The Gas Laws

1
The Gas Laws
2
The Gas Laws

• The gas laws describe HOW gases behave.
• They can be predicted by theory.
• The amount of change can be calculated with
  mathematical equations.

3
Standard Atmospheric Pressure

• One atmosphere is equal to 760 mm Hg,
  760 torr, or 101.3 kPa (kilopascals).

4
Standard Atmospheric Pressure

• Perform the following pressure conversions.

a) 144 kPa _____ atm
(1.42)
b) 795 mm Hg _____ atm
(1.05)
5
Standard Atmospheric Pressure

• Perform the following pressure conversions.

c) 669 torr ______ kPa
(89.2)
d) 1.05 atm ______ mm Hg
(798)
6
Standard Atmospheric Pressure

• Air pressure at higher altitudes, such as on a
  mountaintop, is slightly lower than air pressure
  at sea level.

7
Standard Atmospheric Pressure

• Air pressure is measured using a barometer.

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9
Pressure and the Number of
Molecules

• More molecules mean more collisions between the
  gas molecules themselves and more collisions
  between the gas molecules and the walls of the
  container.
• Number of molecules is DIRECTLY proportional to
  pressure.

10
Pressure and the Number of
Molecules

• Doubling the number of gas particles in a
  basketball doubles the pressure.

11
Pressure and the Number of
Molecules

• Gases naturally move from areas of high pressure
  to low pressure because there is empty space to
  move in.

12

• If you double the number of molecules,

1 atm
13

• If you double the number of molecules, you double
  the pressure.

2 atm
14

• As you remove molecules from a container,

4 atm
15

• As you remove molecules from a container, the
  pressure decreases.

2 atm
16

• As you remove molecules from a container, the
  pressure decreases until the pressure inside
  equals the pressure outside.

1 atm
17
Changing the Size (Volume) of the Container

• In a smaller container, molecules have less room
  to move.
• The molecules hit the sides of the container more
  often, striking a smaller area with the same
  force.

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Changing the Size (Volume) of the Container

• As volume decreases, pressure increases.
• Volume and pressure are INVERSELY proportional.

19

• As the pressure on a gas increases,

1 atm
4 Liters
20

• As the pressure on a gas increases, the volume
  decreases.

2 atm
2 Liters
21
Temperature and Pressure

• Raising the temperature of a gas increases the
  pressure if the volume is held constant.
• At higher temperatures, the particles in a gas
  have greater kinetic energy.

22
Temperature and Pressure

• They move faster and collide with the walls of
  the container more often and with greater force,
  so the pressure rises.

23
300 K

• If you start with 1 liter of gas at 1 atm
  pressure and 300 K and heat it to 600 K, one of
  2 things happens.

24
600 K
300 K

• Either the volume will increase to 2 liters at
  1 atm,

25
600 K
300 K

• or the pressure will increase to 2 atm while the
  volume remains constant.

26
Ideal Gases

• In this unit we will assume the gases behave
  ideally.
• Ideal gases do not really exist, but this makes
  the math easier and is a close approximation.

27
Kinetic Molecular Theory of Gases

• Gas particles are much smaller than the spaces
  between them. The particles have negligible
  volume.
• There are no attractive or repulsive forces
  between gas molecules.

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Kinetic Molecular Theory of Gases

• Gas particles are in constant, random motion.
  Until they bump into something (another particle
  or the side of a container), particles move in a
  straight line.

29
Kinetic Molecular Theory of Gases

• No kinetic energy is lost when gas particles
  collide with each other or with the walls of
  their container.
• All gases have the same kinetic energy at a given
  temperature.

30
Temperature

• Temperature is a measure of the average kinetic
  energy of the particles in a sample of matter.

31
Ideal Gases

• There are no gases for which this is true.
• Real gases behave more ideally at high
  temperature and low pressure.

