1. Gases

2. Elements that exist as gases at 25 0 C and 1 atmosphere 5.1

4. Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower densities than liquids and solids. 5.1 Physical Characteristics of Gases

5. Sea level1 atm 4 miles0.5 atm 10 miles0.2 atm 5.2

6. Gas Pressure and SI units

7. What is the pressure in atm. in an airplane cabin if the barometer reading is 688 mmHg?

8. Convert 732 mmHg to kPa.

9. Manometers  Device used to measure gas pressure; not atmospheric pressure.

10. 5.2 An open manometer, filled with mercury and connected to a container of hydrogen. The mercury level is 62 mm higher in the arm of the tube connected to the gas. Atmospheric pressure is 97.7 kPa. What is the pressure of the hydrogen in kilopascals?

11. An open manometer, filled with mercury and connected to a container of hydrogen. The mercury level is 120 mm higher in the arm of the tube connected to the atmosphere. Atmospheric pressure is 0.995 atm. What is the pressure of the hydrogen in kilopascals?

12. A closed manometer is filled with mercury and connected to a container of nitrogen. The difference is the height of mercury in the two arms is 691 mm. What is the pressure of the nitrogen in kilopascals? And atmospheres? And torr?

13. P  1/V P x V = constant P 1 x V 1 = P 2 x V 2 5.3 Boyle’s Law Constant temperature Constant amount of gas

14. Boyle’s

17. An inflated helium balloon with a volume of 0.55 L at sea level (1.0 atm) is allowed to rise to a height of 6.5 km where the pressure is about 0.40 atm. Assuming the temperature remains constant, what is the final volume of the balloon?

18. Variation of gas volume with temperature at constant pressure. 5.3 V  TV  T V = constant x T V 1 /T 1 = V 2 /T 2 T (K) = t ( 0 C) + 273.15 Charles’ Law Temperature must be in Kelvin

19. As T increasesV increases 5.3

21. Argon is an inert gas used in lightbulbs to retard the vaporization of the tungsten filament. A certain lightbulb containing argon at 1.20 atm and 18 o C is heated to 85 o C at constant volume. Calculate the final pressure in kPa.

22. Gay-Lussac’s A 30.0 L sample of nitrogen inside a metal container at 20.0 °C is placed inside an oven whose temperature is 50.0 °C. The pressure inside the container at 20.0 °C was at 3.00 atm. What is the pressure of the nitrogen after its temperature is increased?

23. Avogadro’s Law V  number of moles (n) V = constant x n V 1 /n 1 = V 2 /n 2 5.3 Constant temperature Constant pressure

24. A 1.50L balloon containing 2.76 g of N 2 gas is punctured by a safety pin. How many moles of N 2 will be in the balloon if the volume changes to 0.45L?

25. Combined Gas Law  If a fixed amount of gas occupies 2.53 m 3 at a temperature of -15 o C and 191 Torr, what volume will it occupy at 25 o C and 1142 torr?

26. Ideal Gas Equation

27. Values of ‘R’

28. What is an ideal gas?  Hypothetical gas  Approximates gas behavior so we can use our formula.  Conditions where real gases really depart from ideal gas behavior:  High pressure  Low temperature  For ideal gas equation, we are assuming our gases can be fairly described as ‘ideal.’

29. What is the pressure exerted by 0.508 mol of O 2 in a 15.0 L container at 303 K?

30. How many grams of N 2 gas are there in a sample that occupies 35.0 L at a pressure of 3.15 atm at a temperature of 579 o C?

31. What is the volume occupied by 16.0 g of ethane gas at 720 torr and 18 o C?

32. Molar Mass Determination  If 0.550 g of a gas occupies 0.200 L at 0.968 atm and 289 K, what is the molar mass of the gas?

33. Gas Density: MP = dRT  Calculate the density of methane gas, CH 4, in grams per liter at 25 o C and 0.978 atm.

34.  What is the molar mass of a gaseous hydrocarbon having a density of 2.42 g/L at 20.0 o C and 762 torr? Predict the molecular formula.

35. Gas Stoichiometry  Sodium azide (NaN 3 ) is used in some automobile airbags. The nitrogen gas produced quickly inflates the bag between the driver and the windshield and dashboard. Calculate the volume of N 2 generated at 80 o C and 823 mmHg by the decomposition of 60.0 g of NaN 3. (Rxn next slide)

36.  2 NaN 3 (s)  2 Na (s) + 3 N 2 (g)

37.  The pressure of carbon dioxide inside the cabin of a submarine having a volume of 2.4 x 10 5 L is 7.9 x 10 -3 atm at 312 K. A solution of lithium hydroxide of negligible volume is introduced into the cabin. Eventually the pressure of CO 2 falls to 1.2 x 10 -4 atm. How many grams of lithium carbonate are formed in this process? 2 LiOH (aq) + CO 2 (g)  Li 2 CO 3 (aq) + H 2 O (l)

39. Dalton’s Law of Partial Pressures V and T are constant P1P1 P2P2 P total = P 1 + P 2 5.6

41. To see how each partial pressure is related to total pressure: Do PART OVER WHOLE or P A / P T and P B / P T

42. Mole Fraction  Dimensionless quantity that expresses ratio of the number of moles of one gas to the number of moles of all gases present.

