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Chapter 11 – Molecular Composition of Gases

Chapter 11 – Molecular Composition of Gases. Gay-Lussac’s Law of Combining Volumes of Gases. hydrogen gas + oxygen gas  water vapor 2 volumes + 1 volume  2 volumes hydrogen + chlorine hydrogen chloride gas 1 volume + 1 volume  2 volumes

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Chapter 11 – Molecular Composition of Gases

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  1. Chapter 11 – Molecular Composition of Gases Honors Chemistry, Chapter 11 Page 1

  2. Gay-Lussac’s Law of Combining Volumes of Gases hydrogen gas + oxygen gas  water vapor 2 volumes + 1 volume  2 volumes hydrogen + chlorinehydrogen chloride gas 1 volume + 1 volume  2 volumes • Gay-Lussac’s law of combining volumes of gases states that at constant temperature and pressure , the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers. Honors Chemistry, Chapter 11 Page 2

  3. Avogadro’s Law • Avogadro’s law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. V = kn Where V is volume n is the number of moles k is a constant Honors Chemistry, Chapter 11 Page 3

  4. Avogadro’s Law • Assume hydrogen, oxygen and chlorine are diatomic molecules. H2(g) + Cl2(g)  2HCl(g) 1 vol. + 1 vol.  2 vol. and 2H2(g) + O2(g)  2H2O(g) 2 vol. + 1 vol.  2 vol. Honors Chemistry, Chapter 11 Page 4

  5. Molar Volume The volume occupied by one mole of a gas at STP is known as the standard molar volume of a gas and has a volume of 22.41410 L (22.4 L for our purposes). • (STP – Standard Temperature and Pressure: 0oC. and 1 atm.) Honors Chemistry, Chapter 11 Page 5

  6. Sample Problem 11-1 • What is the volume of 0.0680 mole of oxygen gas at STP? moles of O2 volume of O2 in liters 0.068 mol O2 x 22.4 L/mol = 1.52 L O2 Honors Chemistry, Chapter 11 Page 6

  7. Sample Problem 11-2 • What is the mass in grams of 98.0 mL of SO2 at STP? Vol. of SO2 in liters  mol of SO2 mass of SO2 mol mass of SO2=32.00+32.07= 64.07 g/mol 98.0 mL x 1L/1000 mL x 1 mol SO2/ 22.4 L x 64.07 g SO2/ mol SO2 = 0.280 g SO2 Honors Chemistry, Chapter 11 Page 7

  8. Thought Problem • Consider a container with mass of 1 kg and an internal volume of 22.4 L. : • If the container is filled with air, how much water would the container displace if placed in a container of water? Honors Chemistry, Chapter 11 Page 8

  9. Thought Problem • How much would the container weigh when filled with air? • How much would the container weigh when evacuated? • How much would the container weigh when filled with nitrogen? oxygen? hydrogen? Honors Chemistry, Chapter 11 Page 9

  10. Chapter 11, Section 1 Review • State the law of combining volumes. • State Avogadro’s law and explain its significance. • Define standard molar volume of a gas, and use it to calculate gas masses and volumes. • Use standard molar volume to calculate the molar mass of a gas. Honors Chemistry, Chapter 11 Page 10

  11. Idea Gas Law • Boyle’s Law: V a 1/P • Charles’s Law: V a T • Avogadro’s Law: V a n or V a nT/P or V = nRT/P or PV = nRT Where R is the Ideal Gas Constant Honors Chemistry, Chapter 11 Page 11

  12. Ideal Gas Constant R = _PV_ = _(1 atm)(22.4140 L)_ nT (1 mol)(273.15 K) = 0.082057 L atm/(mol K) Honors Chemistry, Chapter 11 Page 12

  13. Numerical Values of the Ideal Gas Constant Honors Chemistry, Chapter 11 Page 13

  14. Sample Problem 11-3 • What is the pressure in atmospheres exerted by 0.500 mol of nitrogen gas in a 10.0 L container at 298 K? V = 10.0 L n = 0.500 mol of N2 T = 298 K P = nRT/V = 0.500 mol N2 x 0.0821 L atm/ (mol K) x 298 K / 10.0 L = 1.22 atm Honors Chemistry, Chapter 11 Page 14

  15. Sample Problem 11-4 • What is the volume, in liters, of 0.250 mol of oxygen at 20 oC. and 0.974 atm pressure? • P = 0.974 atm • n = 0.250 mol of Oxygen • T = 20 oC. or 273.2 + 20 = 293.2 K • V = nRT/P = 0.250 x 0.0821 (L atm)/(mol K) x 293.2 K / 0.974 atm = 6.17 L O2 Honors Chemistry, Chapter 11 Page 15

  16. Molar Mass • PV = nRT = m RT / M (n = m / M) Where m is mass and M is molar mass • Solve for M M = m RT/(PV) Honors Chemistry, Chapter 11 Page 16

  17. Gas Density • D = m/V m = DV • PV = m RT/ M • PV = DV RT/M • D = M P / (RT) Honors Chemistry, Chapter 11 Page 17

  18. Problem 11-6 • At 28oC. and 0.974 atm, 1.00 L of a gas has a mass of 5.16 g. What is the molar mass of this gas? What is the gas? • P = 0.974 atm V = 1.00 L • T = 28oC. + 273 = 301 K m = 5.16 g. M = m RT/PV = 5.16 g x [0.0821 L atm / (mol K)] x 301 K / ( 0.974 atm x 1.00 L) = 131 g/mol Honors Chemistry, Chapter 11 Page 18