32
Ideal Gases

• At low temperature, the gas molecules move more
  slowly, so attractive forces are no longer
  negligible.
• As the pressure on a gas increases, the molecules
  are forced closer together and attractive forces
  are no longer negligible.
• Therefore, real gases behave more ideally at high
  temperature and low pressure.

33
Avogadros Law

• Avogadros law states that equal volumes of
  different gases (at the same temperature and
  pressure) contain equal numbers of atoms or
  molecules.

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Avogadros Law
2 Liters of Helium
2 Liters of Oxygen

• has the same number of particles as ..

35
Avogadros Law

• The molar volume for a gas is the volume that one
  mole occupies at 0.00ºC and 1.00 atm.
• 1 mole 22.4 L at STP (standard temperature and
  pressure).
• As a result, the volume of gaseous reactants and
  products can be expressed as small whole numbers
  in reactions.

36
Problem

• How many moles are in 45.0 L of a gas at STP?

2.01 moles
37
Problem

• How many liters are in 0.636 moles of a gas at
  STP?

14.2 L
38
Avogadros Law

• V K x n (K is some constant)
• V / n K
• Easier to use V1

V2

n1
n2
39
Example

• Consider two samples of nitrogen gas. Sample 1
  contains 1.5 mol and has a volume of 36.7 L.
  Sample 2 has a volume of 16.5 L at the same
  temperature and pressure. Calculate the number
  of moles of nitrogen in sample 2.

40
Example

• Sample 1 contains 1.5 mol and has a volume of
  36.7 L. Sample 2 has a volume of 16.5 L.
  Calculate the number of moles of nitrogen in
  sample 2.

• V1

V2
36.7 L
16.5 L

n1
n2
1.5 mol
n2 0.67 mol
41
Problem

• If 0.214 mol of argon gas occupies a volume of
  652 mL at a particular temperature and pressure,
  what volume would 0.375 mol of argon occupy under
  the same conditions?

V2 1140 mL
42
Problem

• If 46.2 g of oxygen gas occupies a volume of 100.
  L at a particular temperature and pressure, what
  volume would 5.00 g of oxygen gas occupy under
  the same conditions?

V2 10.8 L
43
Boyles Law

• At Boyles law states that the pressure and
  volume of a gas at
  constant temperature are
  inversely proportional.
  
• Inversely proportional
  means as one goes up
  the other goes down.

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Boyles Law
45
Boyles Law

• P x V K (K is some constant)
• P1 V1 P2 V2

46
Boyles Law

• The P-V graph for Boyles law results in a
  hyperbola because pressure and volume are
  inversely proportional.

47
P
V
48
Example

• A balloon is filled with 25 L of air at 1.0 atm
  pressure. If the pressure is changed to 1.5 atm,
  what is the new volume?

49
Example

• First, make sure the pressure and volume units in
  the question match.
• A balloon is filled with 25 L of air at 1.0
  atm pressure. If the pressure is changed to 1.5
  atm, what is the new volume?

THEY DO!
50
Example

• A balloon is filled with 25 L of air at 1.0
  atm pressure. If the pressure is changed to 1.5
  atm, what is the new volume?

• P1

V1
P2

V2
V2
1.0 atm
1.5 atm
(25 L)
V2 17 L
51
Problem

• A balloon is filled with 73 L of air at 1.3 atm
  pressure. What pressure is needed to change the
  volume to 43 L?

P2 2.2 atm
52
Problem

• A gas is collected in a 242 cm3 container. The
  pressure of the gas in the container is measured
  and determined to be 87.6 kPa. What is the
  volume of this gas at standard pressure?

V2 209 cm3
53
Problem

• A gas is collected in a 24.2 L container. The
  pressure of the gas in the container is
  determined to be 756 mm Hg. What is the
  pressure of this gas if the volume increases to
  30.0 L?

