The Chemistry of Gases

1. The Chemistry of Gases

2. A Gas • Uniformly fills any container. • Mixes completely with any other gas • Exerts pressure on its surroundings.

3. Pressure • is equal to force/unit area • SI units = Newton/meter2 = 1 Pascal (Pa) • 1 standard atmosphere = 101,325 Pa • 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr

5. Effect of Atmospheric Pressure

7. Standard Pressure Units • 1 atmosphere = • 760 mm Hg = 760 torr • 1.013 x 105 Pa = 101.3 kPa • 14.7 psi (pounds per square inch)

8. Pressure Conversions The pressure of a gas is measured as 49 torr. Represent this as atmospheres and as Pascals. 49 torr| 1 atm = 6.4 x 10-2 atm | 760 torr 49 torr | 1.013 x 105 Pa = 6.5 x 103 Pa | 760 torr

9. Boyle’s Law* • Pressure  Volume = Constant (T = constant) • P1V1 = P2V2 (T = constant) • V 1/P (T = constant) • (*Holds precisely only at very low pressures.)

10. A gas that strictly obeys Boyle’s Law is called an ideal gas.

13. 1.53 L of sulfur dioxide gas at 5600 Pa is changed to 15000 Pa at constant temperature. What is its new volume? P1V1 =P2V2 5600 x 1.53 = 15000 x V2 V2 = 0.57 L 1.0 L of hydrogen gas at 345 torr is connected to an empty 2.5 L flask and allowed to combine. What is its new pressure? 345 x 1.0 = P2 x 3.5 P2 = 98.6 torr

14. Charles’s Law • The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. • V = bT (P = constant) b = a proportionality constant

16. Balloon with Liquid N2

18. Charles’s Law

19. Always Change to KELVIN! K = C + 273

20. A sample of gas at 15o C and 1 atm has a volume of 2.58 L. What is its new volume at 38o C and 1 atm pressure? Pressure remains constant at 1 atm T1 = 15 + 273 = 288 K T2 = 38 + 273 = 311 K V1 = V2 or V1T2 = V2T1 T1 T2 2.58 x 311 = V2 x 288 V2 = 2.79 L

21. Gay-Lussac’s Law • Pressure is directly proportional to the Kelvin Temperature • P = k T • or P1 = P2 • T1 T2

23. Standard Temperature and Pressure • “STP” • P = 1 atmosphere • T = C • The molar volume of an ideal gas is 22.42 liters at STP

24. Combined Gas Law • When all three change use: • P1 V1 = P2 V2 • T1 T2 • orP1V1 T2 = P2V2 T1

25. A cylinder contains 255 mL of CO2 at 27o C and 812 torr. What volume would this occupy at STP? P1= 812 torr T1= 27o C + 273= 300 K V1= 255 mL P2= 1 atm= 760 torr T2 = 0o C = 273 K P1V1T2=P2V2T1 (812)(255)(273)=V2(760)(300) V2= 247.9 mL

26. Avogadro’s Law • For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). • V = an • a = proportionality constant • V = volume of the gas • n = number of moles of gas

28. Ideal Gas Law • An equation of state for a gas. • “state” is the condition of the gas at a given time. • PV = nRT

29. Ideal Gas Law • PV = nRT • R = proportionality constant = 0.08206 L atm  mol • P = pressure in atm • V = volume in liters • n = moles • T = temperature in Kelvins • Holds closely at P < 1 atm

30. Ideal Gas Laws • Can be used to calculate molar masses by gas density • density= mass = molar mass • volume molar volume • At STP, molar volume is 22.4 L

31. Suppose you have a sample of ammonia gas with a volume of 856 mL at a pressure of 932 torr and 28o C. What is the mass of the ammonia present? P= 932 torr / 760 torr = 1.23 atm V = 0.856 L T = 28 + 273= 301 K n = PV = (1.23)(.856) = 0.0426 moles RT (.0821)(301) mass = moles x MM= 0.0426 x 17= 0.724g

32. Dalton’s Law of Partial Pressures • For a mixture of gases in a container, PTotal = P1 + P2 + P3 + . . . Used primarily when collecting gases over water.

33. Mixtures of helium and oxygen are used for deep scuba diving. If 46 L oxygen and 12 L He at 1.0 atm are put into a 5.0 L tank at 25oC, calculate the partial pressures of each gas and the total pressure in the tank. n = PV = (1)(46) and (1)(12) RT (.0821)(298) (.0821)(298) nO2= 1.9 mol nHe = 0.49 mol

34. In the tank, V= 5.0 L PO2 =nRT / V = (1.9)(.0821)(298) / 5.0 = 9.3 atm Phe = (0.49)(.0821)(298)/ 5.0 = 2.4 atm Ptotal = 9.3 + 2.4 = 11.7 atm

35. Homework • #1 p223ff 8, 12, 15, 17, 18, 30

36. Stoichiometry and Gases A sample of solid potassium chlorate decomposes by the equation 2 KClO3 (s) -----> 2 KCl (s) + 3 O2 (g) If 650 mL of oxygen at 22oC and 754 torr is collected over water, how much KClO3 decomposed? PH2O = 21 torr (from table of vapor pressure) PO2 = 754 - 21 = 733 torr / 760 = 0.964 atm nO2 = PV /RT = (.964)(.650) / (.0821)(295) = 0.0259 0.0259 mol O2 | 2 mol KClO3 | 122.6 g KClO3 = 2.11 g | 3 mol O2 | 1 mol KClO3 KClO3

37. Homework • #2 p226ff 32, 35, 38, 39, 41, 42, 44

38. Kinetic Molecular Theory • 1. Volume of individual particles is  zero. • 2. Collisions of particles with container walls cause pressure exerted by gas. • 3. Particles exert no forces on each other. • 4. Average kinetic energy  Kelvin temperature of a gas.

39. The Meaning of Temperature • Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

42. Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. • Effusion: describes the passage of gas into an evacuated chamber.

44. Diffusion Rates

45. Effusion: Diffusion:

46. Find the ratio of the effusion rates of UF6 versus H2. Rate H2 = MMUF6 = 352 =13.2 Rate UF6 MMH2 2

47. Homework • #3 p228ff 53, 54, 68, 70, 72, 76 • #4 p229ff 77, 89, 91, 92 • Super XCR #97

48. Real Gases Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).

50. Real Gases   corrected pressure corrected volume Pideal Videal