Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Copyright © 2010 Pearson Prentice Hall, Inc. Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Gases and Gas Pressure Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Mercury is used in barometers because of its density: 13.6 g/mL. A corresponding water barometer would be 3 stories high! The Journal of Chemical Education published an article about constructing one: de Grys, Hans; Thirty Feet and Rising: Constructing and Using a Water Barometer To Explore Chemical Principles; J. Chem. Educ. 2003, 80, 1156. Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Gases and Gas Pressure Unit area Force Pressure: Conversions 1 atm = 760 mm Hg (exact) 1 torr = 1 mm Hg (exact) 1 bar = 1 x 105 Pa (exact) 1 atm = 101 325 Pa Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Gas Laws Ideal Gas: A gas whose behavior follows the gas laws exactly. The physical properties of a gas can be defined by four variables: P pressure T temperature V volume n number of moles Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Gas Laws Boyle’s Law V  P 1 (constant n and T) PV = k One goes up, the other one goes down. Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Gas Laws Boyle’s Law PinitialVinitial = PfinalVfinal Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Gas Laws Charles’ Law V  T (constant n and P) = k T V One goes up, the other one goes up. Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Gas Laws Charles’ Law = Tfinal Vfinal Tinitial Vinitial Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Gas Laws Avogadro’s Law V  n (constant T and P) = k n V One goes up, the other one goes up. = nfinal Vfinal ninitial Vinitial Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Gas Laws Summary Boyle’s Law: PinitialVinitial = PfinalVfinal = Tfinal Vfinal Tinitial Vinitial Charles’ Law: It is not necessary to know the names of the gas laws in order to solve problems. If one remembers the relationships between pressure, volume, temperature, and moles, then one can determine how to work the problem. ninitial Vinitial nfinal Vfinal Avogadro’s Law: = Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Ideal Gas Law These values are all around 22 L for 1 mol of gas. Is there a mathematical relationship between P, V, n, and T for an ideal gas? Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Ideal Gas Law Boyle’s Law: PV = nRT = k (n and T are constant) = k P nR T V = Charles’ Law: (n and T are constant) = k P RT n V = Avogadro’s Law: (n and T are constant) These three gas laws can be combined into the Ideal gas law. Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Ideal Gas Law Ideal Gas Law: PV = nRT R is the gas constant and is the same for all gases. R = 0.082058 K mol L atm T = 0 °C (273.15 K) Standard Temperature and Pressure (STP) for Gases Standard pressure is actually 1 bar. Gas law problems must use Kelvin!!!!!! P = 1 atm Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Ideal Gas Law What is the volume of 1 mol of gas at STP? (1 atm) (1 mol) 0.082058 K mol L atm (273.15 K) P nRT V = = = 22.414 L The closer the molar volume of a gas is to 22.414 L at STP, the more ideal the behavior. Recall the 22 L in the previous slide with Table 9.4. Copyright © 2010 Pearson Prentice Hall, Inc.

Stoichiometric Relationships with Gases Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Stoichiometric Relationships with Gases The reaction used in the deployment of automobile airbags is the high-temperature decomposition of sodium azide, NaN3, to produce N2 gas. How many liters of N2 at 1.15 atm and 30.0 °C are produced by decomposition of 45.0 g NaN3? 2Na(s) + 3N2(g) 2NaN3(s) Copyright © 2010 Pearson Prentice Hall, Inc.

Stoichiometric Relationships with Gases Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Stoichiometric Relationships with Gases 2Na(s) + 3N2(g) 2NaN3(s) Moles of N2 produced: 45.0 g NaN3 65.0 g NaN3 1 mol NaN3 2 mol NaN3 3 mol N2 x x = 1.04 mol N2 Volume of N2 produced: (1.15 atm) (1.04 mol) 0.082058 K mol L atm (303.2 K) P nRT V = = = 22.5 L Copyright © 2010 Pearson Prentice Hall, Inc.

Partial Pressure and Dalton’s Law Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Partial Pressure and Dalton’s Law Dalton’s Law of Partial Pressures: The total pressure exerted by a mixture of gases in a container at constant V and T is equal to the sum of the pressures of each individual gas in the container. Ptotal = P1 + P2 + … + PN Total moles in mixture Moles of component The result for mole fraction in terms of component and total pressures have been presented without showing the derivation. Mole Fraction (X) = Xi = ntotal ni Xi = Ptotal Pi or Copyright © 2010 Pearson Prentice Hall, Inc.

The Kinetic-Molecular Theory of Gases Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Kinetic-Molecular Theory of Gases A gas consists of tiny particles, either atoms or molecules, moving about at random. The volume of the particles themselves is negligible compared with the total volume of the gas; most of the volume of a gas is empty space. The gas particles act independently of one another; there are no attractive or repulsive forces between particles. Collisions of the gas particles, either with other particles or with the walls of a container, are elastic (constant temperature). The average kinetic energy of the gas particles is proportional to the Kelvin temperature of the sample. Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Copyright © 2010 Pearson Prentice Hall, Inc.

The Kinetic-Molecular Theory of Gases Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Kinetic-Molecular Theory of Gases molar mass average speed Copyright © 2010 Pearson Prentice Hall, Inc.

The Kinetic-Molecular Theory of Gases Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Kinetic-Molecular Theory of Gases Copyright © 2010 Pearson Prentice Hall, Inc.

Graham’s Law: Diffusion and Effusion of Gases Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Graham’s Law: Diffusion and Effusion of Gases Copyright © 2010 Pearson Prentice Hall, Inc.

Graham’s Law: Diffusion and Effusion of Gases Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Graham’s Law: Diffusion and Effusion of Gases Rate  1 m Graham’s Law: m is mass. Copyright © 2010 Pearson Prentice Hall, Inc.

The Behavior of Real Gases Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Behavior of Real Gases The volume of a real gas is larger than predicted by the ideal gas law. Copyright © 2010 Pearson Prentice Hall, Inc.

The Behavior of Real Gases Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Behavior of Real Gases Attractive forces between particles become more important at higher pressures. Particles are closer together at higher pressures due to the increased attractive forces. Copyright © 2010 Pearson Prentice Hall, Inc.

The Behavior of Real Gases Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Behavior of Real Gases van der Waals equation Correction for intermolecular attractions. a n2 P + V - n b = nRT V2 Correction for molecular volume. Copyright © 2010 Pearson Prentice Hall, Inc.

The Earth’s Atmosphere Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Earth’s Atmosphere Copyright © 2010 Pearson Prentice Hall, Inc.

Chapter 9: Gases: Their Properties and Behavior 4/21/2017 Copyright © 2010 Pearson Prentice Hall, Inc.

The Earth’s Atmosphere Chapter 9: Gases: Their Properties and Behavior 4/21/2017 The Earth’s Atmosphere Copyright © 2010 Pearson Prentice Hall, Inc.