P2 610. mm Hg
54
Charles Law

• The volume of a gas is directly proportional to
  the Kelvin temperature if the pressure is held
  constant.
• K C 273

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Charles Law
56
Charles Law

• V K x T (K is some constant)
• V / T K
• Easier to use V1

V2

T1
T2
57
Charles Law

• The V-T graph for Charles law results in a
  straight line because pressure and volume are
  directly proportional.

58
V
T
59
Example

• What is the temperature of a gas that is expanded
  from 2.5 L at 25 ºC to 4.1 L at constant
  pressure?

60
Example

• First, make sure the volume units in the question
  match.
• What is the temperature of a gas that is expanded
  from 2.5 L at 25 ºC to 4.1 L at constant
  pressure?

THEY DO!
61
Example

• Second, make sure to convert degrees Celsius to
  Kelvin.
• What is the temperature of a gas that is expanded
  from 2.5 L at 25 ºC to 4.1 L at constant
  pressure?

K 273
C
25
K 298 K
62
Example

• What is the temperature of a gas that is expanded
  from 2.5 L at 25 ºC to 4.1 L at constant
  pressure?

• V1

V2
2.5 L
4.1 L

T1
T2
298 K
T2 489 K
63
Problem

• What is the final volume of a gas that starts at
  8.3 L and 17 ºC and is heated to 96 ºC?

V2 11 L
64
Problem

• A 225 cm3 volume of gas is collected at 57 ºC.
  What volume would this sample of gas occupy at
  standard temperature?

V2 186 cm3
65
Problem

• A 225 cm3 volume of gas is collected at 42 ºC.
  If the volume is decreased to 115 cm3, what is
  the new temperature?

T2 161 K
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Gay-Lussacs Law

• The temperature and the pressure of a gas are
  directly related at constant volume.

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Gay-Lussacs Law

• P K x T (K is some constant)
• P / T K
• Easier to use P1

P2

T1
T2
68
P
T
69
Example

• What is the pressure inside a 0.250 L can of
  deodorant that starts at 25 ºC and 1.2 atm if the
  temperature is raised to 100 ºC? Volume remains
  constant.

70
Example

• First, make sure the pressure units in the
  question match.
• What is the pressure inside a 0.250 L can of
  deodorant that starts at 25 ºC and 1.2 atm if
  the temperature is raised to 100 ºC?

There is only one pressure unit!
71
Example

• Second, make sure to convert degrees Celsius to
  Kelvin.
• What is the pressure inside a 0.250 L can of
  deodorant that starts at 25 ºC and 1.2 atm if
  the temperature is raised to 100 ºC?

K 273
C
25
K 298 K
72
Example

• What is the pressure inside a 0.250 L can of
  deodorant that starts at 25 ºC and 1.2 atm if
  the temperature is raised to 100 ºC?

K 273
C
100
K 373 K
73
Example

• What is the pressure inside a 0.250 L can of
  deodorant that starts at 25 ºC and 1.2 atm if
  the temperature is raised to 100 ºC?

• P1

P2
1.2 atm

T1
T2
373 K
298 K
P2 1.5 atm
74
Problem

• A can of deodorant starts at 43 ºC and 1.2 atm.
  If the volume remains constant, at what
  temperature will the can have a pressure of 2.2
  atm?

T2 579 K
75
Problem

• A can of shaving cream starts at 25 ºC and
  1.30 atm. If the temperature increases to 37 ºC
  and the volume remains constant, what is the
  pressure of the can?

P2 1.35 atm
76
Problem

• A 12 ounce can of a soft drink starts at STP. If
  the volume stays constant, at what temperature
  will the can have a pressure of 2.20 atm?

T2 601 K
77
The Combined Gas Law

• The gas laws may be combined into a single law,
  called the combined gas law, which relates two
  sets of conditions of pressure, volume, and
  temperature by the following equation.
• P1

V2
V1
P2

T2
T1
78
Example

• A 15 L cylinder of gas at 4.8 atm pressure at 25
  ºC is heated to 75 ºC and compressed to 17 atm.
  What is the new volume?

