1. Molecular Composition of Gases
Chapter 11
Chemistry Chapter 11

2. Gay-Lussac’s law of combining volumes of gases
At constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers
Chemistry Chapter 11

3. Example
When 2 L of hydrogen react with 1 L of oxygen 2 L of water vapor are produced.
Write the balanced chemical equation:
Chemistry Chapter 11

4. You try
When 1 L of hydrogen gas reacts with 1 L of chlorine gas, 2 L of hydrogen chloride gas are produced.
Write the balanced chemical equation:
Chemistry Chapter 11

5. Avogadro's Law
Equal volumes of gases at the same pressure and temperature contain the same number of molecules
Atoms can’t split  diatomic molecules
Gas volume is proportional to the number of molecules
Chemistry Chapter 11

6. Molar Volume 1 mole of any gas contains 6.022 x 1023 molecules.
According to Avogadro’s law, 1 mole of any gas must have the same volume.
Standard molar volume: volume of 1 mole of any gas at STP
22.4 L
Chemistry Chapter 11

7. Example
You are planning an experiment that requires mol of nitrogen monoxide gas. What volume in liters is occupied by this gas at STP?
1.30 L NO
Chemistry Chapter 11

8. You try
A chemical reaction produces 2.56 L of oxygen gas at STP. How many moles of oxygen are in this sample?
0.114 mol O2
Chemistry Chapter 11

9. Example
Suppose you need 4.22 g of chlorine gas. What volume at STP would you need to use?
1.33 L Cl2
Chemistry Chapter 11

10. You try What is the mass of 1.33 x 104 mL of oxygen gas at STP?
19.0 g O2
Chemistry Chapter 11

11. Discuss Explain Gay-Lussac’s law of combining volumes
State Avogadro’s law and explain its significance.
Chemistry Chapter 11

12. Review
Boyles Law:
Charles Law:
Avogadro’s Law:
Chemistry Chapter 11

13. Math
A quantity that is proportional to each of several quantities is also proportional to their product. Therefore:
Chemistry Chapter 11

14. More math Convert a proportionality
to an equality by multiplying by a constant
Chemistry Chapter 11

15. Therefore
We can covert to
Chemistry Chapter 11

16. More neatly
Chemistry Chapter 11

17. This means….
The volume of a gas varies directly with the number of moles and the temperature in Kelvin.
The volume varies indirectly with pressure.
Chemistry Chapter 11

18. What if… n and T are constant? n and P are constant?
nRT is a constant, k
Boyle’s Law
n and P are constant?
nR/P is a constant, k
Charles’s Law
Chemistry Chapter 11

19. What if… P and T are constant? RT/P is a constant, k Avogadro’s law
Chemistry Chapter 11

20. The ideal gas constant R Value depends on units SI units:
Chemistry Chapter 11

21. Other units
Chemistry Chapter 11

22. Solving ideal gas problems
Make sure the R you use matches the units you have.
Make sure all your units cancel out correctly.
Chemistry Chapter 11

23. Example
A 2.07 L cylinder contains 2.88 mol of helium gas at 22 °C. What is the pressure in atmospheres of the gas in the cylinder?
33.7 atm
Chemistry Chapter 11

24. You try
A tank of hydrogen gas has a volume of 22.9 L and holds 14.0 mol of the gas at 12 °C. What is the reading on the pressure gauge in atmospheres?
14.3 atm
Chemistry Chapter 11

25. Example
A reaction yields mol of oxygen gas. What volume in mL will the gas occupy if it is collected at 43 °C and atm pressure?
240. mL
Chemistry Chapter 11

26. You try
A researcher collects 9.09 x 10-3 mol of an unknown gas by water displacement at a temperature of 16 °C and atm pressure (after the partial pressure of the water vapor has been subtracted). What volume of gas in mL does the researcher have?
247 mL
Chemistry Chapter 11

27. Finding mass
Number of moles (n) equals mass (m) divided by molar mass (M).
Chemistry Chapter 11

28. Example
What mass of ethene gas, C2H4, is contained in a 15.0 L tank that has a pressure of 4.40 atm at a temperature of 305 K?
74.0 g
Chemistry Chapter 11

29. You try
NH3 gas is pumped into the reservoir of a refrigeration unit at a pressure of 4.45 atm. The capacity of the reservoir is 19.4 L. The temperature is 24 °C. What is the mass of the gas in kg?
6.03 x 10-2 kg
Chemistry Chapter 11

30. Example
A chemist determines the mass of a sample of gas to be 3.17 g. Its volume is 942 mL at a temperature of 14 °C and a pressure of 1.09 atm. What is the molar mass of the gas?
72.7 g/mol
Chemistry Chapter 11

31. Density
Chemistry Chapter 11

32. You try
The density of dry air at sea level (1 atm) is g/L at 15 °C. What is the average molar mass of the air?
29.0 g/mol
Chemistry Chapter 11

33. Stoichiometry
Involves mass relationships between reactants and products in a chemical reaction
For gases, the coefficients in the balanced chemical equation show volume ratios as well as mole ratios
All volumes must be measured at the same temperature and pressure
Chemistry Chapter 11

34. Volume-Volume calculations
From volume of one gas to volume of another gas
Use volume ratios just like mole ratios in chapter 9
Chemistry Chapter 11

