1. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 1 of 41 Chapter 6: Gases Philip Dutton University of Windsor, Canada Prentice-Hall © 2002 General Chemistry Principles and Modern Applications Petrucci Harwood Herring 8 th Edition

2. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 2 of 41 Contents 6-1Properties of Gases: Gas Pressure 6-2The Simple Gas Laws 6-3Combining the Gas Laws: The Ideal Gas Equation and The General Gas Equation 6-4Applications of the Ideal Gas Equation 6-5Gases in Chemical Reactions 6-6Mixtures of Gases

3. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 3 of 41 Contents 6-6Mixtures of Gases 6-7KineticMolecular Theory of Gases 6-8Gas Properties Relating to the KineticMolecular Theory 6-9Non-ideal (real) Gases Focus on The Chemistry of Air-Bag Systems

4. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 4 of 41 6-1 Properties of Gases: Gas Pressure Gas Pressure Liquid Pressure P (Pa) = Area (m 2 ) Force (N) P = g ·h ·d

5. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 5 of 41 Barometric Pressure Standard Atmospheric Pressure 1.00 atm 760 mm Hg, 760 torr 101.325 kPa 1.01325 bar 1013.25 mbar

6. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 6 of 41 Manometers

7. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 7 of 41 6-2 Simple Gas Laws Boyle 1662 P 1 V PV = constant

8. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 8 of 41 Example 5-6 Relating Gas Volume and Pressure – Boyles Law. P 1 V 1 = P 2 V 2 V2 =V2 = P1V1P1V1 P2P2 = 694 L V tank = 644 L

9. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 9 of 41 Charless Law Charles 1787 Gay-Lussac 1802 V T V = b T

10. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 10 of 41 STP Gas properties depend on conditions. Define standard conditions of temperature and pressure (STP). P = 1 atm = 760 mm Hg T = 0°C = 273.15 K

11. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 11 of 41 Avogadros Law Gay-Lussac 1808 –Small volumes of gases react in the ratio of small whole numbers. Avogadro 1811 –Equal volumes of gases have equal numbers of molecules and –Gas molecules may break up when they react.

12. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 12 of 41 Formation of Water

13. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 13 of 41 Avogadros Law V n or V = c n At STP 1 mol gas = 22.4 L gas At an a fixed temperature and pressure:

14. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 14 of 41 6-3 Combining the Gas Laws: The Ideal Gas Equation and the General Gas Equation Boyles lawV 1/P Charless lawV T Avogadros law V n PV = nRT V nT P

15. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 15 of 41 The Gas Constant R =R = PV nT = 0.082057 L atm mol -1 K -1 = 8.3145 m 3 Pa mol -1 K -1 PV = nRT = 8.3145 J mol -1 K -1 = 8.3145 m 3 Pa mol -1 K -1

16. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 16 of 41 The General Gas Equation R =R = = P2V2P2V2 n2T2n2T2 P1V1P1V1 n1T1n1T1 = P2P2 T2T2 P1P1 T1T1 If we hold the amount and volume constant:

17. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 17 of 41 6-4 Applications of the Ideal Gas Equation

18. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 18 of 41 Molar Mass Determination PV = nRT and n = m M PV = m M RT M = m PV RT

19. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 19 of 41 Example 6-10 Determining a Molar Mass with the Ideal Gas Equation. Polypropylene is an important commercial chemical. It is used in the synthesis of other organic chemicals and in plastics production. A glass vessel weighs 40.1305 g when clean, dry and evacuated; it weighs 138.2410 when filled with water at 25°C (δ=0.9970 g cm -3 ) and 40.2959 g when filled with propylene gas at 740.3 mm Hg and 24.0°C. What is the molar mass of polypropylene? Strategy: Determine V flask. Determine m gas. Use the Gas Equation.

20. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 20 of 41 Example 5-6 Determine V flask : V flask = m H 2 O d H 2 O = (138.2410 g – 40.1305 g) (0.9970 g cm -3 ) Determine m gas : = 0.1654 g m gas = m filled - m empty = (40.2959 g – 40.1305 g) = 98.41 cm 3 = 0.09841 L

21. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 21 of 41 Example 5-6 Use the Gas Equation: PV = nRT PV = m M RT M = m PV RT M = (0.9741 atm)(0.09841 L) (0.6145 g)(0.08206 L atm mol -1 K -1 )(297.2 K) M = 42.08 g/mol

22. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 22 of 41 Gas Densities PV = nRT and d = m V PV =PV = m M RT MP RTV m = d =, n = m M

23. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 23 of 41 6-5 Gases in Chemical Reactions Stoichiometric factors relate gas quantities to quantities of other reactants or products. Ideal gas equation used to relate the amount of a gas to volume, temperature and pressure. Law of combining volumes can be developed using the gas law.

24. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 24 of 41 Example 6-10 Using the Ideal gas Equation in Reaction Stoichiometry Calculations. The decomposition of sodium azide, NaN 3, at high temperatures produces N 2 (g). Together with the necessary devices to initiate the reaction and trap the sodium metal formed, this reaction is used in air-bag safety systems. What volume of N 2 (g), measured at 735 mm Hg and 26°C, is produced when 70.0 g NaN 3 is decomposed. 2 NaN 3 (s) 2 Na(l) + 3 N 2 (g)

25. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 25 of 41 Example 6-10 Determine moles of N 2 : Determine volume of N 2 : n N 2 = 70 g N 3 1 mol NaN 3 65.01 g N 3 /mol N 3 3 mol N 2 2 mol NaN 3 = 1.62 mol N 2 = 41.1 L P nRT V = = (735 mm Hg) (1.62 mol)(0.08206 L atm mol -1 K -1 )(299 K) 760 mm Hg 1.00 atm

26. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 26 of 41 6-6 Mixtures of Gases Partial pressure –Each component of a gas mixture exerts a pressure that it would exert if it were in the container alone. Gas laws apply to mixtures of gases. Simplest approach is to use n total, but....

27. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 27 of 41 Daltons Law of Partial Pressure

28. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 28 of 41 Partial Pressure P tot = P a + P b +… V a = n a RT/P tot and V tot = V a + V b +… VaVa V tot n a RT/P tot n tot RT/P tot = = nana n tot PaPa P tot n a RT/V tot n tot RT/V tot = = nana n tot nana = a Recall

29. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 29 of 41 Pneumatic Trough P tot = P bar = P gas + P H 2 O

30. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 30 of 41 6-7 Kinetic Molecular Theory Particles are point masses in constant, random, straight line motion. Particles are separated by great distances. Collisions are rapid and elastic. No force between particles. Total energy remains constant.

31. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 31 of 41 Pressure – Assessing Collision Forces Translational kinetic energy, Frequency of collisions, Impulse or momentum transfer, Pressure proportional to impulse times frequency

32. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 32 of 41 Pressure and Molecular Speed Three dimensional systems lead to: u m is the modal speed u av is the simple average u rms

33. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 33 of 41 Pressure Assume one mole: PV=RT so: N A m = M: Rearrange:

34. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 34 of 41 Distribution of Molecular Speeds

35. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 35 of 41 Determining Molecular Speed

36. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 36 of 41 Temperature Modify: PV=RT so: Solve for e k : Average kinetic energy is directly proportional to temperature!

37. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 37 of 41 6-8 Gas Properties Relating to the Kinetic-Molecular Theory Diffusion –Net rate is proportional to molecular speed. Effusion –A related phenomenon.

38. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 38 of 41 Grahams Law Only for gases at low pressure (natural escape, not a jet). Tiny orifice (no collisions) Does not apply to diffusion. Ratio used can be: –Rate of effusion (as above) –Molecular speeds –Effusion times –Distances traveled by molecules –Amounts of gas effused.

39. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 39 of 41 6-9 Real Gases Compressibility factor PV/nRT = 1 Deviations occur for real gases. –PV/nRT > 1 - molecular volume is significant. –PV/nRT < 1 – intermolecular forces of attraction.

40. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 40 of 41 Real Gases

41. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 41 of 41 van der Waals Equation P + n2an2a V2V2 V – nb = nRT

42. Prentice-Hall © 2002General Chemistry: Chapter 6Slide 42 of 41 Chapter 6 Questions 9, 13, 18, 31, 45, 49, 61, 63, 71, 82, 85, 97, 104.