1. Gases
Chapter 14

2. Section 13.1
Introduction to gases

3. 13.1 Vocabulary
Review
Gas – State of matter
Kinetic energy – energy due to motion
New
kinetic-molecular theory
elastic collision
temperature
diffusion
pressure
barometer
pascal
Atmosphere
Dalton’s law of partial pressures
Main Idea- Gases expand, diffuse, exert pressure, and can be compressed because they are in a low density state consisting of tiny, constantly-moving particles.

4. Intro to Gases
What is a gas?
A form of matter
Used everywhere!

5. Phases & Properties: PHASE: uniform composition & properties
Solid: matter with a fixed volume & shape
ex. ice cube
Liquid: matter that flows, has a fixed volume & takes the shape of its container
ex. liquid water

6. Gas: Matter that has no definite. volume & takes the shape &
Gas: Matter that has no definite volume & takes the shape & volume of its container
ex. water vapor
ex. He, O2, CO2, H2, Cl2

7. Molecules Move: In solids, molecules close & can hardly move
In liquids, more spread out & move a bit more
In gas, FAR apart & can move freely
SOLID
LIQUID
GAS

8. Pressure: A force applied over a unit of area.
For a gas, press results from gas molecule colliding with the wall of its container
Measured in units called Pascals (Pa) or kiloPascals (kPa)

9. If container not strong enough walls can rupture
Changes to Gases
Adding a gas:
Adds more gas molecules
More collisions
Increased pressure
Ex. Double # of molec = double pressure
If container not strong enough walls can rupture

10. If container not strong enough walls can collapse
Removed a Gas:
Removes gas molecules
Less collisions
Pressure decreases
If container not strong enough walls can collapse
Gases tend to move from area of high concentration to low

11. Change Size of Container:
Decrease container size
Decreases space for molecules to move
Increases collisions
Increases pressure

12. Change Size of Container:
Increase container size
Increases space for molecules to move
Decreases collisions
Decreases pressure

13. Heating a Gas: Gas molecules absorb heat Molecules move more rapidly
Increase collisions
Increase pressure

14. Cooling a Gas: Gas molecules release heat Molecules move more slowly
Decrease collisions
Decrease pressure

15. Summary: Add more gas  Pressure Remove gas  Pressure
Reduce Size  Pressure
Increase Size  Pressure
Increase Temp  Pressure
Decrease Temp  Pressure
All of these beliefs are based on the Kinetic Theory:
A gas is composed of particles
Gas particles move rapidly & are in constant random motion
All collisions are perfectly elastic
Kinetic energy proportional to temperature

16. The Kinetic-Molecular Theory
Kinetic-molecular theory explains the different properties of solids, liquids, and gases.
Atomic composition affects chemical properties.
Atomic composition also affects physical properties.
The kinetic-molecular theory describes the behavior of matter in terms of particles in motion.

17. The Kinetic-Molecular Theory (cont.)
Gases consist of small particles separated by empty space.
Gas particles are too far apart to experience significant attractive or repulsive forces.

18. The Kinetic-Molecular Theory (cont.)
Gas particles are in constant random motion.
An elastic collision is one in which no kinetic energy is lost.

19. The Kinetic-Molecular Theory (cont.)
Kinetic energy of a particle depends on mass and velocity.
Temperature is a measure of the average kinetic energy of the particles in a sample of matter.

20. Explaining the Behavior of Gases
Great amounts of space exist between gas particles.
Compression reduces the empty spaces between particles.

21. Explaining the Behavior of Gases (cont.)
Gases easily flow past each other because there are no significant forces of attraction.
Diffusion is the movement of one material through another.
Effusion is a gas escaping through a tiny opening.

22. Explaining the Behavior of Gases (cont.)
Graham’s law of effusion states that the rate of effusion for a gas is inversely proportional to the square root of its molar mass.
Graham’s law also applies to diffusion.

23. Gas Pressure Pressure is defined as force per unit area.
Gas particles exert pressure when they collide with the walls of their container.

