Understanding Gas Behavior in Chemistry

1. Chapter 11Gases and Their Properties

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3. BEHAVIOR OF GASESChapter 11

4. Importance of Gases • Airbags fill with N2 gas in an accident. • Gas is generated by the decomposition of sodium azide, NaN3. • 2 NaN3f 2 Na + 3 N2 PLAY MOVIE

5. Hot Air Balloons —How Do They Work? PLAY MOVIE

6. THREE STATES OF MATTER PLAY MOVIE

7. General Properties of Gases • There is a lot of “free” space in a gas. • Gases can be expanded infinitely. • Gases occupy containers uniformly and completely. • Gases diffuse and mix rapidly.

8. Properties of Gases Gas properties can be modeled using math. Model depends on— • V = volume of the gas (L) • T = temperature (K) • n = amount (moles) • P = pressure (atmospheres)

9. Pressure Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643)

10. Pressure Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). P of Hg pushing down related to • Hg density • column height

11. Pressure Column height measures P of atmosphere • 1 standard atm= 760 mm Hg = 29.9 inches Hg = about 34 feet of water SI unit is PASCAL, Pa, where 1 atm = 101.325 kPa

12. IDEAL GAS LAW P V = n R T Brings together gas properties. Can be derived from experiment and theory.

13. Boyle’s Law If n and T are constant, then PV = (nRT) = k This means, for example, that P goes up as V goes down. Robert Boyle (1627-1691). Son of Earl of Cork, Ireland.

14. Boyle’s Law A bicycle pump is a good example of Boyle’s law. As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire. PLAY MOVIE

15. Charles’s Law If n and P are constant, then V = (nR/P)T = kT V and T are directly related. Jacques Charles (1746-1823). Isolated boron and studied gases. Balloonist.

16. Charles’s original balloon Modern long-distance balloon

17. Charles’s Law Balloons immersed in liquid N2 (at -196 ˚C) will shrink as the air cools (and is liquefied).

18. Charles’s Law PLAY MOVIE

19. twice as many molecules Avogadro’s Hypothesis Equal volumes of gases at the same T and P have the same number of molecules. V = n (RT/P) = kn V and n are directly related.

20. Avogadro’s Hypothesis The gases in this experiment are all measured at the same T and P. f PLAY MOVIE 2 H2(g) + O2(g) f 2 H2O(g)

21. Combining the Gas Laws • V proportional to 1/P • V prop. to T • V prop. to n • Therefore, V prop. to nT/P • V = 22.4 L for 1.00 mol when • Standard pressure and temperature (STP) • T = 273 K • P = 1.00 atm

22. Using PV = nRT How much N2 is req’d to fill a small room with a volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 oC? R = 0.082057 L•atm/K•mol Solution 1. Get all data into proper units V = 27,000 L T = 25 oC + 273 = 298 K P = 745 mm Hg (1 atm/760 mm Hg) = 0.98 atm

23. Using PV = nRT How much N2 is req’d to fill a small room with a volume of 960 cubic feet (27,000 L) to P = 745 mm Hg at 25 oC? R = 0.082057 L•atm/K•mol Solution 2. Now calc. n = PV / RT n = 1.1 x 103 mol (or about 30 kg of gas)

24. Gases and Stoichiometry 2 H2O2(liq) f 2 H2O(g) + O2(g) Decompose 0.11 g of H2O2 in a flask with a volume of 2.50 L. What is the pressure of O2 at 25 oC? Of H2O? Bombardier beetle uses decomposition of hydrogen peroxide to defend itself.

25. Gases and Stoichiometry 2 H2O2(liq) f 2 H2O(g) + O2(g) Decompose 0.11 g of H2O2 in a flask with a volume of 2.50 L. What is the pressure of O2 at 25 oC? Of H2O? Solution Strategy: Calculate moles of H2O2 and then moles of O2 and H2O. Finally, calc. P from n, R, T, and V.

