Section 5.1 Pressure. Why study gases? An understanding of real world phenomena. An understanding of how science works.

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1 Chapter 5 Gases

2 Section 5.1 Pressure Why study gases? An understanding of real world phenomena. An understanding of how science works. Copyright Cengage Learning. All rights reserved 2

3 Section 5.1 Pressure A Gas Uniformly fills any container. Easily compressed. Mixes completely with any other gas. Exerts pressure on its surroundings. Copyright Cengage Learning. All rights reserved 3

4 Section 5.1 Pressure Pressure force Pr essure = area SI units = Newton/meter 2 = 1 Pascal (Pa) 1 standard atmosphere = 101,325 Pa 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr Copyright Cengage Learning. All rights reserved 4

5 Section 5.1 Pressure Barometer Device used to measure atmospheric pressure. Mercury flows out of the tube until the pressure of the column of mercury standing on the surface of the mercury in the dish is equal to the pressure of the air on the rest of the surface of the mercury in the dish. Copyright Cengage Learning. All rights reserved 5

6 Chapter 5 Manometer Device used for measuring the pressure of a gas in a container. Copyright Cengage Learning. All rights reserved 6

8 Section 5.1 Pressure Pressure Conversions: An Example The pressure of a gas is measured as 2.5 atm. Represent this pressure in both torr and pascals. 760 torr atm = torr 1 atm 101,325 Pa atm = Pa 1 atm Copyright Cengage Learning. All rights reserved 8

10 Section 5.2 The Gas Laws of Boyle, Charles, and Avogadro Liquid Nitrogen and a Balloon What happened to the gas in the balloon? A decrease in temperature was followed by a decrease in the pressure and volume of the gas in the balloon. Copyright Cengage Learning. All rights reserved 10

11 Section 5.2 The Gas Laws of Boyle, Charles, and Avogadro Liquid Nitrogen and a Balloon This is an observation (a fact). It does NOT explain why, but it does tell us what happened. Copyright Cengage Learning. All rights reserved 11

12 Section 5.2 The Gas Laws of Boyle, Charles, and Avogadro Gas laws can be deduced from observations like these. Mathematical relationships among the properties of a gas (Pressure, Volume, Temperature and Moles) can be discovered. Copyright Cengage Learning. All rights reserved 12

13 Section 5.2 The Gas Laws of Boyle, Charles, and Avogadro Boyle s Law Pressure and volume are inversely related (constant T, temperature, and n, # of moles of gas). PV = k (k is a constant for a given sample of air at a specific temperature) P V = P V Copyright Cengage Learning. All rights reserved 13

15 Section 5.2 The Gas Laws of Boyle, Charles, and Avogadro EXERCISE! A sample of helium gas occupies 12.4 L at 23 C and atm. What volume will it occupy at 1.20 atm assuming that the temperature stays constant? 9.88 L Copyright Cengage Learning. All rights reserved 15

16 Section 5.2 The Gas Laws of Boyle, Charles, and Avogadro Charles s Law Volume and Temperature (in Kelvin) are directly related (constant P and n). V=bT (b is a proportionality constant) K = C K is called absolute zero. V T = V T Copyright Cengage Learning. All rights reserved 16

18 Section 5.2 The Gas Laws of Boyle, Charles, and Avogadro EXERCISE! Suppose a balloon containing 1.30 L of air at 24.7 C is placed into a beaker containing liquid nitrogen at 78.5 C. What will the volume of the sample of air become (at constant pressure)? L Copyright Cengage Learning. All rights reserved 18

19 Section 5.2 The Gas Laws of Boyle, Charles, and Avogadro Avogadro s Law Volume and number of moles are directly related (constant T and P). V = an (a is a proportionality constant) n V = n 1 2 V 1 2 Copyright Cengage Learning. All rights reserved 19

