Properties of Gases CHAPTER 11 Chemistry: The Molecular Nature of Matter, 6 th edition

# Properties of Gases CHAPTER 11 Chemistry: The Molecular Nature of Matter, 6 th edition

## Properties of Gases CHAPTER 11 Chemistry: The Molecular Nature of Matter, 6 th edition

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1. Properties of Gases CHAPTER 11 Chemistry: The Molecular Nature of Matter, 6th edition By Jesperson, Brady, & Hyslop

2. CHAPTER 11 Learning Objectives • Describe properties of a gas • Read a barometer & monometer • Unit conversions for moles, temperature, pressure, and volume • Explain relationships between variables of state & predict effect of a change to a system • Apply gas law to stoichiometry, molecular weight, and density problems • Understand the relationship between variables of state in terms of Kinetic Molecular Theory • Calculate mole fractions and partial pressures • Compare rates of effusion • Compute variables of state using the real gas law

3. CHAPTER 11 Lecture Road Map What is a gas? Define & measure variables of state Relationships between variables of state Equation of state for an ideal gas Dalton’s law of partial pressure & gas stoichiometry Kinetic Molecular Theory & Graham’s law Real gas law

4. Guy-Lussacs Law Charles Law Avagadro’s Law Boyles Law Mole Fraction & Mole % Ideal Gas Law Dalton’s Law Volume CHAPTER 11 Properties of Gases Real Gas Law Pressure: Barometers & Monometers Pressure Variables of State Kinetic Molecular Theory Temperature: K, °C, °F Graham’s Law Relationships between variables of state Absolute 0

5. Group Problem In groups of 3-5 brainstorm how to describe a gas. What are some observable properties? What variables would you use to describe a gas?

6. Group Problem • Describe a gas: • Will expand to fill a volume • Mostly empty space so can be compressed • Can expand & contract with temperature • Particles constantly in motion & constantly colliding • Some gases are heavier then others and sink to the floor rather then rise to the ceiling

7. Variables of State Physical Properties of Gases Despite wide differences in chemical properties, all gases more or less obey the same set of physicalproperties • Pressure (P ) • Volume (V ) • Temperature (T ) • Amount = moles (n) Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

8. Variables of State Volume (V) V = l × w × h for a cube V = (4/3) π r3 for a sphere V = π r2 h for a cylinder Units of Volume: Liters (L) 1 L = 0.001 m3 = 1000 cm3 = 1000 mL

9. Variables of State # of Moles (n) Avagadro’s number (NA) allows us to measure the number of particles of a gas as the number of moles: NA = 6.02214129 × 1023 particles/mole We can measure the number of moles of a gas by measuring its mass and knowing its Molar Mass Molar Mass = mass / (# of moles) M = m/n Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

10. Group Problem • How many moles of the CFC pollutant CCl2F2 are in 50.0g?

11. Group Problem Calculate the mass of 3 moles of nerve agent VX: CH3CH2

12. Variables of State Temperature (T) Temperature is measured with a thermometer usually in °C, °F, or Kelvin. 0°C = 273 K 1°C = (1°F -32) × (5/9)

13. Group Problem If Room Temperature (RT) is 25°C, what is RT in Kelvin? °F? Write out a formula to convert °F to K.

14. Group Problem If Room Temperature (RT) is 25°C, what is RT in Kelvin? °F? RT = 25°C + 273 K = 298 K

15. Variables of State Pressure (P) Force = mass × area • Pressure is the force of the collisions of the gas distributed over the surface area of the container walls • Earth exerts gravitational force on everything with mass near it • Atmospheric Pressure of earth: gravity pulling on gases creating a blanket around earth Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

16. Group Problem • Calculate Atmospheric Pressure on Earth. • Identify information needed • Research • Solve

17. Group Problem Calculate Atmospheric Pressure on Earth.

18. Variables of State Pressure (P) A vacuum exerts zero pressure on a containers walls. Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

19. Variables of State Pressure (P) Measure Atmospheric pressure with a barometer. ToricelliBarometer: • Tube that is 80 cm in length • Sealed at one end • Filled with mercury • In dish filled with mercury Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

20. Variables of State Pressure (P) • Atmospheric pressure • Pushes down on mercury • Forces mercury up tube • Weight of mercury in tube • Pushes down on mercury in dish • When two forces balance • Mercury level stabilizes • Read atmospheric pressure Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

21. Variables of State Pressure (P) • If atmospheric pressure is high • Pushes down on mercury in dish & increase level in tube • If atmospheric pressure is low • Pressure on mercury in dish less than pressure from column & decreaselevel in tube Therefore: • Height of mercury in tube is the atmospheric pressure Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

22. Variables of State Pressure (P) • measured with a barometer • P=g×d×h • d=density of the liquid • g= gravitational acceleration • h=height of the column supported Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

