Honors Chemistry, Chapter 11

1
Chapter 11 Molecular Composition of Gases
2
Gay-Lussacs Law of Combining Volumes of Gases

• hydrogen gas oxygen gas ? water vapor
• 2 volumes 1 volume ? 2 volumes
• hydrogen chlorine?hydrogen chloride gas
• 1 volume 1 volume ? 2 volumes
• Gay-Lussacs law of combining volumes of gases
  states that at constant temperature and pressure
  , the volumes of gaseous reactants and products
  can be expressed as ratios of small whole numbers.

3
Avogadros Law

• Avogadros law states that equal volumes of gases
  at the same temperature and pressure contain
  equal numbers of molecules.
• V kn
• Where V is volume
• n is the number of moles
• k is a constant

4
Avogadros Law

• Assume hydrogen, oxygen and chlorine are diatomic
  molecules.
• H2(g) Cl2(g) ? 2HCl(g)
• 1 vol. 1 vol. ? 2 vol.
• and
• 2H2(g) O2(g) ? 2H2O(g)
• 2 vol. 1 vol. ? 2 vol.

5
Molar Volume

• The volume occupied by one mole of a gas at STP
  is known as the standard molar volume of a gas
  and has a volume of 22.41410 L (22.4 L for our
  purposes).
• (STP Standard Temperature and Pressure 0oC.
  and 1 atm.)

6
Sample Problem 11-1

• What is the volume of 0.0680 mole of oxygen gas
  at STP?
• moles of O2 ? volume of O2 in liters
• 0.068 mol O2 x 22.4 L/mol 1.52 L O2

7
Sample Problem 11-2

• What is the mass in grams of 98.0 mL of SO2 at
  STP?
• Vol. of SO2 in liters ? mol of SO2 ?
  mass of SO2
• mol mass of SO232.0032.07 64.07 g/mol
• 98.0 mL x 1L/1000 mL x 1 mol SO2/ 22.4 L x
  64.07 g SO2/ mol SO2 0.280 g SO2

8
Thought Problem

• Consider a container with mass of 1 kg and an
  internal volume of 22.4 L.
• If the container is filled with air, how much
  water would the container displace if placed in a
  container of water?

9
Thought Problem

• How much would the container weigh when filled
  with air?
• How much would the container weigh when
  evacuated?
• How much would the container weigh when filled
  with nitrogen? oxygen? hydrogen?

10
Chapter 11, Section 1 Review

• State the law of combining volumes.
• State Avogadros law and explain its
  significance.
• Define standard molar volume of a gas, and use it
  to calculate gas masses and volumes.
• Use standard molar volume to calculate the molar
  mass of a gas.

11
Idea Gas Law

• Boyles Law V a 1/P
• Charless Law V a T
• Avogadros Law V a n
• or V a nT/P
• or V nRT/P
• or PV nRT
• Where R is the Ideal Gas Constant

12
Ideal Gas Constant

• R _PV_ _(1 atm)(22.4140 L)_
• nT (1 mol)(273.15 K)
• 0.082057 L atm/(mol K)

13
Numerical Values of the Ideal Gas Constant
14
Sample Problem 11-3

• What is the pressure in atmospheres exerted by
  0.500 mol of nitrogen gas in a 10.0 L container
  at 298 K?
• V 10.0 L n 0.500 mol of N2
• T 298 K
• P nRT/V 0.500 mol N2 x
• 0.0821 L atm/ (mol K) x 298 K / 10.0 L
• 
  1.22 atm

15
Sample Problem 11-4

• What is the volume, in liters, of 0.250 mol of
  oxygen at 20 oC. and 0.974 atm pressure?
• P 0.974 atm
• n 0.250 mol of Oxygen
• T 20 oC. or 273.2 20 293.2 K
• V nRT/P
• 0.250 x 0.0821 (L atm)/(mol K) x 293.2 K /
  0.974 atm 6.17 L O2

16
Molar Mass

• PV nRT m RT / M (n m / M)
• Where m is mass and M is molar mass
• Solve for M
• M m RT/(PV)

17
Gas Density

• D m/V m DV
• PV m RT/ M
• PV DV RT/M
• D M P / (RT)

18
Problem 11-6

• At 28oC. and 0.974 atm, 1.00 L of a gas has a
  mass of 5.16 g. What is the molar mass of this
  gas? What is the gas?
• P 0.974 atm V 1.00 L
• T 28oC. 273 301 K m 5.16 g.
• M m RT/PV
• 5.16 g x 0.0821 L atm / (mol K) x 301 K /
  ( 0.974 atm x 1.00 L) 131 g/mol

19
Example Density Problem

• The density of a gas was found to be 2.0 g/L at
  1.50 atm and 27oC. What is the molar mass of the
  gas? What is the gas?
• D 2.0 g/L T 27oC. 273 300 K
• P 1.50 atm
• D M P / (RT)
• M DRT / P
• 2.0 g/L x 0.0821 L atm / (mol K) x 300 K /
  1.50 atm 33 g/mol

20
Chapter 11, Section 2 Review

• State the ideal gas law.
• Derive the gas constant and discuss the units.
• Using the ideal gas law, calculate pressure,
  volume, temperature or amount of gas when the
  other three quantities are known.