20 Section 5.2 The Gas Laws of Boyle, Charles, and Avogadro EXERCISE! If 2.45 mol of argon gas occupies a volume of 89.0 L, what volume will 2.10 mol of argon occupy under the same conditions of temperature and pressure? 76.3 L Copyright Cengage Learning. All rights reserved 20

21 Section 5.3 The Ideal Gas Law We can bring all of these laws together into one comprehensive law: V = bt (constant P and n) V = an (constant T and P) V = k (constant T and n) P PV = nrt (where R = L atm/mol K, the universal gas constant) Copyright Cengage Learning. All rights reserved 21

22 Section 5.3 The Ideal Gas Law EXERCISE! An automobile tire at 23 C with an internal volume of 25.0 L is filled with air to a total pressure of 3.18 atm. Determine the number of moles of air in the tire mol Copyright Cengage Learning. All rights reserved 22

23 Section 5.3 The Ideal Gas Law EXERCISE! What is the pressure in a L tank that contains kg of helium at 25 C? 114 atm Copyright Cengage Learning. All rights reserved 23

24 Section 5.3 The Ideal Gas Law EXERCISE! At what temperature (in C) does 121 ml of CO 2 at 27 C and 1.05 atm occupy a volume of 293 ml at a pressure of 1.40 atm? 696 C Copyright Cengage Learning. All rights reserved 24

25 Section 5.4 Gas Stoichiometry Molar Volume of an Ideal Gas For 1 mole of an ideal gas at 0 C and 1 atm, the volume of the gas is L mol L atm/k mol K nrt V = = = L P atm STP = standard temperature and pressure 0 C and 1 atm Therefore, the molar volume is L at STP. Copyright Cengage Learning. All rights reserved 25

26 Section 5.4 Gas Stoichiometry EXERCISE! A sample of oxygen gas has a volume of 2.50 L at STP. How many grams of O 2 are present? 3.57 g Copyright Cengage Learning. All rights reserved 26

27 Section 5.4 Gas Stoichiometry Molar Mass of a Gas Molar mass = drt P g L atm K g L mol K = = atm mol d = density of gas T = temperature in Kelvin P = pressure of gas R = universal gas constant Copyright Cengage Learning. All rights reserved 27

28 Section 5.4 Gas Stoichiometry EXERCISE! What is the density of F 2 at STP (in g/l)? 1.70 g/l Copyright Cengage Learning. All rights reserved 28

29 Section 5.5 Dalton s Law of Partial Pressures For a mixture of gases in a container, P Total = P 1 + P 2 + P The total pressure exerted is the sum of the pressures that each gas would exert if it were alone. Copyright Cengage Learning. All rights reserved 29

31 Section 5.5 Dalton s Law of Partial Pressures EXERCISE! Consider the following apparatus containing helium in both sides at 45 C. Initially the valve is closed. After the valve is opened, what is the pressure of the helium gas? 2.00 atm 9.00 L 3.00 atm 3.00 L Copyright Cengage Learning. All rights reserved 31

32 Section 5.5 Dalton s Law of Partial Pressures EXERCISE! 27.4 L of oxygen gas at 25.0 C and 1.30 atm, and 8.50 L of helium gas at 25.0 C and 2.00 atm were pumped into a tank with a volume of 5.81 L at 25 C. Calculate the new partial pressure of oxygen atm Calculate the new partial pressure of helium atm Calculate the new total pressure of both gases atm Copyright Cengage Learning. All rights reserved 32

33 Section 5.6 The Kinetic Molecular Theory of Gases So far we have considered what happens, but not why. In science, what always comes before why. Copyright Cengage Learning. All rights reserved 33

34 Section 5.6 The Kinetic Molecular Theory of Gases Postulates of the Kinetic Molecular Theory 1) The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be negligible (zero). Copyright Cengage Learning. All rights reserved 34

35 Section 5.6 The Kinetic Molecular Theory of Gases Postulates of the Kinetic Molecular Theory 2) The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas. Copyright Cengage Learning. All rights reserved 35

