1. Chapter 11
Gases

2. 10. 1 Kinetic Molecular Theory
State the kinetic-molecular theory of matter, and describe how it explains certain properties of matter.
List the five assumptions of the kinetic-molecular theory of gases.
Define the terms ideal gas and real gas.
Describe each of the following characteristic properties of gases: expansion, density, fluidity, compressibility, diffusion, and effusion.
Describe the conditions under which a real gas deviates from “ideal” behavior.

3. What is the Kinetic Molecular Theory?
Break it down:
Kinetic: movement
Molecular: particles
Theory: tested ideas
Tested ideas about the
movement of particles!
This theory is used to explain the energy and forces that cause the properties of solids, liquids, and gases.

4. KMT of Gases
Ideal gas: hypothetical gas that satisfies all 5 ideas of KMT
pressure is not too high
temperature is not too low
Gases consist of large numbers of tiny particles that are far apart relative to their size.
Most of the volume is empty space
Collisions between gas particles and between particles and container walls are elastic collisions.
elastic collision when there is no net loss of total kinetic energy

5. KMT cont. Gas particles are in continuous, rapid, random motion.
There are no forces of attraction between gas particles.
The temperature of a gas depends on the average kinetic energy of the particles of the gas.
The kinetic energy of any moving object is given by the following equation:

6. Effusion Because gases have motion, they can travel.
Effusion: process by which gas particles pass through a tiny opening
What determines have fast a gas effuses? Mass
Gases at the same temperature have the same KE so…
Heavier gases  travel slower
Lighter gases  travel faster

7. Gas Behavior KMT applies only to ideal gasses.
Which parts are not true for real gases?

8. 11.1 Gases and Pressures
Define pressure, give units of pressure, and describe how pressure is measured.
State the standard conditions of temperature and pressure and convert units of pressure.
Use Dalton’s law of partial pressures to calculate partial pressures and total pressures.

9. 4 Variables of Gases What causes pressure? Pressure (P) Volume (V)
Temperature (T) Mols (n)
What causes pressure?
 collisions of the gas molecules with each other and with surfaces with which they come into contact.
 depends on volume (mL or L), temperature (oF, oC, K), and the number of molecules present (mol, mmol).

10. Equation for Pressure
Pressure (P): the force per unit area on a surface.
Pressure = Force
Area
 More force on a given area, the greater the pressure.
 smaller the area is on which a given force acts, the greater the pressure.

11. Pressure Video

12. Relationship Between Pressure, Force and Area

13. Measuring Pressure
barometer: device used to measure atmospheric pressure
Pressure of atmosphere supports a column of Hg about 760 mm above surface of mercury in dish
Can change depending on weather & elevation

14. Measuring Pressure

15. Units for Measuring Pressure
mm Hg : millimeters of mercury
A pressure of 1 mm Hg is also called 1 torr in honor of Torricelli for his invention of the barometer.
atm : atmosphere of pressure
kPa : kiloPascal
Others…
psi : pounds per square inch
Bar
torr
1 atm = kPa = 760 mmHg = 760 torr

16. Review- Units of Pressure

17. Pressure Conversions a. millimeters of mercury (mm Hg) and
The average atmospheric pressure in Denver, Colorado is atm. Express this pressure in:
a. millimeters of mercury (mm Hg) and
b. kilopascals (kPa)
Given: atmospheric pressure = atm
Unknown: a. pressure in mm Hg
b. pressure in kPa

18. Pressure Conversions AnswersB)

19. STP STP : Standard Temperature & Pressure
1.0 atm (or any of units of equal value)
0 oC
Used by scientists to compare volumes of gases

20. Dalton’s Law of Partial Pressures
The pressure of each gas in a mixture is called the partial pressure.
John Dalton discovered that the pressure exerted by each gas in a mixture is independent of that exerted by other gases present.
Dalton’s law of partial pressures: the total pressure of a gas mixture is the sum of the partial pressures of each gas.

21. Dalton’s Law of Partial Pressures
Dalton derived the following equation:
PT = P1 + P2 + P3 + …
Total Pressure = sum of pressures of each individual gas

22. Dalton’s Law of Partial Pressures

23. Gases Collected by Water Displacement
Water molecules at the liquid surface evaporate and mix with the gas molecules. Water vapor, like other gases, exerts a pressure known as vapor pressure.
Gases produced in the laboratory are often collected over water. The gas produced by the reaction displaces the water in the reaction bottle.

