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CHAPTER 12

CHAPTER 12. GASES AND KINETIC-MOLECULAR THEORY. CHAPTER GOALS. Comparison of Solids, Liquids, and Gases Composition of the Atmosphere and Some Common Properties of Gases Pressure Boyle’s Law: The Volume-Pressure Relationship

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CHAPTER 12

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  1. CHAPTER 12 • GASES AND KINETIC-MOLECULAR THEORY

  2. CHAPTER GOALS • Comparison of Solids, Liquids, and Gases • Composition of the Atmosphere and Some Common Properties of Gases • Pressure • Boyle’s Law: The Volume-Pressure Relationship • Charles’ Law: The Volume-Temperature Relationship; The Absolute Temperature Scale • Standard Temperature and Pressure • The Combined Gas Law Equation • Avogadro’s Law and the Standard Molar Volume

  3. CHAPTER GOALS • Summary of Gas Laws: The Ideal Gas Equation • Determination of Molecular Weights and Molecular Formulas of Gaseous Substances • Dalton’s Law of Partial Pressures • Mass-Volume Relationships in Reactions Involving Gases • The Kinetic-Molecular Theory • Diffusion and Effusion of Gases • Real Gases: Deviations from Ideality

  4. Comparison of Solids, Liquids, and Gases • The density of gases is much less than that of solids or liquids. • Gas molecules must be very far apart compared to liquids and solids.

  5. Composition of the Atmosphere and Some Common Properties of Gases Composition of Dry Air

  6. Pressure • Pressure is force per unit area. • lb/in2 • N/m2 • Gas pressure as most people think of it.

  7. Pressure • Atmospheric pressure is measured using a barometer. • Definitions of standard pressure • 76 cm Hg • 760 mm Hg • 760 torr • 1 atmosphere • 101.3 kPa Hg density = 13.6 g/mL

  8. Boyle’s Law: The Volume-Pressure Relationship • V  1/P or • V= k (1/P) or PV = k • P1V1 = k1 for one sample of a gas. • P2V2 = k2 for a second sample of a gas. • k1 = k2 for the same sample of a gas at the same T. • Thus we can write Boyle’s Law mathematically as P1V1 = P2V2

  9. Boyle’s Law: The Volume-Pressure Relationship • Example 12-1: At 25oC a sample of He has a volume of 4.00 x 102 mL under a pressure of 7.60 x 102 torr. What volume would it occupy under a pressure of 2.00 atm at the same T?

  10. Boyle’s Law: The Volume-Pressure Relationship • Notice that in Boyle’s law we can use any pressure or volume units as long as we consistently use the same units for both P1 and P2 or V1 and V2. • Use your intuition to help you decide if the volume will go up or down as the pressure is changed and vice versa.

  11. Charles’ Law: The Volume-Temperature Relationship; The Absolute Temperature Scale absolute zero = -273.15 0C

  12. Charles’ Law: The Volume-Temperature Relationship; The Absolute Temperature Scale • Charles’s law states that the volume of a gas is directly proportional to the absolute temperature at constant pressure. • Gas laws must use the Kelvin scale to be correct. • Relationship between Kelvin and centigrade.

  13. Charles’ Law: The Volume-Temperature Relationship; The Absolute Temperature Scale • Mathematical form of Charles’ law.

  14. Charles’ Law: The Volume-Temperature Relationship; The Absolute Temperature Scale • Example 12-2: A sample of hydrogen, H2, occupies 1.00 x 102 mL at 25.0oC and 1.00 atm. What volume would it occupy at 50.0oC under the same pressure? T1 = 25 + 273 = 298 T2 = 50 + 273 = 323

  15. Standard Temperature and Pressure • Standard temperature and pressure is given the symbol STP. • It is a reference point for some gas calculations. • Standard P  1.00000 atm or 101.3 kPa • Standard T  273.15 K or 0.00oC

  16. The Combined Gas Law Equation • Boyle’s and Charles’ Laws combined into one statement is called the combined gas law equation. • Useful when the V, T, and P of a gas are changing.

  17. The Combined Gas Law Equation • Example 12-3: A sample of nitrogen gas, N2, occupies 7.50 x 102 mL at 75.00C under a pressure of 8.10 x 102 torr. What volume would it occupy at STP?

  18. The Combined Gas Law Equation • Example 12-4 : A sample of methane, CH4, occupies 2.60 x 102 mL at 32oC under a pressure of 0.500 atm. At what temperature would it occupy 5.00 x 102 mL under a pressure of 1.20 x 103 torr? You do it!

  19. The Combined Gas Law Equation

  20. Avogadro’s Law and theStandard Molar Volume

  21. Avogadro’s Law and theStandard Molar Volume • Avogadro’s Law states that at the same temperature and pressure, equal volumes of two gases contain the same number of molecules (or moles) of gas. • If we set the temperature and pressure for any gas to be STP, then one mole of that gas has a volume called the standard molar volume. • The standard molar volume is 22.4 L at STP. • This is another way to measure moles. • For gases, the volume is proportional to the number of moles. • 11.2 L of a gas at STP = 0.500 mole • 44.8 L = ? moles

  22. Avogadro’s Law and theStandard Molar Volume • Example 12-5: One mole of a gas occupies 36.5 L and its density is 1.36 g/L at a given temperature and pressure. (a) What is its molar mass? (b) What is its density at STP?

