Section 2: The Ideal Gas Law
The ideal gas law relates the number of particles to pressure,
temperature, and volume.
K
What I Know
W
What I Want to Find Out
L
What I Learned
Essential Questions
• How does Avogadro’s principle relate the number of particles of gas to
the gas’s volume?
• How is the amount of gas present related to its pressure, temperature,
and volume by the ideal gas law?
• What are the properties of real gases and of ideal gases?
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The Ideal Gas Law
Vocabulary
Review
New
• mole
• Avogadro’s principle
• molar volume
• standard temperature and
pressure (STP)
• ideal gas constant (R)
• ideal gas law
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The Ideal Gas Law
Avogadro's Principle
•
Avogadro’s principle states that equal volumes of gases at the same
temperature and pressure contain equal numbers of particles.
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The Ideal Gas Law
Avogadro's Principle
•
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.
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The Ideal Gas Law
MOLAR VOLUME
Use with Example Problem 5.
KNOWN
UNKNOWN
Problem
m = 2.00 kg
V=?L
The main component of natural gas
used for home heating and cooking is
methane (CH4). Calculate the volume
that 2.00 kg of methane gas will
occupy at STP.
T = 0.00ºC
Response
ANALYZE THE PROBLEM
The number of moles can be
calculated by dividing the mass of the
sample, m, by its molar mass, M. The
gas is at STP (0.00°C and 1.00 atm
pressure), so you can use the molar
volume to convert from the number of
moles to the volume.
P = 1.00 atm
SOLVE FOR THE UNKNOWN
Determine the molar mass for methane.
•
Determine the molecular mass.
M = 1 C atom
12.01 amu
+ 4H atoms
1 C atom
1.01 amu
= 12.01 amu + 4.04 amu = 16.05 amu
1 H atom
•
Express the molecular mass as g/mol to
arrive at the molar mass.
= 16.05 g/mol
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The Ideal Gas Law
MOLAR VOLUME
SOLVE FOR THE UNKNOWN (continued)
EVALUATE THE ANSWER
Determine the number of moles of methane.
The amount of methane present is much
more than 1 mol, so you should expect a
large volume, which is in agreement with
the answer. The unit is liters, a volume unit,
and there are three significant figures.
•
Convert the mass from kg to g.
2.00 kg
•
1000 g
1 kg
= 2.00 × 103 g
Divide mass by molar mass to determine
the number of moles.
m 2.00 × 103 g
=
= 125 mol
M 16.05 g/mol
Use the molar volume to determine the
volume of methane at STP.
•
Use the molar volume, 22.4 L/mol, to
convert from moles to the volume.
V = 125 mol ×
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22.4 L
= 2.80 × 103 L
1 mol
The Ideal Gas Law
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
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The Ideal Gas Law
The Ideal Gas Law
•
The ideal gas constant is represented by R and is 0.0821 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.
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The Ideal Gas Law
The Ideal Gas Law
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The Ideal Gas Law
THE IDEAL GAS LAW
Use with Example Problem 6.
Problem
KNOWN
UNKNOWN
V = 3.0 L
n = ? mol
T = 3.00 × 102 K
Calculate the number of moles of
ammonia gas (NH3) contained in a 3.0-L
vessel at 3.00 × 102 K with a pressure of
1.50 atm.
P = 1.50 atm
L·atm
R = 0.0821
mol·K
Response
SOLVE FOR THE UNKNOWN
ANALYZE THE PROBLEM
You are given the volume, temperature,
and pressure of a gas sample. Use the
ideal gas law, and select the value of R
that contains the pressure units given in
the problem. Because the pressure and
temperature are close to STP, but the
volume is much smaller than 22.4 L, it
would make sense if the calculated
answer were much smaller than 1 mol.
Use the ideal gas law. Solve for n, and
substitute the known values.
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•
State the ideal gas law.
PV = nRT
•
Solve for n.
n=
PV
RT
The Ideal Gas Law
THE IDEAL GAS LAW
SOLVE FOR THE UNKNOWN (continued)
EVALUATE THE ANSWER
•
The answer agrees with the prediction
that the number of moles present will be
significantly less than 1 mol. The unit of
the answer is the mole, and there are two
significant figures.
Substitute V = 3.0 L, T = 3.00 × 102 K,
P = 1.50 atm, and R = 0.0821 L •
atm/mol • K.
n=
•
(1.50 atm)(3.0 L)
0.0821 L·atm (3.00 × 102 K)
mol·K
Multiply and divide numbers and units.
n=
(1.50 atm)(3.0 L)
= 0.18 mol
0.0821 L·atm (3.00 × 102 K)
mol·K
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The Ideal Gas Law
The Ideal Gas Law—Molar Mass and Density
•
Molar mass and the ideal gas law:
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The Ideal Gas Law
The Ideal Gas Law—Molar Mass and Density
•
Density and the ideal gas law:
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The Ideal Gas Law
Gases
Go to your ConnectED resources to play Video Lab: Gases.
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The Ideal Gas Law
Real Versus Ideal Gases
•
Ideal gases follow the assumptions of the kinetic-molecular theory.
•
Characteristics of ideal gases:
– 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.
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The Ideal Gas Law
Real Versus Ideal Gases
•
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.
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The Ideal Gas Law
Gasses, Pressure and Scuba Diving
Go to your ConnectED resources to play Video: Leagues Under
the Sea.
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The Ideal Gas Law
Review
Essential Questions
• How does Avogadro’s principle relate the number of particles of gas
to the gas’s volume?
• How is the amount of gas present related to its pressure,
temperature, and volume by the ideal gas law?
• What are the properties of real gases and of ideal gases?
Vocabulary
•
•
Avogadro’s
principle
molar volume
Copyright © McGraw-Hill Education
•
standard
temperature and
pressure (STP)
•
•
ideal gas constant (R)
ideal gas law
The Ideal Gas Law