Gases
Section 13.1 The Gas Laws
Section 13.2 The Ideal Gas Law
Section 13.3 Gas Stoichiometry
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Section 13.1 The Gas Laws
• State the relationships among pressure, temperature,
and volume of a constant amount of gas.
• Apply the gas laws to problems involving the
pressure, temperature, and volume of a constant
amount of gas.
scientific law: describes a relationship in nature that
is supported by many experiments
Section 13.1 The Gas Laws (cont.)
Boyle’s law
absolute zero
Charles’s law
Gay-Lussac’s law
combined gas law
For a fixed amount of gas, a change in
one variable—pressure, temperature,
or volume—affects the other two.
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
• Practice p 443
• The volume of a gas at 99 kPa is 300 ml. If
the pressure is increased to 188 kPa, what
will be the new volume?
• The pressure of a sample of helium in a 1 L
container is 0.988 atm. What is the new
pressure if the sample is placed in a 2 L
container?
• Air trapped in a cylinder fitted with a piston
occupies 145.7 mL at 1.08 atm pressure.
What is the new volume when the piston is
depressed, increasing the pressure by 25%?
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.
Charles's Law (cont.)
Charles's Law (cont.)
• 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.
• Practice p 446
• A balloon is 4.3 L at 350 K. What volume
will the gas in the balloon occupy at
250K?
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.
Gay-Lussac's Law (cont.)
The Combined Gas Law
• The combined gas law states the
relationship among pressure, temperature,
and volume of a fixed amount of gas.
The Combined Gas Law (cont.)
Section 13.1 Assessment
Boyle’s Law explains which relationship
of properties in gases?
A. pressure and volume
B. amount and pressure
D
A
0%
C
D. volume and temperature
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. temperature and volume
Section 13.1 Assessment
Atoms are in their lowest energy state at
what temperature?
A. 0° Celsius
B. 0° Fahrenheit
D
A
0%
C
D. 0 kelvin
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. –100° Celsius
Section 13.2 The Ideal Gas Law
• Relate number of particles and volume using
Avogadro’s principle.
• Relate the amount of gas present to its pressure,
temperature, and volume using the ideal gas law.
• Compare the properties of real and ideal gases.
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
Section 13.2 The Ideal Gas Law (cont.)
Avogadro’s principle
molar volume
ideal gas constant (R)
ideal gas law
The ideal gas law relates the number of
particles to pressure, temperature, and
volume.
Avogadro's Principle
• Avogadro’s principle states that equal
volumes of gases at the same temperature
and pressure contain equal numbers of
particles.
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.
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
The Ideal Gas Law (cont.)
• 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.
The Ideal Gas Law (cont.)
The Ideal Gas Law—Molar Mass and Density
• Molar mass and the ideal gas law
The Ideal Gas Law—Molar Mass and Density
(cont.)
• Density and the ideal gas law
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.
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.
Section 13.2 Assessment
Which of the following is NOT one of the
related physical properties described in
the ideal gas law?
A. pressure
A
0%
D
D. temperature
C
C. density
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. volume
Section 13.2 Assessment
3.00 mol of O2 at STP occupies how much
volume?
A. 30.0 L
B. 22.4 L
D
A
0%
C
D. 67.2 L
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 25.4 L
Section 13.3 Gas Stoichiometry
• Determine volume ratios for gaseous reactants and
products by using coefficients from chemical equations.
• Apply gas laws to calculate amounts of gaseous
reactants and products in a chemical reaction.
coefficient: the number written in front of a reactant or
product in a chemical equation, which tells the
smallest number of particles of the substance involved
in the reaction
When gases react, the coefficients in the
balanced chemical equation represent
both molar amounts and relative
volumes.
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.
Stoichiometry and Volume-Volume Problems
• Coefficients in a balanced equation
represent volume ratios for gases.
Stoichiometry and Volume-Mass Problems
• Mass must be found by converting to
moles or volumes.
• Plastics are some of the products created
with polymers.
• One component of polymers is ethene gas,
or ethylene.