79
Example

• First, make sure the volume units in the question
  match.
• A 15 L cylinder of gas at 4.8 atm pressure at 25
  ºC is heated to 75 ºC and compressed to 17 atm.
  What is the new volume?

There is only one volume unit!
80
Example

• Second, make sure the pressure units in the
  question match.
• A 15 L cylinder of gas at 4.8 atm pressure at 25
  ºC is heated to 75 ºC and compressed to 17 atm.
  What is the new volume?

They do!
81
Example

• Third, make sure to convert degrees Celsius to
  Kelvin.
• A 15 L cylinder of gas at 4.8 atm pressure at 25
  ºC is heated to 75 ºC and compressed to 17 atm.
  What is the new volume?

K 273
C
25
K 298 K
82
Example

• A 15 L cylinder of gas at 4.8 atm pressure at 25
  ºC is heated to 75 ºC and compressed to 17 atm.
  What is the new volume?

K 273
C
75
K 348 K
83
Example

• A 15 L cylinder of gas at 4.8 atm pressure at 25
  ºC is heated to 75 ºC and compressed to 17 atm.
  What is the new volume?

• P1

P2
V1
V2
4.8 atm
(15 L)
17 atm

T1
T2
298 K
348 K
V2 4.9 L
84
Problem

• If 6.2 L of gas at 723 mm Hg at 21 ºC is
  compressed to 2.2 L at 4117 mm Hg,
  what is the temperature of the gas?

T2 594 K
85
Problem

• A sample of nitrogen monoxide has a volume of
  72.6 mL at a temperature of 16 C and a pressure
  of 104.1 kPa. What volume will the sample occupy
  at 24 C and 99.3 kPa?

V2 78.2 mL
86
Problem

• A hot air balloon rises to an altitude of 7000 m.
  At that height the atmospheric pressure drops to
  300. mm Hg and the temperature cools to - 33 C.
  Suppose on the hot air balloon there was a small
  balloon filled to 1.00 L at sea level and a
  temperature of 27 C. What would its volume
  ultimately be when it reached the height of 7000
  m?

V2 2.03 L
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Daltons Law of Partial Pressures

• Daltons 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 in the
  mixture, as shown below.
• PTotal P1 P2 P3
• The partial pressure is the contribution by that
  gas.

88
Example

• On the next slide, determine the pressure in the
  fourth container if all of the gas molecules from
  the 1st three containers are placed in the 4th
  container.

89
2 atm
1 atm
3 atm
atm
6
??
90
Problem

• What is the total pressure in a balloon filled
  with air if the pressure of the oxygen is 170 mm
  Hg and the pressure of nitrogen is 620 mm Hg?

790 mm Hg
91
Example

• In a second balloon the total pressure is 1.30
  atm. What is the pressure of oxygen (in mm Hg) if
  the pressure of nitrogen is 720. mm Hg?

92
Example

• The two gas units do not match. We must convert
  the 1.30 atm into mm Hg.

760 mm Hg
1.30 atm
988 mm Hg

1 atm
93
Example

• PTotal P1 P2 P3

988 mm Hg 720 mm Hg Poxygen
268 mm Hg Poxygen
94
Problem

• A container has a total pressure of 846 torr and
  contains carbon dioxide gas and nitrogen gas.
  What is the pressure of carbon dioxide (in kPa)
  if the pressure of nitrogen is 50. kPa?

63 kPa
95
Problem

• When a container is filled with 3 moles
  of H2, 2 moles of O2 and 4 moles of N2, the
  pressure in the container is 8.7 atm. The
  partial pressure of H2 is _____.

2.9 atm
96
Daltons Law of Partial Pressures

• It is common to synthesize gases and collect them
  by displacing a volume of water.

97
Problem

• Hydrogen was collected over water at 21C on a
  day when the atmospheric pressure is 748 torr.
  The volume of the gas sample collected was 300.
  mL. The vapor pressure of water at 21C is
• 18.65 torr. Determine the partial pressure of
  the dry gas.