  23. Summary of Gas Laws:The Ideal Gas Law • Boyle’s Law - V  1/P (at constant T & n) • Charles’ Law – V  T (at constant P & n) • Avogadro’s Law – V  n (at constant T & P) • Combine these three laws into one statement V  nT/P • Convert the proportionality into an equality. V = nRT/P • This provides the Ideal Gas Law. PV = nRT • R is a proportionality constant called the universal gas constant.

  24. Summary of Gas Laws:The Ideal Gas Law • We must determine the value of R. • Recognize that for one mole of a gas at 1.00 atm, and 273 K (STP), the volume is 22.4 L. • Use these values in the ideal gas law.

  25. Summary of Gas Laws:The Ideal Gas Law • R has other values if the units are changed. • R = 8.314 J/mol K • Use this value in thermodynamics. • R = 8.314 kg m2/s2 K mol • Use this later in this chapter for gas velocities. • R = 8.314 dm3 kPa/K mol • This is R in all metric units. • R = 1.987 cal/K mol • This the value of R in calories rather than J.

  26. Summary of Gas Laws:The Ideal Gas Law • Example 12-6: What volume would 50.0 g of ethane, C2H6, occupy at 1.40 x 102 oC under a pressure of 1.82 x 103 torr? • To use the ideal gas law correctly, it is very important that all of your values be in the correct units! • T = 140 + 273 = 413 K • P = 1820 torr (1 atm/760 torr) = 2.39 atm • 50 g (1 mol/30 g) = 1.67 mol

  27. Summary of Gas Laws:The Ideal Gas Law

  28. Summary of Gas Laws:The Ideal Gas Law • Example 12-7: Calculate the number of moles in, and the mass of, an 8.96 L sample of methane, CH4, measured at standard conditions. You do it!

  29. Summary of Gas Laws:The Ideal Gas Law

  30. Summary of Gas Laws:The Ideal Gas Law • Example 12-8: Calculate the pressure exerted by 50.0 g of ethane, C2H6, in a 25.0 L container at 25.0oC. You do it!

  31. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances • Example 12-9: A compound that contains only carbon and hydrogen is 80.0% carbon and 20.0% hydrogen by mass. At STP, 546 mL of the gas has a mass of 0.732 g . What is the molecular (true) formula for the compound? • 100 g of compound contains 80 g of C and 20 g of H.

  32. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances

  33. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances

  34. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances • Example 12-10: A 1.74 g sample of a compound that contains only carbon and hydrogen contains 1.44 g of carbon and 0.300 g of hydrogen. At STP 101 mL of the gas has a mass of 0.262 gram. What is its molecular formula? You do it!

  35. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances

  36. Determination of Molecular Weights and Molecular Formulas of Gaseous Substances

  37. Dalton’s Law of Partial Pressures • Dalton’s law states that the pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases. Ptotal = PA + PB + PC + .....

  38. Dalton’s Law of Partial Pressures • Example 12-11: If 1.00 x 102 mL of hydrogen, measured at 25.0 oC and 3.00 atm pressure, and 1.00 x 102 mL of oxygen, measured at 25.0 oC and 2.00 atm pressure, were forced into one of the containers at 25.0 oC, what would be the pressure of the mixture of gases?

  39. Dalton’s Law of Partial Pressures • Vapor Pressure is the pressure exerted by a substance’s vapor over the substance’s liquid at equilibrium.

  40. Dalton’s Law of Partial Pressures • Example 12-12: A sample of hydrogen was collected by displacement of water at 25.0 oC. The atmospheric pressure was 748 torr. What pressure would the dry hydrogen exert in the same container?

  41. Dalton’s Law of Partial Pressures • Example 12-13: A sample of oxygen was collected by displacement of water. The oxygen occupied 742 mL at 27.0 oC. The barometric pressure was 753 torr. What volume would the dry oxygen occupy at STP? You do it!

  42. Dalton’s Law of Partial Pressures

  43. Mass-Volume Relationships in Reactions Involving Gases

  44. Mass-Volume Relationships in Reactions Involving Gases • In this section we are looking at reaction stoichiometry, like in Chapter 3, just including gases in the calculations. 2 mol KClO3 yields 2 mol KCl and 3 mol O2 2(122.6g) yields 2 (74.6g) and 3 (32.0g) Those 3 moles of O2 can also be thought of as: 3(22.4L) or 67.2 L at STP

  45. Mass-Volume Relationships in Reactions Involving Gases • Example 12-14: What volume of oxygen measured at STP, can be produced by the thermal decomposition of 120.0 g of KClO3? You do it!

  46. Mass-Volume Relationships in Reactions Involving Gases

  47. The Kinetic-Molecular Theory • The basic assumptions of kinetic-molecular theory are: • Postulate 1 • Gases consist of discrete molecules that are relatively far apart. • Gases have few intermolecular attractions. • The volume of individual molecules is very small compared to the gas’s volume. • Proof - Gases are easily compressible.

  48. The Kinetic-Molecular Theory • Postulate 2 • Gas molecules are in constant, random, straight line motion with varying velocities. • Proof - Brownian motion displays molecular motion.

  49. The Kinetic-Molecular Theory • Postulate 3 • Gas molecules have elastic collisions with themselves and the container. • Total energy is conserved during a collision. • Proof - A sealed, confined gas exhibits no pressure drop over time.

  50. The Kinetic-Molecular Theory • Postulate 4 • The kinetic energy of the molecules is proportional to the absolute temperature. • The average kinetic energies of molecules of different gases are equal at a given temperature. • Proof - Brownian motion increases as temperature increases.

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