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Chapter 9: Gases and Gas Laws

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  1. Chapter 9 Gases: Their Properties and Behavior

  2. Gases and Gas Pressure

  3. Properties of Gases • Gases mix completely with one another to form homogenous mixtures • Gases can be compressed (keyboard cleaner) • Gases exert pressure on what ever is around them (balloon, film canister) • Gases expand into whatever volume is available (coke bottle and balloon) • Gases are described in terms of their temperature and pressure, the volume occupied and the amount of gas present (gas properties)

  4. Properties of Gases • Pressure (P) Pressure = force / area Force = mass x acceleration • Units of Pressure • Atmosphere (atm) • Torr • Pascals (Pa) • mmHg • Pressure conversions • 1 atm = 1.01325 x 105 Pa • 1 atm = 760 torr • 1 atm = 760 mmHg

  5. Problem • Convert these pressure values. • 120 mmHg to atm • 100 kPa to mmHg • 270 torr to atm

  6. Properties of Gases • Volume (V) • mL • L • cm3 • Amount of gas (n) – moles • Temperature (T) - Kelvins

  7. Kinetic Molecular Theory • A gas is composed of molecules whose size is much smaller than the distance between them • Gas molecules move randomly at various speeds and in every possible direction

  8. Kinetic Molecular Theory • Except when gas molecules collide, forces of attraction and repulsion between them are negligible • When collisions between molecules occur, they are elastic • The average kinetic energy of gas molecules is proportional to the absolute temperature (liquid N2 ballons, can, solar bag) Ek = ½ (mass)(speed)2

  9. Distribution of molecular speeds at three temperatures.

  10. Relationship between molar mass and molecular speed.

  11. Problem • Place these gases in order of increasing average molecular speed at 25oC: Kr, CH4, N2, and CH2Cl2

  12. The Gas Laws • Gas properties • Gases are described in terms of their temperature and pressure, the volume occupied and the amount of gas present (gas properties) • Gas Laws can be derived using • Kinetic Molecular Theory

  13. The Gas Laws • The Pressure-Volume Relationship: Boyle’s Law • The volume (V) of an ideal gas varies inversely with the applied pressure (P) when temperature (T) and the amount (n, moles) are constant • PiVi = PfVf

  14. Problems • A sample of nitrogen gas at 298 K and 745 torr has a volume of 37.42 L. What volume will it occupy if the pressure is increased to 894 torr at constant temperature? • A)22.3 L • B)31.2 L • C)44.9 L • D)112 L • E)380 L

  15. Problems • A sample of carbon dioxide gas at 125°C and 248 torr occupies a volume of 275 L. What will the gas pressure be if the volume is increased to 321 L at 125°C? • A)212 torr • B)289 torr • C)356 torr • D)441 torr • E)359 torr

  16. The Gas Laws • The Temperature-Volume Relationship – Charles’s Law • The volume (V) of an ideal gas varies directly with absolute temperature (T) when pressure (P) and amount (n) are constant. • Vi / Ti = Vf / Tf

  17. Problems • A sample container of carbon monoxide occupies a volume of 435 mL at a pressure of 785 torr and a temperature of 298 K. What would its temperature be if the volume were changed to 265 mL at a pressure of 785 torr? • A)182 K • B)298 K • C)387 K • D)489 K • E)538 K

  18. Problems • A 0.850-mole sample of nitrous oxide, a gas used as an anesthetic by dentists, has a volume of 20.46 L at 123°C and 1.35 atm. What would be its volume at 468°C and 1.35 atm? • A)5.38 L • B)10.9 L • C)19.0 L • D)38.3 L • E)77.9 L

  19. The Combined Gas Law • Combined Gas Law – used when a specific amount of gas is exposed to two different conditions • P1V1 / T1 = P2V2 / T2

  20. Problems • A sample of propane, a component of LP gas, has a volume of 35.3 L at 315 K and 922 torr. What is its volume at STP? • A)25.2 L • B)30.6 L • C)33.6 L • D)37.1 L • E)49.2 L

  21. Problems • Calculate the pressure of a helium sample at -207.3°C and 768 mL if it exerts a pressure of 175 kPa at 25.0°C and 925 mL. • A)32.1 kPa • B)46.6 kPa • C)657 kPa • D)953 kPa • E)340 kPa

  22. Problems • A carbon dioxide sample weighing 44.0g occupies 32.68 L at 65°C and 645 torr. What is its volume at STP? • A)22.4 L • B)31.1 L • C)34.3 L • D)35.2 L • E)47.7 L

  23. The Gas Laws • The Amount-Volume Relationship: Avogadro’s Law • The volume (V) of an ideal gas varies directly with amount (n) when temperature (T) and pressure (P) are constant • V1 / n1 = V2 / n2