24. Gas Pressure (cont.)
The particles in the earth’s atmosphere exert pressure in all directions called air pressure.
There is less air pressure at high altitudes because there are fewer particles present, since the force of gravity is less.

25. Gas Pressure (cont.) Torricelli invented the barometer.
Barometers are instruments used to measure atmospheric air pressure.

26. Gas Pressure (cont.) The SI unit of force is the newton (N).
One pascal(Pa) is equal to a force of one Newton per square meter or N/m2.
One atmosphere is equal to 760 mm Hg or kilopascals.

27. Gas Pressure (cont.)

28. Gas Pressure (cont.)
Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the pressures of all the gases of the mixture.
The partial pressure of a gas depends on the number of moles, size of the container, and temperature and is independent of the type of gas.

29. Gas Pressure (cont.)
Ptotal = P1 + P2 + P3 +...Pn
Partial pressure can be used to calculate the amount of gas produced in a chemical reaction.

30. 13.1 Check
The average of kinetic energy of particles in a substance is measured by its ____.
A. mass
B. density
C. temperature
D. pressure A B C D

31. 13.1 Check
One mole of oxygen in a 5.0 liter container has the same partial pressure as one mol of hydrogen in the same container. This is a demonstration of what law?
A. law of conservation of mass
B. law of definite proportions
C. law of conservation of energy
D. Dalton’s law of partial pressures A B C D

32. Section 14.1.
The simple gas laws

33. 14.1 Vocabulary
Review
Gas – State of matter
Kinetic energy – energy due to motion
New
Boyle’s law
absolute zero
Charles’s law
Gay-Lussac’s law
Main Idea- For a fixed amount of gas, a change in one variable—pressure, temperature, or volume—affects the other two.

34. Before starting…. Gases behave in different ways & obey “laws”
But when we are discussing gases we assume that we are dealing with an ideal gas.
An ideal gas follows the gas laws at all conditions of temperature & pressure
There are, however, exceptions!

35. P1V1 = P2V2 where P = pressure and V = volume
Boyle's Law
Boyle’s law states that the volume of a fixed amount of gas held at a constant temperature varies inversely with the pressure.
P1V1 = P2V2 where P = pressure and V = volume

36. P1V1 = P2V2 So… if volume decreases, then pressure increases
if volume increases, then pressure decreases

37. Example
A balloon is filled with 30L of He gas at 100kPa. What is the volume when the balloon rises to an altitude where the pressure is 25kPa?
P1V1 = P2V
(100kPa)(30L) = (25kPa)(V2)
V2 = (100kPa)(30L)
(25kPa)
V2 = 120L

38. Example
The pressure on 2.50L of anesthetic gas is changed from 100kPa to 40kPa. What will be the new volume if the temperature remains constant?
P1V1 = P2V2
(100kPa)(2.50L) = (40kPa)(V2)
V2 = (100kPa)(2.50L)
(40kPa)
V2 = 6.25L

39. Charles's Law
As temperature increases, so does the volume of gas when the amount of gas and pressure do not change.
Kinetic-molecular theory explains this property.

40. Charles's Law (cont.)

41. Charles's Law (cont.) T1 T2 Note: 0oC = 273.15K
Absolute zero is zero on the Kelvin scale.
Charles’s law states that the volume of a given amount of gas is directly proportional to its kelvin temperature at constant pressure.
V1 = V2
T1 T2
Note: 0oC = K

42. Example V1 = V2 T1 T2 10L = V2 293K 313K V2 = 10.7L
A balloon inflated in a room at 20oC has a volume of 10L. The room is then heated to 40oC. What is the new volume of the balloon if the pressure is unchanged?
V1 = V2
T1 T2
10L = V2
293K 313K
V2 = 10.7L
This makes sense – volume should increase when temperature increases!
T1 = 20oC = 293K
T2 = 40oC = 313K

43. Gay-Lussac's Law
Gay-Lussac’s law states that the pressure of a fixed amount of gas varies directly with the kelvin temperature when the volume remains constant.