24. Particle Model for a Gas Collected Over Water

25. Gases Collected by Water Displacement (ctd)
Step 1: Raise bottle until water level inside matches the water level outside. (Ptot = Patm)
Step 2: Dalton’s Law of Partial Pressures states:
Patm = Pgas + PH2O
To get Patm, record atmospheric pressure.
Step 3: look up the value of PH2O at the temperature of the experiment in a table, you can then calculate Pgas.

26. Dalton’s Law of Partial Pressures Sample Problem
KClO3 decomposes and the oxygen gas was collected by water displacement. The barometric pressure and the temperature during the experiment were torr and 20.0°C. respectively. What was the partial pressure of the oxygen collected?
Given:
PT = Patm = torr
PH2O = 17.5 torr (vapor pressure of water at °C, from table A-8 in your book)
Patm = PO2 + PH2O
Unknown: PO2 in torr

27. Dalton’s Law Sample Problem Solution
Patm = PO2 + PH2O
PO2 = Patm - PH2O
substitute the given values of Patm and into the equation: PO2 =731.0 torr – 17.5 torr = torr

28. Mole Fractions (X)
mole fraction: ratio of the number of moles of one component of a mixture to the total number of moles
Mole fraction of a gas(XA) =
Moles of gas A (nA)
Total number of moles of a gas
(ntot)

29. Calculating Partial Pressure
Partial pressures can be determined from mole fractions using the following equation:
PA = XA PT

30. 11.2 The Gas Laws
Use the kinetic-molecular theory to explain the relationships between gas volume, temperature and pressure.
Use Boyle’s law to calculate volume-pressure changes at constant temperature.
Use Charles’s law to calculate volume-temperature changes at constant pressure.
Use Gay-Lussac’s law to calculate pressure-temperature changes at constant volume.
Use the combined gas law to calculate volume-temperature-pressure changes.

31. Boyle’s Law
If you increase the pressure on a gas in a flexible container, what happens to the volume?
If you decrease the pressure, what happens the volume?
Pressure and volume are ________ related.
P1V1 = P2V2
Variables: pressure & volume
Constant: temperature, amount of gas

32. Boyle’s Law

33. Boyle’s Law Video

34. Boyle’s Law Problem P1 = 0.947 atm P2 = 0.987 atm V1 = 150.0 mL V2 = ?
A sample of oxygen gas has a volume of mL when its pressure is atm. What will the volume of the gas be at a pressure of atm if the temperature remains constant?
P1 = atm P2 = atm
V1 = mL V2 = ?

35. Boyle’s Law Problem Solution

36. Charles’ Law
If you increase the temperature of gas, what will happen to the volume?
If you decrease the temperature of a gas, what will happen to the volume?
Volume and temperature are ______ related.
Variables: volume & temperature
Constant: pressure & amount of gas

37. Charles’ Law

38. Charles’ Law Video

39. Temperature in Charles Law
To Convert to Kelvin
K = °C.
absolute zero: when all motion stops
O K = -273 oC

40. Charles’ Law Problem V1 = 752 mL V2 = ? T1 = 25°C T2 = 50°C
A sample of neon gas occupies a volume of 752 mL at 25°C. What volume will the gas occupy at 50°C if the pressure remains constant? Temperature must be in KELVIN!!!
V1 = 752 mL V2 = ?
T1 = 25°C T2 = 50°C

41. Charles’ Law Sample Problem Solution

42. Gay-Lussac’s Law
If you increase the temperature of a gas what will happen to the pressure?
If you decrease the temperature of gas what will happen to the pressure?
Pressure and temperature are _____ related.
Variables: pressure & temperature
Constant: volume & amount of gas

43. Gay-Lussac’s Law

44. GL Law Video

45. Gay-Lussac’s Law Problem
The gas in a container is at a pressure of 3.00 atm at 25°C. Directions on the container warn the user not to keep it in a place where the temperature exceeds 52°C. What would the gas pressure in the container be at 52°C? Temperature must also be in KELVIN!!!
P1 = 3.00 atm P2 = ?
T1 = 25°C T2 = 52°C

46. Gay-Lussac’s Law Problem Solution
P2 = P1T2 = (3.00 atm) (325 K) = 3.27 atm
T K

47. Constant: amount of gas
The Combined Gas Law
Constant: amount of gas
combined gas law: used when pressure, temperature, and volume change within a system
NOTE: P & V are directly related to T, while P is inversely related to V

