1. Gases
Chapter 9

2. Unit Objectives 3.0 Define key terms and concepts.
3.6 Explain the properties of gases.
3.7 Explain how pressure, volume, temperature, and moles relate using the gas laws.
3.8 Solve gas law problems using Charles Law, Boyle's Law, the Combined Gas Law, and the Ideal Gas Law.

3. Unit Objectives
3.9 Apply the gas laws to predict how a gas will respond if pressure, volume, temperature, or moles of gas are changed.
3.10 Calculate the density and molar mass of a gas.
3.11 Calculate the theoretical yield for a gas in a chemical reaction.
3.12 Calculate the pressure of a mixture of gases.

4. Unit Objectives
3.13 Calculate the partial pressure of each gas in a mixture.
3.14 Explain the Kinetic Molecular Theory of Gases.
3.15 Explain the difference between ideal and non-ideal gases.

5. Properties of Gases
Gases are made up of particles that are relatively far apart and move randomly in all directions and at rapid speeds
Assume the volume and shape of their containers.
Are the most compressible of the states of matter.
Will mix evenly and completely when confined
to the same container.
Have much lower densities than liquids
and solids.

6. Properties of Gases, Pressure
Force acting on a certain area
Can be measured in atm, mmHg, torr, Pascal
1atm=760torr=760mmHg=101,325Pa
Gases exert pressure on the sides of the container they occupy. The more particles of gas present, the greater the pressure.
Heating gas particles will increase the speed at which these particles hit the sides of the container and therefore, increase the pressure.

7. Atmospheric Pressure Atmospheric Pressure
Pressure the air exerts on the earth
Atmospheric pressure increases as the temperature increases and decreases as the elevation increases.
Gases at atmospheric
pressure are covalent
compounds.

8. Properties of Gases, Volume
Gas fills the container it occupies.
As the volume of the container that holds a gas decreases, the pressure the gas exerts on the container increases.
Volume is measured in L
and mL

9. Properties of Gas, Temperature
The temperature of a gas is related to the energy of the gas particles.
As the temperature of a gas increases, the pressure the gas exerts increases
Temperature is measured in K.

10. Units and Conversions Celsius to Kelvins Celsius + 273 = Kelvins
Standard Temperature and Pressure (STP)
0° C at 1 atm

11. Boyle’s Law

12. Boyle’s Law Relates Pressure to Volume
As Pressure increases, Volume Decreases proportionately. (inverse relationship)
Temperature and number of moles of gas remain constant
P1V1 = P2V2

13. Boyle’s Law

14. 1.6L of hydrogen gas is placed in a container under a pressure of 400 mmHg. If the pressure is increased to 550 mmHg, what is the new volume?

15. Oxygen gas is placed in a 2. 1L container at STP
Oxygen gas is placed in a 2.1L container at STP. What is the pressure if the volume of the container is decreased to 1.3L?

16. Charles Law Relates Temperature and Volume
As Temperature increases, Volume increases proportionately (direct relationship)
V1T2 = V2T1

17. A balloon contains 2. 5L of air at STP
A balloon contains 2.5L of air at STP. When liquid nitrogen is poured over the balloon, the volume of the balloon is decreased to 1.2L. What is the new temperature of the balloon?

18. An expandable container with an initial volume of 0
An expandable container with an initial volume of 0.65L at 280K is heated up by 50K. What is the volume of the container after heating?

19. Gay-Lussac’s Law Relates pressure and temperature.
As temperature increases, pressure increases proportionately (direct relationship)
P1T2 = P2T1

20. The initial pressure of a container of water vapor at 110°C is 1.69atm. If the temperature of the container is cooled to 80°C at constant volume, what is the new pressure of the container?

21. Combined Gas Law
Relates temperature, pressure, and volume while n remains constant
P1V1T2 = P2V2T1

22. A gas has an initial pressure of 1
A gas has an initial pressure of 1.2 atm, a volume of 23 liters, and a temperature of 200 K. The pressure is then raised to 850mmHg and increase the temperature to 300 K, what is the new volume of the gas?

23. A gas has an initial pressure of 5 atm, a volume of 1,250mL, and a temperature of 20°C. What is the pressure if the final volume is 2.2L and the temperature is increased by 35K?