44. Gay-Lussac's Law (cont.)

45. Example:
Gas that was left in a hairspray can is at a pressure of 200kPa and a temp of 21oC. Someone throws the can in a hot fire and its temperature rises to 900oC. What is the internal pressure on the can?
P1 = P2
T1 T2
200 kPa = P2
294 K K
P2 = (200 kPa)(1173K)
(294K)
P2 = 798kPa

46. 14.1 Check
Boyle’s Law explains which relationship of properties in gases?
A. pressure and volume
B. amount and pressure
C. temperature and volume
D. volume and temperature A B C D

47. 14.1 Check
Atoms are in their lowest energy state at what temperature?
A. 0° Celsius
B. 0° Fahrenheit
C. –100° Celsius
D. 0 kelvin A B C D

48. 1L = V2 273K 546K Vol. would double Pressure would double
What would happen to the vol. if the temp.
of a gas were doubled? Pressure?
V1 = V2
T1 T2
1L = V2
273K 546K
Vol. would double
Pressure would double

49. For spring break a family drives from Colorado to Florida
For spring break a family drives from Colorado to Florida. When they arrive in Florida, your car tire bursts. Explain.
Colorado – low temp, so low press & vol
Florida – higher temp, so vol & pressure increases
Tire can’t hold & bursts

50. High temp (Charles) & low press (Boyle)
You are filling up helium balloons. Under which conditions will you be able to fill the most balloons?
a. Low press b. High press
c. High temp d. Low temp
High temp (Charles) & low press (Boyle)

51. The combined gas law and avogadro’s principle
Section 14.2
The combined gas law and avogadro’s principle

52. 14.2 Vocabulary
Review
mole: an SI base unit used to measure the amount of a substance; the amount of a pure substance that contains 6.02 × 1023 representative particles
New
combined gas law
Avogadro’s principle
molar volume
Main Idea – Boyle’s, Charles’s, and Gay-Lussac’s laws can be combined into a single equation in which all 3 variables, temp, pressure, and volume, change.

53. The Combined Gas Law
The combined gas law states the relationship among pressure, temperature, and volume of a fixed amount of gas.

54. The Combined Gas Law (cont.)

55. Avogadro's Principle
Avogadro’s principle states that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.

56. Avogadro's Principle (cont.)
The molar volume of a gas is the volume 1 mol occupies at 0.00°C and 1.00 atm of pressure.
0.00°C and 1.00 atm are called standard temperature and pressure (STP).
At STP, 1 mol of gas occupies 22.4 L.

57. Example:
A cylinder of compressed oxygen gas has a volume of 30L & 100 kPa pressure at 27oC. The cylinder is cooled until the pressure is 5.0 kPa. What is the new temp of the gas in the cylinder?
P1 = 100kPa V1 = 30L T1 = = 300K
P2 = 5.0kPa V2 = 30L T2 = ?
P1V1 = P2V2
T1 T2
(100kPa)(30L) = (5.0kPa)(30L)
(300K) ?
T2 = 15K or –258oC

58. 14.2 Check A B C D 3.00 mol of O2 at STP occupies how much volume?
A L
B L
C L
D L A B C D

59. Section 14.3
The ideal gas law

60. 14.3 Vocabulary
Review
mole
New
ideal gas constant (R)
ideal gas law
Main Idea - The ideal gas law relates the number of particles to pressure, temperature, and volume.

61. The Ideal Gas Law
Ideal gas particles occupy a negligible volume and are far enough apart to exert minimal attractive or repulsive forces on each other.
Combined gas law to ideal gas law

62. The Ideal Gas Law (cont.)
The ideal gas constant is represented by R and is L•atm/mol•K when pressure is in atmospheres.
The ideal gas law describes the physical behavior of an ideal gas in terms of pressure, volume, temperature, and amount.

