is the total pressure in the vessel?

82. Example 10.10 What is the total pressure exerted by a mixture of 2.00 g of H 2 and 8.00 g N 2 at 273K in a 10.0 L vessel?

83. Partial Pressure and Mole Fractions 33. We can relate the amount of a given gas in a mixture to its partial pressure.

84. Partial Pressure and Mole Fraction P 1 = n 1 RT/V = n 1 P t n t RT/V n t

85. Partial Pressure and Mole Fraction 34. The ratio n 1 / n t is called the _mole_fraction of gas 1, which we denote X 1.

86. Partial Pressure and Mole Fraction 35. The mole fraction, X, is a dimensionless number that expresses the _ratio_of the number of moles of one component to the total number of moles in the mixture.

87. For example, The mole fraction of N 2 in air is.78 (78% of the molecules are N 2 ) If the barometric pressure is 760 torr then the partial pressure of N 2 is :.78 ( 760 torr) = 590 torr.

88. Example 10.11 A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5 mol percent CO 2, 18.0 mol percent O 2, and 80.5 mol percent Ar. (a) calculate the partial pressure of O 2 in the mixture if the total pressure of the atmosphere is to be 745 torr. (b) If this atmosphere is to be held in a 120L space at 295 K how many moles of O 2 are needed?

89. Collecting Gases over water 36. The total pressure inside the inverted container is the sum of the pressure of gas collected and the pressure of water vapor in equilibrium with liquid water.

92. Collecting Gases over water P total = P gas + P H20

93. Collecting Gases over water P total = P gas + P H20 Appendix B has a listing of the pressure exerted by water vapor at various temperatures.

94. A sample of KClO 3 is partially decomposed producing O 2 gas that is collected over water. The volume of gas collected is.250L at 26º C and 765 torr total pressure. (a) How many moles of O 2 are collected? (b) How many grams of KClO 3 were decomposed? Example 10.12

95. 37. The Kinetic Molecular Theory assumes the following concepts about gases are true a) Gas particles do not attract or repel each other. Kinetic Molecular Theory

96. b.) Gas particles are much smaller than the distances between them ( the particles take up virtually no space) Kinetic Molecular Theory

97. c.) Gas particles are in constant, random motion Kinetic Molecular Theory

98. d) No kinetic energy is lost when gas particles collide with each other or with the walls of the container Kinetic Molecular Theory

99. e.)All gases have the same average kinetic energy at a given temperature. Kinetic Molecular Theory

100. 38.Pressure is caused by collisions of molecules with the wall of the container. The magnitude of the pressure is determined by both how often and how forcefully the molecules strike the wall. E= ½ mu 2 where u is the average mean squared speed. E is the kinetic energy. Kinetic Molecular Theory

101. E= ½ mu 2 where u is the average mean squared speed. E is the kinetic energy. Kinetic Molecular Theory

102. 39.Kinetic molecular theory explains Boyles law because when volume increases there are fewer collisions with container wall so pressure decreases. Kinetic Molecular Theory

103. 40. Gay – Lussac’s law ( P 1 /T 1 = P 2 /T 2 ) is explained because when temperature is increased at constant volume, the particles have more kinetic energy and strike the container more often and forcefully. Therefore, pressure increases. Kinetic Molecular Theory

104. A sample of O 2 gas initially at STP is compressed to a smaller volume at constant temperature. What effect does this change have on (a) the average kinetic energy of O 2 molecules (b) the average speed of O 2 molecules(c) the total number of collisions of O 2 molecules with the container walls in a unit of time. (d) the number of collisions of O 2 molecules with a unit area of container wall per unit time? Example 10.13

105. (a)Average kinetic energy is dependent on temperature so compression doesn’t affect kinetic energy. (b)If average kinetic energy remains the same, speed remains the same. Example 10.13

106. ( c) number of collisions increases because the molecules are in a smaller volume (d) # of collisions increases. Example 10.13

107. 41.The random motion of gas particles causes the gases to mix until they are evenly distributed. Molecular Effusion and Diffusion

108. 42.Diffusion is the term used to describe the movement of one material through another. Molecular Effusion and Diffusion

109. 43.Effusion is related to the diffusion. During effusion a gas escapes through an opening Molecular Effusion and Diffusion

111. 44.Both diffusion and effusion are dependent on mass( size) of the particles. Molecular Effusion and Diffusion

113. Rate of effusion α 1 /√molar mass b / molar mass A The rate of effusion of gasses is proportional to the inverse of the square of their molar masses. 45.Grahams Law of Effusion

114. Ammonia has a molar mass of 17 g/mol. Hydrogen chloride has a molar mass of 36.5 g/mol. What is the ratio of their diffusion rates? For example

115. 46.According to the kinetic molecular theory, all gases at the same temperature have the same kinetic energy. Since all gases have different masses, that means the velocity of the particles must be different. KE = ½ mv 2

116. 47. The lighter particles must have greater speed.

118. U = √ 3RT/M U = root mean square speed ( rms) R = gas constant T = temperature in kelvin M= molar mass

119. 48. b/c M is in the denominator, the greater the mass the smaller the speed. The larger the temp, the larger the speed. ( page 390 – Figure 10.19)

120. Example problem 10.14 Calculate the rms of an N 2 molecule at 25ºC.

121. 49. Diffusion, like effusion is faster for light molecules.

122. In 1846, Thomas Graham discovered that the effusion rate of a gas is inversely proportional to the square of its molar mass. The rates of diffusion of the two gases ( r 1 and r 2 ) are inversely proportional to the square of their respective molar masses. r 1 / r 2 = √M 2 /M 1

123. Example 10.15 An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only.355 times that of O 2 at the same temperature. What is the identity of the unknown gas?

124. Real Gases: Deviations from Ideal Behavior

125. 50.In order for a gas to behave according to ideal gas laws predict, the molecules of gas can occupy no space and have no intermolecular attraction

126. 51.At very high pressures and low temperatures gases display non-ideal behavior.

127. 52.At lower pressures ( lower than 10 atmospheres) the deviation is low enough to neglect..

128. 53.As temperature increases, the properties of a gas more nearly approach that of an ideal gas. As temperatures increase, the forces of attraction become less significant.

129. 54.As temperature increases, the properties of a gas more nearly approach that of an ideal gas. As temperatures increase, the forces of attraction become less significant.

130. Engineers and scientists who work with gases at high pressures or low temperatures cannot use the ideal gas equation.

131. Johannes Van der Waals developed an equation to predict the behavior of real gases

132. Van der Waals equation: P = (nRT/V – nb ) - ( n 2 a/v 2 ) Correction for volume of correction for molecular Moleculesattraction

133. Van der Waals equation: P = (nRT/V – nb ) - ( n 2 a/v 2 ) Correction for volume of correction for molecular Moleculesattraction

134. 54. volume is decreased by nb. “b” is a measure of the actual volume occupied by a mole of gas molecules.

135. 55.Pressure is decreased by the factor n 2 a/v 2 which accounts for the attractive force between gas molecules.

136. Look at table 10.3 Notice that the larger molecules not only have larger volumes, but also greater intermolecular forces.