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Chapter 9: Gases and Gas Laws

Learn about the properties and behavior of gases, including their pressure, volume, temperature, and amount, as well as the gas laws that govern their relationships. Understand Boyle's Law, Charles's Law, Avogadro's Law, and the ideal gas law. Practice solving problems and applying gas laws to stoichiometry.

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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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