  24. The Ideal Gas Law • Boyle’s, Charles’s and Avogadro’s Laws can be combined to form the Ideal Gas Law • PV = nRT • R – ideal gas constant • R = 0.0821 atm L / mol K • R = 62.36 torr L / mol K • R = 8.314 J / mol K

  25. Problems • A sample of nitrogen gas is confined to a 14.0 L container at 375 torr and 37.0°C. How many moles of nitrogen are in the container? • A)0.271 mol • B)2.27 mol • C)3.69 mo1 • D)206 mol • E)227 mol

  26. Stoichiometric Relationships with Gases • Various questions can be asked that relate gas laws to stoichiometry.

  27. Problems • A 250.0-mL sample of ammonia, NH3(g), exerts a pressure of 833 torr at 42.4°C. What mass of ammonia is in the container? • A)0.0787 g • B)0.180 g • C)8.04 g • D)17.0 g • E)59.8 g

  28. Stoichiometric Relationships with Gases • The ideal gas law can be used to determine density if the molar mass of the gas is known or the molar mass if the mass of gas is known d = m / V = PM / RT • Density increases with molar mass

  29. Problems • 9What is the density of carbon dioxide gas at -25.2°C and 98.0 kPa? • A)0.232 g/L • B)0.279 g/L • C)0.994 g/L • D)1.74 g/L • E)2.09 g/L

  30. Problems • A flask with a volume of 3.16 L contains 9.33 grams of an unknown gas at 32.0°C and 1.00 atm. What is the molar mass of the gas? • A)7.76 g/mol • B)66.1 g/mol • C)74.0 g/mol • D)81.4 g/mol • E)144 g/mol

  31. Problems • Dr. I. M. A. Brightguy adds 0.1727 g of an unknown gas to a 125-mL flask. If Dr. B finds the pressure to be 736 torr at 20.0°C, is the gas likely to be methane, CH4, nitrogen, N2, oxygen, O2, neon, Ne, or argon, Ar? • A)CH4 • B)N2 • C)Ne • D)Ar • E)O2

  32. Partial Pressures and Dalton’s Law • Dalton’s Law of Partial Pressures – the total pressure exerted by a mixture of gases is the sum of the partial pressures of the individual gases in the mixture. • Since all gases in a mixture occupy the same volume and are at the same temperature then the pressure is directly related to the moles of gas ntotal = ngas1 +ngas2 …..

  33. Partial Pressures and Dalton’s Law • Placing ntotal into the ideal gas law PtotalV = ntotalRT Ptotal = ntotalRT / V Ptotal = Pgas1 + Pgas2 + …..,

  34. Partial Pressures and Dalton’s Law Pgas1 / Ptotal = ngas1 / ntotal ngas1 / ntotal = Xgas1 • Xgas1 is called the mole fraction • All mole fractions = 1

  35. Problems • What is the pressure in a 7.50-L flask if 0.15 mol of carbon dioxide is added to 0.33 mol of oxygen? The temperature of the mixture is 48.0°C. • A)0.252 atm • B)0.592 atm • C)1.69 atm • D)3.96 atm • E)4.80 atm

  36. Problems • If 0.750 L of argon at 1.50 atm and 177°C and 0.235 L of sulfur dioxide at 95.0 kPa and 63.0°C are added to a 1.00-L flask and the flask's temperature is adjusted to 25.0°C, what is the resulting pressure in the flask? • A)0.0851 atm • B)0.244 atm • C)0.946 atm • D)1.74 atm • E)1.86 atm

  37. Partial Pressures and Dalton’s Law • Collecting Gas over water – most common way of determining the # moles of a gas sample as long as the gas is not water soluble.

  38. Problems • Small quantities of hydrogen can be prepared by the addition of hydrochloric acid to zinc. A sample of 195 mL of hydrogen was collected over water at 25°C and 753 torr. What mass of hydrogen was collected? (Pwater = 24 torr at 25°C) • A)0.00765 g • B)0.0154 g • C)0.0159 g • D)0.0164 g • E)0.159 g

  39. Behavior of Ideal Gases • Ideal Gas Law provides fairly accurate predictions for the pressure, volumes and temperatures of most gases except • At extremely high pressures • Extremely low temperatures

  40. Optional Homework • Text – 9.26, 9.28, 9.36, 9.44, 9.46, 9.48, 9.50, 9.52, 9.54, 9.56, 9.62, 9.64, 9.66, 9.74, 9.78, 9.90, 9.96, 9.104, 9.106 • Chapter 9 Homework on the website

  41. Required Homework • Chapter 9 Assignment

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