21
Chapter 11, Section 2 Review

• Using the ideal gas law, calculate the molar mass
  or density of a gas.
• Reduce the ideal gas law to Boyles law,
  Charless law, and Avogadros law. Describe the
  conditions under which each applies.

22
Stoichiometry of Gases

• Coefficients indicate molecule, mole, and volume
  ratios in gas reactions.
• For Example
• 2CO(g) O2(g) ? 2CO2(g)
• 2 molecules 1 molecule 2 molecules
• 2 mol 1 mol 2 mol
• 2 volumes 1 volume 2 volumes

23
Volume Ratios

• Volume Ratios from the CO O2 Reaction
• 2 vol CO / 1 vol O2 or 1 vol O2 / 2 vol CO
• 2 vol CO / 2 vol CO2 or 2 vol CO2 / 2 vol CO
• 1 vol O2 / 2 vol CO2 or 2 vol CO2 / 1 vol O2

24
Sample Problem 11-7

• What is the volume, in liters, of oxygen required
  for the complete combustion of 0.350 L of
  propane? What will the volume of CO2 be?
  (Assume constant T and P.)
• C3H8(g) 5O2(g) ? 3CO2(g) 4H2O(g)
• 0.350L C3H8 x 5 vol O2 / 1 vol C3H8 1.75 L O2
• 0.350L C3H8 x 3 vol CO2 / 1vol C3H8 1.05 L CO2

25
Volume-Mass and Mass-Volume Calculations

• We can use the ideal gas law to calculate
  problems like
• gas vol A ? moles A ? moles B ? mass B
• or
• mass A ? moles A ? moles B ? gas vol B

26
Sample Problem 11-8

• How many grams of calcium carbonate must be
  decomposed to produce 5.00 L of carbon dioxide at
  STP?
• CaCO3(s) D CaO(s) CO2(g)
• n PV/RT (1atm)(5.00 L CO2) / 0.0821
  L atm /(mol K)/(273 K) 0.223 mol CO2
• or
• n 5.00L CO2 / (22.4 L/mol)0.233 mol CO2

27
Sample Problem 11-8 continued
Molecular Weight of CaCO3? 100.09 g
CaCO3/mol 0.223 mol CO2 x 1 mol CaCO3 / (1 mol
CO2) x 100.09 g CaCO3/1 mol CaCO3 22.4 g
CaCO3
28
Sample Problem 11-9

• How many liters of hydrogen at at 35oC. and 0.980
  atm are needed to completely react with 875 grams
  of tungsten oxide?
• WO3(s) 3H2(g) ? W(s) 3H2O(l)
• Molar Mass of WO3? 231.84 g/mol
• 875 g WO3 x 1 mol WO3 / (231.84 g WO3) x 3 mol H2
  / (1 mol WO3) 11.3 mol H2

29
Sample Problem 11-9 Continued
V nRT/P (11.3 mol H2) x 0.0821 L atm / (mol
K) x 308 K / (0.980 atm) 292 L H2
30
Chapter 11, Section 3 Review

• Explain how Gay-Lussacs law and Avogadros law
  apply to volumes of gases in chemical reactions.
• Use a chemical equation to specify volume ratios
  for gaseous reactants or products, or both.
• Use volume ratios and the gas laws to calculate
  volumes, masses, or molar amounts of gaseous
  reactants or products.

31
Diffusion and Effusion

• Diffusion is the process where two gases
  gradually mix spontaneously due to the constant
  motion of the gas molecules.
• Effusion is the process whereby the molecules of
  a gas confined in a container randomly pass
  through a tiny opening in the container.

32
Average Kinetic Energy

• For two gases at the same temperature
• Avg kinetic energy ½ MAvA2 ½ MBvB2
• MAvA2 MBvB2
• vA2 / vB2 MB / MA
• vA MB
• --------- ------------
• vB MA

33
Grahams Law of Effusion

• Grahams law of effusion states that the rates of
  effusion of gases at the same temperature and
  pressure are inversely proportional to the square
  roots of their molar masses.
• Rate of effusion of A MB
  DensityB
• ---------------------------- -------
  -------------
• Rate of effusion of B MA
  DensityA

34
Sample Problem 11-10

• Compare the rates of effusion of hydrogen and
  oxygen at the same temperature and pressure.
• Rate of effusion of H2 MO2 32.00
  g/mol
• ---------------------------- -------
  -------------
• Rate of effusion of O2 MH2
  2.02 g/mol
• 
  3.98

35
Chapter 11, Section 4 Review

• State Grahams law of effusion.
• Determine the relative rates of effusion of two
  gases of know molar masses.
• State the relationship between the molecular
  velocities of two gases and their molar masses.