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by Steven S. Zumdahl & Donald J. DeCoste University of Illinois

Introductory Chemistry: A Foundation, 6 th Ed. Introductory Chemistry, 6 th Ed. Basic Chemistry, 6 th Ed. by Steven S. Zumdahl & Donald J. DeCoste University of Illinois. Chapter 13 Gases. Properties of Gases. Expand to completely fill their container Take the shape of their container

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by Steven S. Zumdahl & Donald J. DeCoste University of Illinois

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  1. Introductory Chemistry: A Foundation, 6th Ed. Introductory Chemistry, 6th Ed. Basic Chemistry, 6th Ed. by Steven S. Zumdahl & Donald J. DeCoste University of Illinois

  2. Chapter 13Gases

  3. Properties of Gases • Expand to completely fill their container • Take the shape of their container • Low density • Much less than solid or liquid state • Compressible • Mixtures of gases are always homogeneous • Fluid

  4. Gas Pressure • Pressure = total force applied to a certain area • Larger force = larger pressure • Smaller area = larger pressure • Gas pressure caused by gas molecules colliding with container or surface • More forceful or more frequent collisions mean higher gas pressure

  5. Air Pressure • Constantly present when air present • Decreases with altitude • Less air = less pressure • Varies with weather conditions

  6. Air Pressure (cont.) • Measured using a barometer • Column of mercury supported by air pressure • Longer mercury column supported = higher pressure • Force of the air on the surface of the mercury balanced by the pull of gravity on the column of mercury

  7. Measuring Pressure of a Trapped Gas A device (called a manometer) for measuring the pressure of a gas in a container.

  8. Measuring Pressure of a Trapped Gas(cont.)

  9. Units of Gas Pressure • Atmosphere (atm) • Height of a column of mercury (mm Hg, in Hg) • Torr • Pascal (Pa) • Pounds per square inch (psi, lbs/in2) • 1.000 atm = 760.0 mm Hg = 29.92 in Hg = 760.0 torr = 101,325 Pa = 101.325 kPa = 14.69 psi

  10. Boyle’s Law • Pressure is inversely proportional to volume • Constant T and amount of gas • As P increases, V decreases by the same factor. • P x V = constant • P1 x V1 = P2 x V2

  11. Boyle’s Law (cont.)

  12. Boyle’s Law (cont.)

  13. Example using Boyle’s Law: What is the new volume if a 1.5 L sample of Freon-12 at 56 torr is compressed to 150 torr?

  14. Example (cont.) • Choose the correct gas law: Since we are looking at the relationship between pressure and volume we use Boyle’s Law. P1 x V1 = P2 x V2 • Solve equation for the unknown variable:

  15. Example (cont.) • Plug in the known values and calculate the unknown: P1 = 56 torr P2 = 150 torr V1 = 1.5 L V2 = ? L

  16. Practice Problem 13.2 A A sample of helium gas has a pressure of 3.54 atm in a container with a volume of 23.1 L. This sample is transferred to a new container and the pressure is measured to be 1.87 atm. What is the volume of the new container? Assume constant temperature. Answer: V2 = 43.7 L

  17. Practice Problem 13.2 B A steel tank of argon gas has a pressure of 34.6 atm. If all of the argon is transferred to a new tank with a volume of 456 L, the pressure is measured to be 2.94 atm. What is the volume of the original container? Assume constant temperature. Answer: V1 = 38.7 L

  18. Absolute Zero • Theoretical temperature at which a gas would have zero volume and no pressure • Calculated by extrapolation • 0 K = -273.15 °C = -459 °F • Kelvin T = Celsius T + 273.15 • Never attainable (though we’ve gotten really close) • All gas law problems use Kelvin temperature scale.

  19. Charles’ Law • Volume is directly proportional to temperature • Constant P and amount of gas • V = constant x T (T must be measured in Kelvin) • V1 = V2 T1 T2

  20. Charles’ Law (cont.)

  21. Charles’ Law (cont.)

  22. Practice Problem 13.4 A A sample of oxygen gas has a volume of 4.55 L at 25°C. Calculate the volume of the oxygen gas when the temperature is raised to 45°C. Assume constant pressure • V1 = V2 T1 T2 Answer: V2 = 4.86 L

  23. Avogadro’s Law • Volume directly proportional to the number of gas molecules • V = constant x n (moles) • Constant P and T • More gas molecules = larger volume

  24. Avogadro’s Law (cont.) • Count number of gas molecules by moles • One mole of any ideal gas occupies 22.414 L at standard conditions = molar volume • Equal volumes of gases contain equal numbers of molecules. • It doesn’t matter what the gas is!

  25. Practice Problem 13.7 A If 2.55 mol of helium gas occupies a volume of 59.5 L at a particular temperature and pressure, what volume does 7.83 mol of helium occupy under the same conditions? Answer: 183 L

  26. Practice Problem 13 .7 B If 4.35 g of neon gas occupies a volume of 15.0 L at a particular temperature and pressure, what volume does 2.00 g of neon gas occupy under the same conditions? Answer: 6.88 L

  27. Ideal Gas Law • By combining the proportionality constants from the gas laws we can write ageneral equation. • R is called the gas constant. • The value of R depends on the units of P and V. • Generally use R = 0.08206 when P in atm and V in L PV =nRT

  28. Ideal Gas Law (cont.) • Use the ideal gas law when you have gas at one set of conditions • Most gases obey this law when pressure is low (at or below 1 atm) and temperature is high (above 0°C).