24. What are your questions?

25. Avogadro’s Law Relates volume and moles (n)
Equal numbers of molecules of different gases at the same temperature and pressure occupy equal space.

26. Avogadro's Law

27. The Ideal Gas Law
An ideal gas is a hypothetical gas whose pressure-volume-temperature behavior can be completely explained by the ideal gas equation.
Ideal gas behavior assumes two conditions:
Gas molecules do not exert any force on each other.
The volume of the molecules is negligible compared to the volume of the container.
An ideal gas will occupy 22.4L at STP.

28. The Ideal Gas Law Where the gas constant, R=0.0821L·atm/mol·K
Temperature is in Kelvins
n is moles
Volume is in Liters
Pressure is in atm

29. A sealed jar contains 0.25 moles of oxygen gas at 20°C under atm. What is the volume in the container?

30. An 1. 8 liter container holds 5. 35 grams of nitrogen gas at 45°C
An 1.8 liter container holds 5.35 grams of nitrogen gas at 45°C. What is the pressure in the container?

31. A 15L container of hydrogen sulfide gas is stored at 25°C and 750mmHg
A 15L container of hydrogen sulfide gas is stored at 25°C and 750mmHg. How many grams of gas are located in the container?

32. Boyle’s Law Charles's Law Gay-Lussac’s Law Avogadro’s Law
Relates Pressure and Volume
Pressure increases, volume decreases (Indirect Relationship)
P1V1=P2V2
Boyle’s Law
Relates Volume and Temperature
Temperature increases, volume increases (Direct Relationship)
V1T2=V2T1
Charles's Law
Relates Pressure and Temperature
Temperature increases, pressure increases (Direct Relationship)
P1T2=P2T1
Gay-Lussac’s Law
Relates Volume and Moles of Gas
As the number of moles of gas increases, so does the volume of the gas (Direct Relationship)
V1n2 = V2n1
Avogadro’s Law
Relates Pressure, Temperature, and Volume
P1V1T2=P2V2T1
Combined Gas Law
Relates Pressure, Volume, Temperature, and Moles
PV=nRT
Ideal Gas Law

33. Density and Molar Mass of a Gas
The density of a gas in directly proportional to its molecular weighy (i.e., gases with a higher molecular weight will be denser).
Chlorine gas (70g/mole) is more dense than oxygen gas (32g/mole).
By combining the Ideal Gas Law and the formulas for molarity and density, we can determine the density and molar mass of a gas with the formula
M=dRT P
Where M is the molar mass
Where d is the density in g/L

34. What is the density of oxygen gas in g/L at 25ºC and 800torr?

35. At what temperature is the density of carbon tetrachloride 3
At what temperature is the density of carbon tetrachloride 3.15g/L if the gas is held under 1.25atm of pressure?

36. A sample of a gaseous substance at 25ºC and 0
A sample of a gaseous substance at 25ºC and 0.862atm has a density of 2.26g/L. What is the molecular weight of the gas?

37. Gas Stoichiometry
Can calculate the amount of gas (in grams, moles or volume) using stoichiometry and the gas laws.
Amount of Reactant (grams or volume)
Moles of Reactant
Moles of Product
Amount of Reactant (grams or volume)

38. If the following reaction were conducted at 55ºC at 0
If the following reaction were conducted at 55ºC at 0.986atm, Mg(s) + HCl(aq)  MgCl2(aq) + H2(g) how many liters of hydrogen gas would be produced?

39. How many milliliters of chlorine gas can be obtained at 40ºC and 787mmHg from 9.41g of hydrogen chloride, according to the following equation? KMnO4(s) + HCl(aq)  H2O(l) + KCl(aq) + MnCl2(aq) + Cl2(g)

40. Air bags in automobiles are inflated from a rapid production of nitrogen gas from the reaction of sodium azide, NaN3, with iron (III) oxide as illustrated in the following reaction: NaN3(s) + Fe2O3(aq) +  Na2O(s) + Fe(s) + N2(g) How many grams of sodium azide would be required to provide 75.0L of nitrogen gas at 25ºC and 748mmHg?

41. When introduced to an electrical current, water undergoes decomposition into oxygen gas and hydrogen gas. In order to produce 25L of oxygen gas, how many grams of water are required? Assume this reaction is conducted at STP.

