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1. 14.3 Ideal Gases >
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Chapter 14
The Behavior of Gases
14.1 Properties of Gases
14.2 The Gas Laws
14.3 Ideal Gases
14.4 Gases: Mixtures and Movements

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How can you calculate the
amount of a contained gas when the
pressure, volume, and temperature
are specified?
Ideal Gas Law
Ideal Gas Law

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Suppose you want to calculate the number
of moles (n) of a gas in a fixed volume at a
known temperature and pressure.
Ideal Gas Law

4. 14.3 Ideal Gases >
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Suppose you want to calculate the number
of moles (n) of a gas in a fixed volume at a
known temperature and pressure.
• The volume occupied by a gas at a
specified temperature and pressure
depends on the number of particles.
Ideal Gas Law

5. 14.3 Ideal Gases >
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Suppose you want to calculate the number
of moles (n) of a gas in a fixed volume at a
known temperature and pressure.
• The volume occupied by a gas at a
specified temperature and pressure
depends on the number of particles.
• The number of moles of gas is directly
proportional to the number of particles.
Ideal Gas Law

6. 14.3 Ideal Gases >
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Suppose you want to calculate the number
of moles (n) of a gas in a fixed volume at a
known temperature and pressure.
• The volume occupied by a gas at a
specified temperature and pressure
depends on the number of particles.
• The number of moles of gas is directly
proportional to the number of particles.
• Moles must be directly proportional to
volume.
Ideal Gas Law

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You can introduce moles into the
combined gas law by dividing each side of
the equation by n.
Ideal Gas Law

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You can introduce moles into the
combined gas law by dividing each side of
the equation by n.
• This equation shows that (P  V)/(T  n) is a
constant.
Ideal Gas Law

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You can introduce moles into the
combined gas law by dividing each side of
the equation by n.
P1  V1 P2  V2
T1  n1 T2  n2
=
• This equation shows that (P  V)/(T  n) is a
constant.
• This constant holds for what are called ideal
gases—gases that conform to the gas laws.
Ideal Gas Law

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If you know the values for P, V, T, and n
for one set of conditions, you can calculate
a value for the ideal gas constant (R).
P  V
T  n
R =
Ideal Gas Law

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If you know the values for P, V, T, and n
for one set of conditions, you can calculate
a value for the ideal gas constant (R).
• Recall that 1 mol of every gas occupies
22.4 L at STP (101.3 kPa and 273 K).
P  V
T  n
R =
Ideal Gas Law

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If you know the values for P, V, T, and n
for one set of conditions, you can calculate
a value for the ideal gas constant (R).
• Recall that 1 mol of every gas occupies
22.4 L at STP (101.3 kPa and 273 K).
• Insert the values of P, V, T, and n into
(P  V)/(T  n).
P  V
T  n
R = =
101.3 kPa  22.4 L
273 K  1 mol
Ideal Gas Law

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If you know the values for P, V, T, and n
for one set of conditions, you can calculate
a value for the ideal gas constant (R).
• Recall that 1 mol of every gas occupies
22.4 L at STP (101.3 kPa and 273 K).
• Insert the values of P, V, T, and n into
(P  V)/(T  n).
P  V
T  n
R = =
101.3 kPa  22.4 L
273 K  1 mol
R = 8.31 (L·kPa)/(K·mol)
Ideal Gas Law

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The gas law that includes all four
variables—P, V, T, n—is called the ideal
gas law.
P  V = n  R  T
PV = nRT
or
Ideal Gas Law

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When the pressure, volume, and
temperature of a contained gas are
known, you can use the ideal gas law
to calculate the number of moles of the
gas.
Ideal Gas Law

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At 34o
C, the pressure inside
a nitrogen-filled tennis ball
with a volume of 0.148 L is
212 kPa. How many moles of
nitrogen gas are in the tennis
ball?
Sample Problem 14.5
Using the Ideal Gas Law

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Use the ideal gas law (PV = nRT) to calculate
the number of moles (n).
KNOWNS
P = 212 kPa
V = 0.148 L
T = 34
o
C
R = 8.31 (L·kPa)/(K·mol)
UNKNOWN
n = ? mol N2
Analyze List the knowns and the
unknown.
1
Sample Problem 14.5

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Convert degrees Celsius to kelvins.
Calculate Solve for the unknown.
2
T = 34o
C + 273 = 307 K
Sample Problem 14.5

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State the ideal gas law.
Calculate Solve for the unknown.
2
P  V = n  R  T
Sample Problem 14.5

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Rearrange the equation to isolate n.
Calculate Solve for the unknown.
2
n =
R  T
P  V
Isolate n by dividing
both sides by (R  T):
=
R  T
n  R  T
P  V
R  T
P  V = n  R  T
Sample Problem 14.5

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Substitute the known values for P, V,
R, and T into the equation and solve.
Calculate Solve for the unknown.
2
n = 1.23  10–2 mol N2
n =
8.31 (L·kPa) / (K·mol)  307 K
212 kPa  0.148 L
n =
R  T
P  V
Sample Problem 14.5

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• A tennis ball has a small volume and
is not under great pressure.
• It is reasonable that the ball contains
a small amount of nitrogen.
Evaluate Does the result make sense?
3
Sample Problem 14.5

23. 14.3 Ideal Gases >
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A deep underground cavern
contains 2.24 x 106 L of
methane gas (CH4) at a
pressure of 1.50 x 103 kPa and
a temperature of 315 K. How
many kilograms of CH4 does
the cavern contain?
Sample Problem 14.6
Using the Ideal Gas Law