739.25 torr
98
Problem

• A sample of oxygen gas is saturated with water
  vapor at 27ºC. The total pressure of the mixture
  is 772 mm Hg and the vapor pressure of water is
  26.7 mm Hg at 27ºC. What is the partial pressure
  of the oxygen gas?

745.3 mm Hg
99
Remember Ideal Gases Dont Exist

• Molecules do take up space.
• There are attractive forces otherwise, there
  would be no liquids.

100
The Ideal Gas Law

• P V n R T
• Pressure times volume equals the number of moles
  (n) times the ideal gas constant (R) times the
  temperature in Kelvin.

101
The Ideal Gas Law

• R 0.0821 (L atm)/(mol K)
• R 8.314 (L kPa)/(mol K)
• R 62.4 (L mm Hg)/(mol K)
• The one you choose depends on the unit for
  pressure!

102
Example

• How many moles of air are there in a 2.0 L bottle
  at 19 ºC and 747 mm Hg?

• Choose the value of R based on the pressure unit.

• Since mm Hg are use, R 62.4.

103
Example

• Second, make sure to convert degrees Celsius to
  Kelvin.
• How many moles of air are there in a 2.0 L
  bottle at 19 ºC and 747 mm Hg?

K 273
C
19
K 292 K
104
Example

• How many moles of air are there in a 2.0 L
  bottle at 19 ºC and 747 mm Hg?

292 K

• P

R

T
V
n
747
(292)
(2.0)
62.4
n 0.082 mol
105
Example

• What is the pressure in atm exerted by 1.8 g of
  H2 gas in a 4.3 L balloon at 27 ºC?

• Choose the value of R based on the pressure unit.

• Since atm is requested, R 0.0821.

106
Example

• Second, make sure to convert degrees Celsius to
  Kelvin.
• What is the pressure in atm exerted by 1.8 g of
  H2 gas in a 4.3 L balloon at 27 ºC?

K 273
C
27
K 300. K
107
Example

• What is the pressure in atm exerted by
• 1.8 g of H2 gas in a 4.3 L balloon at 27 ºC?

300. K

• P

R

T
V
n
0.90
(300.)
(4.3)
(0.0821)
P 5.2 atm
108
Example

• Next, convert grams to moles.
• What is the pressure in atm exerted by 1.8 g of
  H2 gas in a 4.3 L balloon at 300. K?

1.8 g H2
mol H2
1
__
0.90 mol H2
g H2
2.0
__
109
Example

• What is the pressure in atm exerted by
• 1.8 g of H2 gas in a 4.3 L balloon at
  27 ºC?

0.90 mol
300. K

• P

R

T
V
n
0.90
(300.)
(4.3)
(0.0821)
P 5.2 atm
110
Problem

• Sulfur hexafluoride (SF6) is a colorless,
  odorless and very unreactive gas. Calculate the
  pressure (in atm) exerted by 1.82 moles
  of the gas in a steel vessel of volume 5.43 L at
  69.5 ºC.

P 9.42 atm
111
Problem

• Calculate the volume (in liters) occupied by 7.40
  g of CO2 at STP.

V 3.77 L
112
Example

• Next, you will have to change grams to moles.
• What is the pressure in atm exerted by 1.8 g of
  H2 gas in a 4.3 L balloon at 27 ºC?

1.8 g
1 mol
0.90 mol

2.0 g
113
Problem

• A sample of nitrogen gas kept in a container of
  volume 2.30 L and at a temperature of 32 ºC
  exerts a pressure of 476 kPa. Calculate the
  number of moles of gas present.

n 0.432 mol
114
Problem

• A 1.30 L sample of a gas has a mass of 1.82 g at
  STP. What is the molar mass of the gas?

31.4 g/mol
115
Problem

• Calculate the mass of nitrogen gas that can
  occupy 1.00 L at STP.

28.0 g