35. Example
Xenon gas reacts with fluorine gas to produce the compound xenon hexafluoride, XeF6. Write the balanced equation for this reaction.
Xe(g) + 3F2(g)  XeF6(g)
If a researcher needs 3.14 L of XeF6 for an experiment, what volumes of xenon and fluorine should be reacted?
3.14 L of Xe and 9.42 L of F2
Chemistry Chapter 11

36. Example
Nitric acid can be produced by the reaction of gaseous nitrogen dioxide with water. 3NO2(g) + H2O(l)  2HNO3(l) + NO(g)
If 708 L of NO2 gas react with water, what volume of NO gas will be produced?
236 L
Chemistry Chapter 11

37. You try
What volume of hydrogen gas is needed to react completely with 4.55 L of oxygen gas to produce water vapor?
9.10 L
Chemistry Chapter 11

38. You try
At STP, what volume of oxygen gas is needed to react completely with 2.79 x 10-2 mol of carbon monoxide gas, CO, to form gaseous carbon dioxide?
0.312 L
Chemistry Chapter 11

39. You try
Fluorine gas reacts violently with water to produce hydrogen fluoride and ozone according to the following equation: 3F2(g) + 3H2O(l)  6HF(g) + O3(g)
What volumes of O3 and HF gas would be produced by the complete reaction of 3.60 x 104 mL of fluorine gas?
1.20 x 104 mL O3 and 7.20 x 104 mL HF
Chemistry Chapter 11

40. You try
Ammonia is oxidized to make nitrogen monoxide and water 4NH3(g) + 5O2(g)  4NO(g) + 6H2O(l)
At STP, what volume of oxygen will be used in a reaction of 125 mol of NH3? What volume of NO will be produced?
3.50 x 103 L O2 and 2.80 x 103 L NO
Chemistry Chapter 11

41. Volume-mass and mass-volume
Converting from volume to mass or from mass to volume
Must convert to moles in the middle
Ideal gas law may be useful for finding standard conditions
Chemistry Chapter 11

42. Example
Aluminum granules are a component of some drain cleaners because they react with sodium hydroxide to release both heat and gas bubbles, which help clear the drain clog. The reaction is: 2NaOH(aq) + 2Al(s) + 6H2O (l)  2NaAl(OH)4(aq) + 3 H2(g)
What mass of aluminum would be needed to produce 4.00 L of hydrogen gas at STP?
3.21 g
Chemistry Chapter 11

43. Example
Air bags in cars are inflated by the sudden decomposition of sodium azide, NaN3 by the following reaction: 2NaN3(s)  3N2(g) + 2Na(s)
What volume of N2 gas, measured at 1.30 atm and 87 °C, would be produced by the reaction of 70.0 g of NaN3?
36.6 L
Chemistry Chapter 11

44. You try
What volume of chlorine gas at 38°C and 1.63 atm is needed to react completely with 10.4 g of sodium to form NaCl?
3.54 L Cl2
Chemistry Chapter 11

45. Example
A sample of ethanol burns in O2 to form CO2 and H2O according to the following reaction. C2H5OH + 3O2  2CO2 + 3H2O
If the combustion uses 55.8 mL of oxygen measured at 2.26 atm and 40.°C, what volume of CO2 is produced when measured at STP?
73.3 mL CO2
Chemistry Chapter 11

46. You try
Dinitrogen pentoxide decomposes into nitrogen dioxide and oxygen. If 5.00 L of N2O5 reacts at STP, what volume of NO2 is produced when measured at 64.5 °C and 1.76 atm?
7.02 L NO2
Chemistry Chapter 11

47. Review
Diffusion: the gradual mixing of gases due to their random motion
Effusion: gases in a container randomly pass through a tiny opening in the container
Chemistry Chapter 11

48. Rate of effusion Depends on relative velocities of gas molecules.
Velocity varies inversely with mass
Lighter particles move faster
Chemistry Chapter 11

49. Kinetic energy Depends only on temperature Equals
For two gases, A and B, at the same temperature
Each M stands for molar mass
Chemistry Chapter 11

50. Algebra time
Chemistry Chapter 11

51. Rate of effusion Depends on relative velocities of gas molecules.
Chemistry Chapter 11

52. Graham’s law of effusion
The rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses.
Chemistry Chapter 11

53. Graham’s law
Graham experimented with densities of gases, not molar masses.
Density and molar mass are directly proportional
So we can replace molar mass with density in the equation
Chemistry Chapter 11

54. Use of Graham’s law Finding the molar mass
Compare rates of effusion of a gas with known molar mass and a gas with unknown molar mass
Use Graham’s law equation to solve for the unknown M
Used to separate isotopes of uranium
Chemistry Chapter 11

55. Example
Compare the rates of effusion of hydrogen and helium at the same temperature and pressure.
Hydrogen diffuses about 1.41 times faster
Chemistry Chapter 11

56. Example
Nitrogen effuses through a pinhole 1.7 times as fast as another gaseous element at the same conditions. Estimate the other element’s molar mass and determine its probable identity.
81 g/mol, krypton
Chemistry Chapter 11

57. You try
Estimate the molar mass of a gas that effuses at 1.6 times the effusion rate of carbon dioxide.
17 g/mol
Chemistry Chapter 11