42. What are your questions?

43. Dalton’s Law of Partial Pressure
Gasses are not often found in the world in pure form, but rather in mixtures.
Partial Pressure
The pressures of individual gas components in the mixture
Dalton’s Law of Partial Pressures
The total pressure of a mixture of gases is the sum of the pressure each gas exerts by itself
PT = P1 + P2 + P3…

44. Dalton’s Law of Partial Pressure

45. Dalton’s Law of Partial Pressure
The total pressure of a mixture of gas is dependant on the number of moles of a gas, not the type of gas
Mole Fraction
A quantity that expresses the ratio for the moles of one component to the number of moles of all components present.
Xi = moles of component
total moles of solution

46. Dalton’s Law of Partial Pressure
If a mixture contains more than 2 gases, the partial pressure of each of the gases is related to the total pressure
Pi = XiPT

47. A mixture of gas contains 1. 9 moles Cl2 and 0. 87 moles of H2S
A mixture of gas contains 1.9 moles Cl2 and 0.87 moles of H2S. What is the partial pressure of each of these gases if the total pressure is 1.8atm?

48. If a mixture of gases contains 1. 2 moles of H2 gas at 1. 2atm and 5
If a mixture of gases contains 1.2 moles of H2 gas at 1.2atm and 5.7moles of O2 gas at 1.6atm, what is the total pressure of the mixture?

49. A mixture of gas contains 1. 4 moles O2, 3. 9 moles H2, and 2
A mixture of gas contains 1.4 moles O2, 3.9 moles H2, and 2.8 moles N2. What is the partial pressure of each of these gases if the total pressure is 3.1atm?

50. Dalton’s Law of Partial Pressure

51. Magnesium is reacted with HCl according to the following reaction: Mg(s) + HCl(aq)  MgCl2(aq) + H2(g) If 3.6L of H2 was collected over water at 25ºC and at 1.1atm, how much magnesium metal was consumed in the reaction? (The vapor pressure of water at 25ºC is atm)

52. Potassium metal will react completely with water according to the following reaction: K(aq) + H2O(l)  KOH(aq) + H2(g) If 1,250mL of H2 was collected over water at 25ºC and 0.986atm, how many grams of potassium metal were consumed in the reaction? (The vapor pressure of water at 25ºC is atm)

53. Oxygen gas can be produced by heating potassium chlorate with manganese dioxide as a catalyst, as shown in this reaction: 2KClO3(s) 2KCl(s) + 2O2(g) How many grams of O2 would be produced from 1.5g of KClO3? If this gas was collected over water at 23ºC and a total pressure of 745mmHg, what volume would it occupy? (Vapor pressure of water at 23ºC is 22.4mmHg)
MnO2

54. What are your questions?

55. Kinetic Theory of Molecular Gases
Gas laws help predict the behavior of gases but don’t explain what changes occur at the molecular level.
Boltzmann and Maxwell determined that the physical properties of gases can be explained by the movement of the individual gas molecules.
Energy of gases measured in joules (J)
Kinetic Energy
Energy of motion

56. Kinetic Theory of Molecular Gases
A gas consists of small particles (atoms or molecules) that are in constant motion, moving randomly and rapidly in straight paths.
The attractive forces between the particles of a gas and be neglected since they are so far apart.
The actual volume occupied by gas molecules is extremely small compared to the distance between molecules
Energy is conserved in collisions between gas molecules because it is transferred from one molecule to another.
The average kinetic energy of gas molecules is proportional to the Kelvin Temperature. Any two gases at the same temperature will have the same kinetic energy.

57. Non-Ideal Gas Behavior
Ideal gas behavior assumes two conditions:
Gas molecules do not exert any force on each other.
The volume of the molecules is negligible compared to the volume of the container.
If a gas doesn’t satisfy these two conditions, it is called a Non-Ideal or Real Gas.
Forces from other gas molecules will effect the force other gas molecules exert on a container.
The volume of the gas molecules is also factored out of the total volume of the container.

58. van der Waals Equation

59. van der Waals Equation

60. If 21. 4g of H2O vapor occupies 2
If 21.4g of H2O vapor occupies 2.5L at 53ºC, what is the pressure of this gas using the ideal gas equation and the van der Waals equation?

61. What are your questions?