36 Section 5.6 The Kinetic Molecular Theory of Gases Postulates of the Kinetic Molecular Theory 3) The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other. Copyright Cengage Learning. All rights reserved 36

37 Section 5.6 The Kinetic Molecular Theory of Gases Postulates of the Kinetic Molecular Theory 4) The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas. Copyright Cengage Learning. All rights reserved 37

38 Section 5.6 The Kinetic Molecular Theory of Gases Kinetic Molecular Theory To play movie you must be in Slide Show Mode PC Users: Please wait for content to load, then click to play Mac Users: CLICK HERE Copyright Cengage Learning. All rights reserved 38

39 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! You are holding two balloons of the same volume. One contains helium, and one contains hydrogen. Complete each of the following statements with different or the same and be prepared to justify your answer. He H 2 Copyright Cengage Learning. All rights reserved 39

40 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! The pressures of the gas in the two balloons are. He H 2 Copyright Cengage Learning. All rights reserved 40

41 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! The temperatures of the gas in the two balloons are. He H 2 Copyright Cengage Learning. All rights reserved 41

42 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! The numbers of moles of the gas in the two balloons are. He H 2 Copyright Cengage Learning. All rights reserved 42

43 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! The densities of the gas in the two balloons are. He H 2 Copyright Cengage Learning. All rights reserved 43

44 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! Sketch a graph of: I. Pressure versus volume at constant temperature and moles. Copyright Cengage Learning. All rights reserved 44

45 Section 5.6 The Kinetic Molecular Theory of Gases Molecular View of Boyle s Law To play movie you must be in Slide Show Mode PC Users: Please wait for content to load, then click to play Mac Users: CLICK HERE Copyright Cengage Learning. All rights reserved 45

46 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! Sketch a graph of: II. Volume vs. temperature ( C) at constant pressure and moles. Copyright Cengage Learning. All rights reserved 46

47 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! Sketch a graph of: III. Volume vs. temperature (K) at constant pressure and moles. Copyright Cengage Learning. All rights reserved 47

48 Section 5.6 The Kinetic Molecular Theory of Gases Molecular View of Charles s Law To play movie you must be in Slide Show Mode PC Users: Please wait for content to load, then click to play Mac Users: CLICK HERE Copyright Cengage Learning. All rights reserved 48

49 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! Sketch a graph of: IV. Volume vs. moles at constant temperature and pressure. Copyright Cengage Learning. All rights reserved 49

50 Section 5.6 The Kinetic Molecular Theory of Gases Molecular View of the Ideal Gas Law To play movie you must be in Slide Show Mode PC Users: Please wait for content to load, then click to play Mac Users: CLICK HERE Copyright Cengage Learning. All rights reserved 50

51 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! V Ne = 2V Ar Ne Which of the following best represents the mass ratio of Ne:Ar in the balloons? 1:1 1:2 2:1 1:3 3:1 Copyright Cengage Learning. All rights reserved 51 Ar

52 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! You have a sample of nitrogen gas (N 2 ) in a container fitted with a piston that maintains a pressure of 6.00 atm. Initially, the gas is at 45 C in a volume of 6.00 L. You then cool the gas sample. Copyright Cengage Learning. All rights reserved 52

53 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! Which best explains the final result that occurs once the gas sample has cooled? a) The pressure of the gas increases. b) The volume of the gas increases. c) The pressure of the gas decreases. d) The volume of the gas decreases. e) Both volume and pressure change. Copyright Cengage Learning. All rights reserved 53

54 Section 5.6 The Kinetic Molecular Theory of Gases CONCEPT CHECK! The gas sample is then cooled to a temperature of 15 C. Solve for the new condition. (Hint: A moveable piston keeps the pressure constant overall, so what condition will change?) 5.43 L Copyright Cengage Learning. All rights reserved 54