43. A sample of natural gas contains 8.24 moles of methane (CH 4 ), 0.421 mol of ethane (C 2 H 6 ), and 0.116 mol of propane (C 3 H 8 ). If the total pressure is 1.37 atm, what are the partial pressures of the gases?

44. 2KClO 3 (s) 2KCl (s) + 3O 2 (g) Bottle full of oxygen gas and water vapor P T = P O + P H O 22 5.6 Gas Collected Over Water

45. 5.6

46. Oxygen gas generated by the decomposition of potassium chlorate is collected over water. The volume of the oxygen gas collected at 25 o C and atmospheric pressure of 762 mmHg is 128 mL. Calculate the mass, in grams, of oxygen gas obtained.

47. Kinetic Molecular Theory  Ideal gas equation describes HOW gases behave.  Kinetic Molecular Theory explains WHY they behave as they do.  Kinetic molecular theory model was developed over 100 years... Rudolf Clausius published a complete and satisfactory form of the theory in 1857.  Summarized in the following 5 statements:

48. 1) Gases consist of large numbers of molecules that are in continuous, random, straight-line motion. 2) The volume of all the molecules of the gas is negligible compared to the total volume in which the gas is contained. 3) Attractive and repulsive forces between gas molecules are negligible. 4) Energy can be transferred between molecules, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant. Collisions are perfectly elastic.

49. 5) The average kinetic energy of the molecules is proportional to the absolute temperature. At any given temperature, the molecules of all gases have the same average kinetic energy.

50. Kinetic theory of gases and … Compressibility of Gases Boyle’s Law P  collision rate with wall Collision rate  number density Number density  1/V P  1/V Charles’ Law P  collision rate with wall Collision rate  average kinetic energy of gas molecules Average kinetic energy  T P  TP  T 5.7

51. Kinetic theory of gases and … Avogadro’s Law P  collision rate with wall Collision rate  number density Number density  n P  nP  n Dalton’s Law of Partial Pressures Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas P total =  P i 5.7

52. The distribution of speeds for nitrogen gas molecules at three different temperatures The distribution of speeds of three different gases at the same temperature 5.7 u rms = 3RT M 

53. Average speed vs. RMS Speed

54. Calculate the rms speeds, u, of an N 2 molecule and He atom at 25 o C.

55. Gas Effusion vs. Diffusion  Effusion – escape of gas molecules though a tiny hole into an evacuated space.

56. Graham’s Law of Effusion  1846 – Thomas Graham  Effusion rate of gas is inversely proportional to the square root of its molar mass. NH 3 17 g/mol HCl 36 g/mol NH 4 Cl

57. Calculate the ratio of effusion rates of N 2 and O 2.

58. An unknown gas composed of a diatomic molecule effuses at a rate that is only 0.355 times that of O 2 at the same temperature. What is the molar mass of the unknown gas?

59. Gas Diffusion  Gradual mixing of gas molecules by virtue of their kinetic properties.  Higher concentration to lower concentration  Gases of ligher molecular weight diffuse faster than those of greater molecular weight.  Slowed due to random collisions.

60. Non-Ideal Gases  Ideal gas law assumes two things: 1. Gas molecules do not exert any force, either attractive or repulsive, on one another. 2. Total volume of gas molecules in a container is negligible to the overall volume of the container.  However, there are two situations where gases are not so ‘ideal.’  High pressure  Low temperature

61. Effect of intermolecular forces on the pressure exerted by a gas. 5.8

62. Volume correction for a non-ideal gas:  In ideal gas equation, V represents volume of container.  Each molecule actually has a finite (even though small) volume.  So….actual volume is less than what we represent in ideal gas equation.

63. 5.8 Van der Waals equation nonideal gas P + (V – nb) = nRT an 2 V2V2 () } corrected pressure } corrected volume

64. Given that 2.50 mol of NH 3 occupy 5.20 L at 47 o C, calculate the pressure of the gas using a) the ideal gas equation and b) van der Waals equation.

65. Calculate the pressure exerted by 4.37 mol of molecular chlorine confined in a volume of 2.45 L at 38 o C. Compare the pressure with the calculated pressure using the ideal gas equation