  29. Practice Problem 13.8 A sample of hydrogen gas, H2, has a volume of 8.56 L at a temperature of 0°C and a pressure of 1.5 atm. Calculate the number of moles of H2 present in this gas sample. (Assume that the gas behaves ideally). Answer: 0.57 mol PV =nRT

  30. Ideal Gas Law (cont.)

  31. Practice Problem 13.8 A A 2.50 mol sample of nitrogen gas has a volume of 5.50 L at a temperature of 27°C. Calculate the pressure of the nitrogen gas Answer: 11.2 atm PV =nRT

  32. Practice Problem 13.8 B A 5.00 mol sample of oxygen gas has a pressure of 1.25 atm at 22°C. What volume does this gas occupy? Answer: 96.8 L PV =nRT

  33. Practice Problem 13.9 A A sample of neon gas has a volume of 3.45 L at 25°C and a pressure of 565 torr. Calculate the number of moles of neon present in this gas sample? Answer: 0.105 mol PV =nRT

  34. Practice Problem 13.9 B A 0.250 mol sample of argon gas has a volume of 9.00 L at a pressure of 875 mm Hg. What is the temperature (in °C) of the gas? Answer: 232 °C PV =nRT

  35. Combined Gas Law

  36. Practice Problem 13.10 A Consider a sample of helium gas at 23°C with a volume of 5.60 L at a pressure of 2.45 atm. The pressure is changed to 8.75 atm and the gas is cooled to 15°C? Calculate the new volume of the gas using the ideal gas law equation Answer: 1.53 L PV =nRT

  37. Practice Problem 13.11 A Consider a sample of hydrogen gas at 63°C with a volume of 3.65 L at a pressure of 4.55 atm. The pressure is changed to 2.75 atm and the gas is cooled to -35°C. Calculate the new volume of the gas. Answer: 4.28 L PV =nRT

  38. Practice Problem 13.11 B Consider a sample of oxygen gas at 27°C with a volume of 9.55 L at a pressure of 2.97 atm. The pressure is changed to 8.25 atm and the gas is heated to 125°C? Calculate the new volume of the gas using the ideal gas law equation Answer: 4.56 L PV =nRT

  39. Scuba divers going deeper than 150ft use a helium and oxygen mixture • Divers experience high pressure under several hundred feet of pressure • Nitrogen gas dissolves in blood under these conditions • Returning to the surface too quickly results in “the bends”

  40. Dalton’s Law of Partial Pressures • The total pressure of a mixture of gases equals the sum of the pressures each gas would exert independently. Partial pressure: the pressure a gas in a mixture would exert if it were alonein the container Ptotal = Pgas A + Pgas B + …

  41. Dalton’s Law (cont.) • Particularly useful for determining the pressure a dry gas would have after it is collected over water Pair = Pwet gas = Pdry gas + Pwater vapor Pwater vapor depends on the temperature, look up in table

  42. Partial Pressures The partial pressure of each gas in a mixture can be calculated using the Ideal Gas Law:

  43. Practice Problem 13.12 Mixtures of helium and oxygen are used in the “air” tanks of underwater divers for deep dives. For a particular dive, 12 L of O2 at 25°C and 1.0 atm and 46 L of He at 25°C at 1 atm were both pumped into a 5.0 L tank. Calculate the partial pressure of each gas in the tank at 25°C Answer: 2.4 atm O2; 9.3 atm He; 11.7 atm total n=RT PV

  44. Partial Pressures When two gases are present, the total pressure is the sum of the partial pressures of the gases.

  45. The total pressure of a mixture of gases depends on the number of moles of gas particles (atoms or molecules) present, not on the identities of the particles. Note that these three samples show the same total pressure because each contains 1.75 mol of gas. The detailed nature of the mixture is unimportant. Partial Pressures

  46. Practice Problem 13.12 A A 5.00 g sample of helium gas is added to a 5.00 g sample of neon gas in a 2.50 L container at 27°C. Calculate the partial pressure of each gas and the total pressure Answer: 12.3 atm He; 2.44 atm Ne; 14.7 atm total PV =nRT

  47. Practice Problem 13.12 B Equal masses of oxygen and nitrogen gas are present in a container. Which gas exerts the larger partial pressure? By what factor? Answer: N2 exerts a partial pressure that is 1.14 times as great as the partial pressure of O2 PV =nRT

  48. Water Vapor Pressure A mixture of gases occurs whenever a gas is collected by displacement of water. The production of oxygen by thermal decomposition of KClO3 2KClO3(s)  2KCl(s) + 3O2(s)

  49. Practice Problem 13.132KClO3(s)  2KCl(s) + 3O2(s) The oxygen produced was collected by displacement of water at 22°C. The resulting mixture of O2 and H2O vapor had a total pressure of 754 torr and a volume of 0.650L. Calculate the partial pressure of O2 in the gas collected and the number of moles of O2 present. The vapor pressure of water at 22°C is 21 torr.

  50. Practice Problem 13.132KClO3(s)  2KCl(s) + 3O2(s) The oxygen produced was collected by displacement of water at 22°C. The resulting mixture of O2 and H2O vapor had a total pressure of 754 torr and a volume of 0.650L. Calculate the partial pressure of O2 in the gas collected and the number of moles of O2 present. The vapor pressure of water at 22°C is 21 torr. Ptotal= PO2+ PH2O Answer: PO2 = 0.964 atm nO2= 2.59 x 10-2mol

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