55 Section 5.6 The Kinetic Molecular Theory of Gases Root Mean Square Velocity u rms = 3RT M R = J/K mol (J = joule = kg m 2 /s 2 ) T = temperature of gas (in K) M = mass of a mole of gas in kg Final units are in m/s. Copyright Cengage Learning. All rights reserved 55

56 Section 5.7 Effusion and Diffusion Diffusion the mixing of gases. Effusion describes the passage of a gas through a tiny orifice into an evacuated chamber. Rate of effusion measures the speed at which the gas is transferred into the chamber. Copyright Cengage Learning. All rights reserved 56

60 Section 5.7 Effusion and Diffusion Graham s Law of Effusion Rate Rate of of effusion effusion for for gas 1 gas 2 M M 2 1 M 1 and M 2 represent the molar masses of the gases. Copyright Cengage Learning. All rights reserved 60

61 Section 5.8 Real Gases An ideal gas is a hypothetical concept. No gas exactly follows the ideal gas law. We must correct for non-ideal gas behavior when: Pressure of the gas is high. Temperature is low. Under these conditions: Concentration of gas particles is high. Attractive forces become important. Copyright Cengage Learning. All rights reserved 61

63 Section 5.8 Real Gases Plots of PV/nRT Versus P for Nitrogen Gas at Three Temperatures Copyright Cengage Learning. All rights reserved 63

64 Section 5.8 Real Gases Real Gases (van der Waals Equation) [ P a ( n / V ) ] V nb nrt obs 2 corrected pressure corrected volume P ideal V ideal Copyright Cengage Learning. All rights reserved 64

65 Section 5.9 Characteristics of Several Real Gases For a real gas, the actual observed pressure is lower than the pressure expected for an ideal gas due to the intermolecular attractions that occur in real gases. Copyright Cengage Learning. All rights reserved 65

66 Section 5.9 Characteristics of Several Real Gases Values of the van der Waals Constants for Some Gases The value of a reflects how much of a correction must be made to adjust the observed pressure up to the expected ideal pressure. A low value for a reflects weak intermolecular forces among the gas molecules. Copyright Cengage Learning. All rights reserved 66

67 Section 5.10 Chemistry in the Atmosphere Air Pollution Two main sources: Transportation Production of electricity Combustion of petroleum produces CO, CO 2, NO, and NO 2, along with unburned molecules from petroleum. Copyright Cengage Learning. All rights reserved 67

68 Section 5.10 Chemistry in the Atmosphere Nitrogen Oxides (Due to Cars and Trucks) At high temperatures, N 2 and O 2 react to form NO, which oxidizes to NO 2. The NO 2 breaks up into nitric oxide and free oxygen atoms. Oxygen atoms combine with O 2 to form ozone (O 3 ). 2 Radiant energy NO ( g ) NO( g ) O( g ) O( g ) O ( g ) O ( g) 2 3 Copyright Cengage Learning. All rights reserved 68

69 Section 5.10 Chemistry in the Atmosphere Concentration for Some Smog Components vs. Time of Day Copyright Cengage Learning. All rights reserved 69

70 Section 5.10 Chemistry in the Atmosphere Sulfur Oxides (Due to Burning Coal for Electricity) Sulfur produces SO 2 when burned. SO 2 oxidizes into SO 3, which combines with water droplets in the air to form sulfuric acid. S(in coal) O ( g) SO ( g) 2 2 2SO ( g ) O ( g ) 2SO ( g) SO ( g ) H O( l ) H SO ( aq) Copyright Cengage Learning. All rights reserved 70

71 Section 5.10 Chemistry in the Atmosphere Sulfur Oxides (Due to Burning Coal for Electricity) Sulfuric acid is very corrosive and produces acid rain. Use of a scrubber removes SO 2 from the exhaust gas when burning coal. Copyright Cengage Learning. All rights reserved 71

Chapter 5: Gases 5.1 Pressure Why study gases? An understanding of real world phenomena. An understanding of how science works.

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