26. Gases and Stoichiometry 2 H2O2(liq) f2 H2O(g) + O2(g) Decompose 0.11 g of H2O2 in a flask with a volume of 2.50 L. What is the pressure of O2 at 25 oC? Of H2O? Solution

27. Gases and Stoichiometry 2 H2O2(liq) f2 H2O(g) + O2(g) Decompose 0.11 g of H2O2 in a flask with a volume of 2.50 L. What is the pressure of O2 at 25 oC? Of H2O? Solution P of O2 = 0.016 atm

28. Gases and Stoichiometry 2 H2O2(liq) f2 H2O(g) + O2(g) What is P of H2O? Could calculate as above. But recall Avogadro’s hypothesis. V n at same T and P P n at same T and V There are 2 times as many moles of H2O as moles of O2. P is proportional to n. Therefore, P of H2O is twice that of O2. P of H2O = 0.032 atm

29. Dalton’s Law of Partial Pressures • 2 H2O2(liq) f2 H2O(g) + O2(g) • 0.032 atm 0.016 atm What is the total pressure in the flask? Ptotal in gas mixture = PA + PB + ... Therefore, Ptotal = P(H2O) + P(O2) = 0.048 atm Dalton’s Law: total P is sum of PARTIAL pressures.

30. Dalton’s Law John Dalton 1766-1844

31. Low density helium Higher Density air GAS DENSITY PLAY MOVIE

32. d and M proportional GAS DENSITY PV = nRT and density (d) = m/V

33. The Disaster of Lake Nyos • Lake Nyos in Cameroon was a volcanic lake. • CO2 built up in the lake and was released explosively on August 21, 1986. • 1700 people and hundreds of animals died. • See Chapter 14 for more information

34. USING GAS DENSITY The density of air at 15 oC and 1.00 atm is 1.23 g/L. What is the molar mass of air? 1. Calc. moles of air. V = 1.00 L P = 1.00 atm T = 288 K n = PV/RT = 0.0423 mol 2. Calc. molar mass mass/mol = 1.23 g/0.0423 mol = 29.1 g/mol

35. KINETIC MOLECULAR THEORY(KMT) Theory used to explain gas laws. KMT assumptions are • Gases consist of molecules in constant, random motion. • P arises from collisions with container walls. • No attractive or repulsive forces between molecules. Collisions elastic. • Volume of molecules is negligible.

36. Kinetic Molecular Theory Because we assume molecules are in motion, they have a kinetic energy. KE = (1/2)(mass)(speed)2 At the same T, all gases have the same average KE. As T goes up for a gas, KE also increases — and so does speed.

37. Kinetic Molecular Theory At the same T, all gases have the same average KE. As T goes up, KE also increases — and so does speed. PLAY MOVIE

38. Root mean square speed Kinetic Molecular Theory Maxwell’s equation where u is the speed and M is the molar mass. • speed INCREASES with T • speed DECREASES with M

39. Distribution of Gas Molecule Speeds • Boltzmann plots • Named for Ludwig Boltzmann doubted the existence of atoms. • This played a role in his suicide in 1906. PLAY MOVIE

40. Velocity of Gas Molecules Molecules of a given gas have a rangeof speeds.

41. Velocity of Gas Molecules Average velocity decreases with increasing mass.

42. DIFFUSION is the gradual mixing of molecules of different gases. GAS DIFFUSION AND EFFUSION

43. EFFUSION is the movement of molecules through a small hole into an empty container. GAS EFFUSION See Figure 11.19

44. GAS DIFFUSION AND EFFUSION Molecules effuse thru holes in a rubber balloon, for example, at a rate (= moles/time) that is • proportional to T • inversely proportional to M. Therefore, He effuses more rapidly than O2 at same T. He

45. GAS DIFFUSION AND EFFUSION Graham’s law governs effusion and diffusion of gas molecules. Rate of effusion is inversely proportional to its molar mass. Thomas Graham, 1805-1869. Professor in Glasgow and London.

46. Gas Diffusionrelation of mass to rate of diffusion • HCl and NH3 diffuse from opposite ends of tube. • Gases meet to form NH4Cl • HCl heavier than NH3 • Therefore, NH4Cl forms closer to HCl end of tube. PLAY MOVIE See Active Figure 11.18

47. Using KMT to Understand Gas Laws Recall that KMT assumptions are • Gases consist of molecules in constant, random motion. • P arises from collisions with container walls. • No attractive or repulsive forces between molecules. Collisions elastic. • Volume of molecules is negligible.

48. Avogadro’s Hypothesis and Kinetic Molecular Theory PLAY MOVIE P proportional to n — when V and T are constant

49. Gas Pressure, Temperature, and Kinetic Molecular Theory PLAY MOVIE P proportional to T — when n and V are constant

50. Boyle’s Law and Kinetic Molecular Theory PLAY MOVIE P proportional to 1/V — when n and T are constant