63. The Ideal Gas Law (cont.)

64. The Ideal Gas Law—Molar Mass and Density
Molar mass and the ideal gas law

65. The Ideal Gas Law—Molar Mass and Density (cont.)
Density and the ideal gas law

66. Example:
A steel cylinder with a volume of 20.0L is filled with nitrogen gas to a pressure of 20,000 kPa at 27oC.
a) How many moles of N2 gas does the cylinder contain?
V = 20.0L
P = 20,000 kPa
T = = 300K
R = 8.31

67. PV = nRT (20)(20000) = (n)(8.31)(300) b) How many grams of nitrogen gas? mass = moles x molar mass mass = 160mol x 28 g/mol
n = 160 moles
mass = 4480 g

68. Example: P = 1500 kPa V = 2.24 x 106 L n = ? R = 8.31 T = 315 K
2.24 x 106L CH4 is at a pressure of 1500kPa & a temp of 42oC. What is the mass of the gas?
P = 1500 kPa V = 2.24 x 106 L n = ? R = 8.31 T = 315 K
PV = nRT
(1500)(2.24 x 106) = (n)(8.31)(315)
n = 1.28 x 106 mol of CH4
mass = (1.28 x 106mol)(16g/mol)
mass = 2.05 x 107 g of CH4

69. Real Versus Ideal Gases
Ideal gases follow the assumptions of the kinetic-molecular theory.
Ideal gases experience:
There are no intermolecular attractive or repulsive forces between particles or with their containers.
The particles are in constant random motion.
Collisions are perfectly elastic.
No gas is truly ideal, but most behave as ideal gases at a wide range of temperatures and pressures.

70. Real Versus Ideal Gases (cont.)
Real gases deviate most from ideal gases at high pressures and low temperatures.
Polar molecules have larger attractive forces between particles.
Polar gases do not behave as ideal gases.
Large nonpolar gas particles occupy more space and deviate more from ideal gases.

71. 14.3 Check
Which of the following is NOT one of the related physical properties described in the ideal gas law?
A. pressure
B. volume
C. density
D. temperature A B C D

72. 14.3 Check
Which of the following is NOT one of the related physical properties described in the ideal gas law?
A. pressure
B. volume
C. density
D. temperature A B C D

73. Section 14.4
Gas law stoichiometry

74. 14.4 Vocabulary
Review
Coefficient
Mole ratio
Main Idea - When gases react, the coefficients in the balanced chemical equation represent both molar amounts and relative volumes.

75. Stoichiometry of Reactions Involving Gases
The gas laws can be applied to calculate the stoichiometry of reactions in which gases are reactants or products.
2H2(g) + O2(g) → 2H2O(g)
2 mol H2 reacts with 1 mol O2 to produce 2 mol water vapor.

76. Stoichiometry and Volume-Volume Problems
Coefficients in a balanced equation represent volume ratios for gases.

77. Example Volume-Volume
What volume of oxygen gas is needed for the complete combustion of 4.00 L of propane gas (C3H8)? Assume constant pressure and temperature.

78. Stoichiometry and Volume-Mass Problems
Mass must be found by converting to moles or volumes.

79. Example Volume-Mass
Ammonia is synthesized from hydrogen and nitrogen gases. N2(g) + 3H2(g) → 2NH3(g) If 5.00 L of nitrogen reacts completely by this reaction at a constant pressure and temperature of 3.00 atm and 298 K, how many grams of ammonia are produced?

80. 14.4 Check
How many mol of hydrogen gas are required to react with 1.50 mol oxygen gas in the following reaction?
2H2(g) + O2(g) → 2H2O(g)
A. 1.00
B. 2.00
C. 3.00
D. 4.00 A B C D

81. 14.4 Check
How many liters of hydrogen gas are required to react with 3.25 liters of oxygen gas in the following reaction?
2H2(g) + O2(g) → 2H2O(g)
A. 2.00
B. 3.25
C. 4.00
D. 6.50 A B C D