48. Combined Gas Law Problem
A helium-filled balloon has a volume of 50.0 L at 25.0°C and 1.08 atm. What volume will it have at atm and 10.0°C? Temperature must be in KELVIN!!
P1 = 1.08 atm P2 = atm
V1 = 50.0 L V2 = ?
T1 = 25.0°C T2 = 10.0°C

49. Combined Gas Law Problem Solution

50. End of Material for Quiz #1

51. 11.3 Gas Volumes and the Ideal Gas Law
State Avogadro’s law and explain its significance.
Define standard molar volume of a gas and use it to calculate gas masses and volumes.
State the ideal gas law.
Using the ideal gas law, calculate pressure, volume, temperature, or amount of gas when the other three quantities are known.

52. Avogadro’s Law
If you increase the amount of moles, what happens to the volume?
If you decrease the amount of moles what happens to the volume?
Amount of moles & volume are ____ related.
Variables: volume , moles
Constants: pressure, temperature
V1 = V2
n1 n2

53. Because of Avogadro’s law equal volumes of gases at constant temperature and pressure contain equal numbers of molecules.
Avogadro determined one mole of any gas (regardless of mass differences) will expand to the same volume every time
standard molar volume of a gas:
L (rounded to 22.4 L)

54. Molar Volume Video

55. Deriving the Ideal Gas Law
Review: Write down the combined gas law; where do you think “n” fits in? If both sides must equal each other, we can set one side equal to a constant. We’ll call this constant “R.”

56. The Ideal Gas Law Equation
PV = nRT
ideal gas law: relates all variables – pressure, volume, moles, temperature

57. Deriving the Ideal Gas Law Constant
R: ideal gas constant
Its value depends on the units chosen for pressure, volume, and temperature in the rest of the equation.
What are the standard conditions for an ideal gas?
P = n =
V = T =
Plug in values into the equation and calculate. What is the constant that you get?
Usually rounded to (Latm/molK)

58. Numerical Values of The Gas Constant “R”
ALWAYS MATCH UP YOUR UNITS!!!!

59. Gas Stoichiometry
Avogadro’s law can be applied in calculating the stoichiometry of reactions involving gases.
The coefficients in chemical equations of gas reactions reflect not only mole ratios, but also volume ratios (assuming conditions remain the same).
Discovered by Dalton, while exploring why water was a ratio of 2H to 1O
example
2H2(g) O2(g) → 2H2O(g)
2 molecules molecule 2 molecules
2 mole mole 2 mol
2 volumes volume volumes

60. Gas Stoichiometry Problem
Number 1 on Practice Sheet
What volume of nitrogen at STP would be required to react with mol of hydrogen to produce ammonia?
N H2  2 NH3

61. Gas Stoichiometry Problem Solution
0.100 mol H2 x 1 mol N2 x 22.4 L N2 3 mol H2 1 mol N2 = L N2

62. Ideal Gas Law Sample Problem
A sample of carbon dioxide with a mass of g was placed in a 350. mL container at 400 K. What is the pressure exerted by the gas?
P = ?
V = 350. mL = L
n = g = ? mol
T = 400 K

63. Ideal Gas Law Problem Solution
P = nRT = mol (.0821 Latm/molK) 400 K
V L
= atm

64. Gas Stoich and Ideal Gas Law
Number 2 on Practice Sheet
What volume of nitrogen at 215OC and 715 mmHg would be required to react with mol of hydrogen to produce ammonia?
N H2  2 NH3
Note: This system is NOT at STP!!

65. Gas Stoichiometry Problem Solution
0.100 mol H2 x 1 mol N2 = mol N2 3 mol H2 P = 715 mmHg V = ? n = mol N2 R = 62.4 LmmHg/molK T = 25OC = 488 K

66. 11.4 Diffusion and Effusion
Describe the process of diffusion.
State Graham’s law of effusion.
State the relationship between the average molecular velocities of two gases and their molar masses.

67. Diffusion and Effusion
REMEMBER:
EFFUSION: process when the molecules of a gas confined in a container randomly pass through a tiny opening in the container
DIFFUSION: the gradual mixing of two or more gases due to their spontaneous, random motion

68. Graham’s Law of Effusion

69. 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.

70. Sample Problem
What is the rate of effusion of hydrogen if oxygen has a velocity of 175 m/s at the same temperature and pressure.

71. Graham’s Law of Effusion, continued
Substitute the given values into the equation:
Hydrogen rate of effusion is …

72. Graham’s Law- Visual Problem