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Calculate the number of moles (n) using the ideal gas
law. Use the molar mass of methane to convert moles
to grams. Then convert grams to kilograms.
KNOWNS
P = 1.50  103 kPa
V = 2.24  103 L
T = 315 K
R = 8.31 (L·kPa)/(K·mol)
molar massCH4
= 16.0 g
UNKNOWN
m = ? kg CH4
Analyze List the knowns and the
unknown.
1
Sample Problem 14.6

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State the ideal gas law.
Calculate Solve for the unknown.
2
P  V = n  R  T
Rearrange the equation to isolate n.
n =
R  T
P  V
Sample Problem 14.6

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Substitute the known quantities into the
equation and find the number of moles
of methane.
Calculate Solve for the unknown.
2
n =
8.31 (L·kPa)/(K·mol)  315 K
(1.50  106 kPa)  (2.24  106 L)
n = 1.28  106 mol CH4
Sample Problem 14.6

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Do a mole-mass conversion.
Calculate Solve for the unknown.
2
1.28  106 mol CH4 
16.0 g CH4
1 mol CH4
= 20.5  106 g CH4
= 2.05  107 g CH4
Sample Problem 14.6

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Convert from grams to kilograms.
Calculate Solve for the unknown.
2
2.05  106 g CH4 
1 kg
103 g
= 2.05  104 kg CH4
Sample Problem 14.6

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• Although the methane is
compressed, its volume is still very
large.
• So it is reasonable that the cavern
contains a large amount of methane.
Evaluate Does the result make sense?
3
Sample Problem 14.6

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How would you rearrange the ideal gas
law to isolate the temperature, T?
PV
nR
T =
A.
nR
PV
T =
C.
PR
nV
T =
B.
RV
nP
T =
D.

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How would you rearrange the ideal gas
law to isolate the temperature, T?
PV
nR
T =
A.
nR
PV
T =
C.
PR
nV
T =
B.
RV
nP
T =
D.

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Ideal Gases and Real Gases
Ideal Gases and Real Gases
Under what conditions are real gases
most likely to differ from ideal gases?

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Ideal Gases and Real Gases
An ideal gas is one that follows the gas
laws at all conditions of pressure and
temperature.

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Ideal Gases and Real Gases
An ideal gas is one that follows the gas
laws at all conditions of pressure and
temperature.
• Its particles could have no volume.

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Ideal Gases and Real Gases
An ideal gas is one that follows the gas
laws at all conditions of pressure and
temperature.
• Its particles could have no volume.
• There could be no attraction between
particles in the gas.

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Ideal Gases and Real Gases
There is no gas for which these
assumptions are true.
• So, an ideal gas does not exist.

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Ideal Gases and Real Gases
At many conditions of temperature and
pressure, a real gas behaves very much
like an ideal gas.

38. 14.3 Ideal Gases >
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Ideal Gases and Real Gases
At many conditions of temperature and
pressure, a real gas behaves very much
like an ideal gas.
• The particles in a real gas
have volume.

39. 14.3 Ideal Gases >
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Ideal Gases and Real Gases
At many conditions of temperature and
pressure, a real gas behaves very much
like an ideal gas.
• The particles in a real gas
have volume.
• There are attractions
between the particles.

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Ideal Gases and Real Gases
At many conditions of temperature and
pressure, a real gas behaves very much
like an ideal gas.
• The particles in a real gas
have volume.
• There are attractions
between the particles.
• Because of these attractions,
a gas can condense, or even
solidify, when it is
compressed or cooled.

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Real gases differ most from an ideal
gas at low temperatures and high
pressures.
Ideal Gases and Real Gases

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Interpret Graphs
This graph shows how real gases
deviate from the ideal gas law at
high pressures.

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What are the characteristics of
an ideal gas?

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What are the characteristics of
an ideal gas?
The particles of an ideal gas have
no volume, and there is no
attraction between them.

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Certain types of fog machines use dry ice
and water to create stage fog. What phase
changes occur when stage fog is made?
CHEMISTRY & YOU

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Certain types of fog machines use dry ice
and water to create stage fog. What phase
changes occur when stage fog is made?
CHEMISTRY & YOU
Dry ice doesn’t melt—it sublimes. As
solid carbon dioxide changes to gas,
water vapor in the air condenses and
forms a white fog. Dry ice can exist
because gases don’t obey the
assumptions of kinetic theory at all
conditions.

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Key Concepts and Key Equation
When the pressure, volume, and temperature
of a contained gas are known, you can use
the ideal gas law to calculate the number of
moles of the gas.
Real gases differ most from an ideal gas at
low temperatures and high pressures.
Key Equation: ideal gas law
P  V = n  R  T or PV = nRT

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Glossary Terms
• ideal gas constant: the constant in the
ideal gas law with the symbol R and the
value 8.31 (L·kPa)/(K·mol)
• ideal gas law: the relationship PV = nRT,
which describes the behavior of an ideal
gas

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Kinetic Theory
BIG IDEA
• Ideal gases conform to the assumptions of
kinetic theory.
• The behavior of ideal gases can be predicted
by the gas laws.
• With the ideal gas law, the number of moles of
a gas in a fixed volume at a known
temperature and pressure can be calculated.
• Although an ideal gas does not exist, real
gases behave ideally under a variety of
temperature and pressure conditions.

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END OF 14.3