23. Variables of State Pressure (P) Typical range of pressure for most places where people live 730 to 760 mm Hg Top of Mt. Everest Atmospheric Pressure = 250 mm Hg Standard Atmosphere (atm) Average pressure at sea level Pressure needed to support column of mercury 760 mm high measured at 0 °C = 1 atm Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

24. Variables of State Pressure (P) SI unit for pressure Pascal = Pa = 1 N/m2 1atm = 101,325 Pa = 101 kPa 100 kPa = 0.9868 atm Other units of pressure 1.013 Bar = 1013 mBar = 1 atm 760 mm Hg = 1 atm 760 torr = 1 atm At sea level 1 torr = 1 mm Hg Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

25. Group Problem Express Pressure in atm and kPa for a gas at 705 mmHg.

26. Variables of State Pressure (P) Open Ended Manometer Pgas > Patm Gas pushes mercury uptube Pgas < Patm Atmosphere pushes mercury downtube Pgas = Patm Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

27. Group Problem CO2 collected in a monometer in a lab with a barometric reading of 97 kPa. What is the Pressure of CO2? 33 mm

28. Variables of State Closed-end Manometer Pressure (P) • Arm farthest from vessel (gas) sealed • Tube filled with mercury • Then open system to flask and some mercury drains out of sealed arm • Vacuum exists above mercury in sealed arm Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

29. Variables of State Closed-end Manometer Pressure (P) • Level of mercury in arm falls, as not enough pressure in the flask to hold up Hg • Patm = 0 • Pgas = PHg • So directly read pressure Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

30. Group Problem What is the pressure of an unknown gas within this closed monometer? Closed monometer 437 mm 205 mm

31. Ideal Gas Law Boyle’s Law Volume will change to equalize pressure with atmosphere is not in a rigid vessel. V α 1/P Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

32. Ideal Gas Law Charles Law If Pressure is constant but freeze a balloon, it decreases in V Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

33. Ideal Gas Law Charles Law If Pressure is constant but freeze a balloon, it decreases in V V α T Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

34. Low T, Low P P High T, High P T (K) Ideal Gas Law Gay Lussac’s Law Volume (V ) and number of moles (n) are constant P increases as T increases Showed that gas pressure is directly proportional to absolute temperature Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

35. Group Problem What happens to gas pressure when you raise the temperature? Pressure increases because the faster moving molecules hit the walls of the container with greater force No change in pressure is observed because the area increased.

36. Ideal Gas Law Combined Gas Law • Boyle’s law: • Charles Law: • Guy-Lussac’s Law: • is equivalent to • For any two conditions: Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

37. Ideal Gas Law Combined Gas Law Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

38. Group Problem N2 + H2 NH3 How much H2 at 0°C and 0.86 atm do you need to react completely with 750 mL of N2 at 1.5 atm and 20°C to form ammonia? What is the number of moles of ammonium produced if the density of hydrogen is 0.08988 g/L? Hint: is this equation balanced?

39. Group Problem A sample of helium gas occupies 500.0 mL at 1.21 atm Calculate the volume of the gas if the pressure is reduced to 491 torr

40. Ideal Gas Law Avagadro’s Law V α n At standard temperature (273 K) And standard pressure (1 atm) 1 mole of any gas will occupy the same volume Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

41. Group Problem What happens to gas pressure when you increase the number of molecules in the container? pressure increases because more molecules hit the walls of the container, thus exert a greater force on the container No pressure change is observed.

42. Ideal Gas Law Putting It All Together If then • R is the universal gas constant Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

43. Group Problem Plug in values of T, V, n and P for 1 mole of gas at STP (1 atm and 0.0 °C) T = 0.0 °C = 273.15 K P = 1 atm V = 22.4 L n = 1 mol R = 0.082057 L atmmol–1 K–1

44. Ideal Gas Law Putting It All Together If then • R is the universal gas constant • R = 0.0821 (L×atm) / (mol×K) • = 8.314 J / (mol×K) • = 8.314 (kg×m2) / (s2×mol×K) • PV = nRT Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

45. Group Problem Calculate Molar Volume = the volume 1 mole of any gas occupies at 1 atm and 273 K

46. Group Problem Compare Molar volume at STP to Room Temperature(25°C) assuming pressure remains constant

47. Group Problem How many liters of N2(g) at 1.00 atm and 25.0 °C are produced by the decomposition of 150. g of NaN3? 2NaN3(s)  2Na(s) + 3N2(g)

48. Group Problem At what temperature will 1.50 moles of CH4 occupy a 1 L container at 10atm?

49. Group Problem • PV = nRT • d = m / V • M = m / n • Write out the ideal gas law in terms of density & then in terms of molar mass

50. Ideal Gas Law Considering Density & Molar Mass • PV = nRT • d = m / V • M = m / n • P (m / d) = nRT • PV = (m / M) RT • RT / P = M / d Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E