  19. Example Density Problem • The density of a gas was found to be 2.0 g/L at 1.50 atm and 27oC. What is the molar mass of the gas? What is the gas? • D = 2.0 g/L T = 27oC. + 273 = 300 K • P = 1.50 atm • D = M P / (RT) • M = DRT / P = 2.0 g/L x [0.0821 L atm / (mol K)] x 300 K / 1.50 atm = 33 g/mol Honors Chemistry, Chapter 11 Page 19

  20. Chapter 11, Section 2 Review • State the ideal gas law. • Derive the gas constant and discuss the units. • Using the ideal gas law, calculate pressure, volume, temperature or amount of gas when the other three quantities are known. Honors Chemistry, Chapter 11 Page 20

  21. Chapter 11, Section 2 Review • Using the ideal gas law, calculate the molar mass or density of a gas. • Reduce the ideal gas law to Boyle’s law, Charles’s law, and Avogadro’s law. Describe the conditions under which each applies. Honors Chemistry, Chapter 11 Page 21

  22. Stoichiometry of Gases • Coefficients indicate molecule, mole, and volume ratios in gas reactions. For Example: 2CO(g) + O2(g)  2CO2(g) 2 molecules 1 molecule 2 molecules 2 mol 1 mol 2 mol 2 volumes 1 volume 2 volumes Honors Chemistry, Chapter 11 Page 22

  23. Volume Ratios Volume Ratios from the CO + O2 Reaction 2 vol CO / 1 vol O2 or 1 vol O2 / 2 vol CO 2 vol CO / 2 vol CO2 or 2 vol CO2 / 2 vol CO 1 vol O2 / 2 vol CO2 or 2 vol CO2 / 1 vol O2 Honors Chemistry, Chapter 11 Page 23

  24. Sample Problem 11-7 • What is the volume, in liters, of oxygen required for the complete combustion of 0.350 L of propane? What will the volume of CO2 be? (Assume constant T and P.) C3H8(g) + 5O2(g)  3CO2(g) + 4H2O(g) 0.350L C3H8 x 5 vol O2 / 1 vol C3H8 = 1.75 L O2 0.350L C3H8 x 3 vol CO2 / 1vol C3H8 =1.05 L CO2 Honors Chemistry, Chapter 11 Page 24

  25. Volume-Mass and Mass-Volume Calculations • We can use the ideal gas law to calculate problems like: gas vol A  moles A  moles B  mass B or mass A  moles A  moles B  gas vol B Honors Chemistry, Chapter 11 Page 25

  26. Sample Problem 11-8 • How many grams of calcium carbonate must be decomposed to produce 5.00 L of carbon dioxide at STP? CaCO3(s) D CaO(s) + CO2(g) n = PV/RT = (1atm)(5.00 L CO2) / [ 0.0821 L atm /(mol K)]/(273 K) = 0.223 mol CO2 or n = 5.00L CO2 / (22.4 L/mol)=0.233 mol CO2 Honors Chemistry, Chapter 11 Page 26

  27. Sample Problem 11-8 continued Molecular Weight of CaCO3? 100.09 g CaCO3/mol 0.223 mol CO2 x 1 mol CaCO3 / (1 mol CO2) x 100.09 g CaCO3/1 mol CaCO3 = 22.4 g CaCO3 Honors Chemistry, Chapter 11 Page 27

  28. Sample Problem 11-9 • How many liters of hydrogen at at 35oC. and 0.980 atm are needed to completely react with 875 grams of tungsten oxide? WO3(s) + 3H2(g)  W(s) + 3H2O(l) Molar Mass of WO3? 231.84 g/mol 875 g WO3 x 1 mol WO3 / (231.84 g WO3) x 3 mol H2 / (1 mol WO3) = 11.3 mol H2 Honors Chemistry, Chapter 11 Page 28

  29. Sample Problem 11-9 Continued V = nRT/P = (11.3 mol H2) x [0.0821 L atm / (mol K)] x 308 K / (0.980 atm) = 292 L H2 Honors Chemistry, Chapter 11 Page 29

  30. Chapter 11, Section 3 Review • Explain how Gay-Lussac’s law and Avogadro’s law apply to volumes of gases in chemical reactions. • Use a chemical equation to specify volume ratios for gaseous reactants or products, or both. • Use volume ratios and the gas laws to calculate volumes, masses, or molar amounts of gaseous reactants or products. Honors Chemistry, Chapter 11 Page 30

  31. Diffusion and Effusion • Diffusion is the process where two gases gradually mix spontaneously due to the constant motion of the gas molecules. • Effusion is the process whereby the molecules of a gas confined in a container randomly pass through a tiny opening in the container. Honors Chemistry, Chapter 11 Page 31

  32. Average Kinetic Energy • For two gases at the same temperature: Avg kinetic energy = ½ MAvA2 = ½ MBvB2 MAvA2 = MBvB2 vA2 / vB2 = MB / MA vA MB --------- = ------------ vB MA Honors Chemistry, Chapter 11 Page 32

  33. Graham’s Law of Effusion • Graham’s law of effusion states that the rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. Rate of effusion of A MB DensityB ---------------------------- = ------- = ------------- Rate of effusion of B MA DensityA Honors Chemistry, Chapter 11 Page 33

  34. Sample Problem 11-10 • Compare the rates of effusion of hydrogen and oxygen at the same temperature and pressure. Rate of effusion of H2 MO2 32.00 g/mol ---------------------------- = ------- = ------------- Rate of effusion of O2 MH2 2.02 g/mol = 3.98 Honors Chemistry, Chapter 11 Page 34

  35. Chapter 11, Section 4 Review • State Graham’s law of effusion. • Determine the relative rates of effusion of two gases of know molar masses. • State the relationship between the molecular velocities of two gases and their molar masses. Honors Chemistry, Chapter 11 Page 35

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