Section 13.3 Assessment
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)
0%
A
D. 4.00
D
C. 3.00
C
B. 2.00
A. A
B. B
C. C
0%
0%
0%
D. D
B
A. 1.00
Section 13.3 Assessment
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)
0%
A
D. 6.50
D
C. 4.00
C
B. 3.25
A. A
B. B
C. C
0%
0%
0%
D. D
B
A. 2.00
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Concepts in Motion
Section 13.1 The Gas Laws
Key Concepts
• Boyle’s law states that the volume of a fixed amount
of gas is inversely proportional to its pressure at
constant temperature.
P1V1 = P2V2
• Charles’s law states that the volume of a fixed amount
of gas is directly proportional to its kelvin temperature
at constant pressure.
Section 13.1 The Gas Laws (cont.)
Key Concepts
• Gay-Lussac’s law states that the pressure of a fixed
amount of gas is directly proportional to its kelvin
temperature at constant volume.
• The combined gas law relates pressure, temperature,
and volume in a single statement.
Section 13.2 The Ideal Gas Law
Key Concepts
• Avogadro’s principle states that equal volumes of gases
at the same pressure and temperature contain equal
numbers of particles.
• The ideal gas law relates the amount of a gas present
to its pressure, temperature, and volume.
PV = nRT
Section 13.2 The Ideal Gas Law (cont.)
Key Concepts
• The ideal gas law can be used to find molar mass if the
mass of the gas is known, or the density of the gas if its
molar mass is known.
• At very high pressures and very low temperatures, real
gases behave differently than ideal gases.
Section 13.3 Gas Stoichiometry
Key Concepts
• The coefficients in a balanced chemical equation
specify volume ratios for gaseous reactants and
products.
• The gas laws can be used along with balanced
chemical equations to calculate the amount of a
gaseous reactant or product in a reaction.
What does the combined gas law relate?
A. pressure and temperature
B. volume and pressure
D
A
0%
C
D. pressure, temperature,
volume, and amount
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. pressure, temperature, and
volume
According to Charles’s law, if pressure
and amount of a gas are fixed, what will
happen as volume is increased?
A. Temperature will decrease.
A
0%
D
D. Mass will decrease.
C
C. Mass will increase.
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. Temperature will increase.
Equal volumes of gases at the same
temperature and pressure contain equal
numbers of particles is stated by:
A. Law of conservation of mass
A
0%
D
D. Ideal gas law
C
C. Avogadro’s principle
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. Boyle’s law
What is the volume of 1.00 mol of chlorine
gas at standard temperature and
pressure?
A. 1.00 L
A
0%
D
D. 44.8 L
C
C. 22.4 L
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. 18.0 L
When do real gases behave differently
than ideal gases?
A. high temperature or low pressure
B. high temperature or high pressure
D
A
0%
C
D. low temperature or high pressure
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. low temperature or low pressure
If two variables are directly proportional,
what happens to the value of one as the
other decreases?
A. increases
A
0%
D
D. none of the above
C
C. remains constant
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. decreases
What conditions represent standard
temperature and pressure?
A. 0.00°C and 0.00atm
B. 1.00°C and 1.00atm
D
A
0%
C
D. 0.00°C and 1.00atm
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 0.00°F and 1.00atm
One mole of gas occupies how much
volume at STP?
A. 1.00 L
B. 2.20 L
D
A
0%
C
D. 33.7 L
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 22.4 L
Which of the following would deviate the
most from an ideal gas?
A. gas in a hot-air balloon
D. gases near absolute zero
0%
B
A
0%
A
B
C
D
0%
0%
D
C. upper atmospheric gases
A.
B.
C.
D.
C
B. water vapor from the reaction
of gaseous hydrogen and oxygen
What volume will 3.50 mol of Xe gas
occupy at STP?
A. 78.4 L
B. 22.4 L
D
A
0%
C
D. 54.4 L
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 25.9 L
Click on an image to enlarge.
Figure 13.3 The Gas Laws
Table 13.1
The Gas Laws
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