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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

Section 13.1 The Gas Laws

• State the relationships among pressure, temperature, and volume of a constant amount of gas.

scientific law: describes a relationship in nature that is supported by many experiments

• Apply the gas laws to problems involving the pressure, temperature, and volume of a constant amount of gas.

Section 13-1

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.

Section 13-1

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

Section 13-1

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.

Section 13-1

Charles's Law (cont.)

Section 13-1

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.

Section 13-1

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.

Section 13-1

Gay-Lussac's Law (cont.)

Section 13-1

The Combined Gas Law

• The combined gas law states the relationship among pressure, temperature, and volume of a fixed amount of gas.

Section 13-1

The Combined Gas Law (cont.)

Section 13-1

1. A
2. B
3. C
4. D

Section 13.1 Assessment

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

Section 13-1

1. A
2. B
3. C
4. D

Section 13.1 Assessment

Atoms are in their lowest energy state at what temperature?

A. 0° Celsius

B. 0° Fahrenheit

C. –100° Celsius

D. 0 kelvin

End of Section 13-1

Section 13-2

Section 13.2 The Ideal Gas Law

• Relate number of particles and volume using Avogadro’s principle.

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

• 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.

Section 13-2

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.

Section 13-2

Avogadro's Principle

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

Section 13-2

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.

Section 13-2

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

Section 13-2

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.

Section 13-2

The Ideal Gas Law (cont.)

Section 13-2

The Ideal Gas Law—Molar Mass and Density

• Molar mass and the ideal gas law

Section 13-2

The Ideal Gas Law—Molar Mass and Density (cont.)

• Density and the ideal gas law

Section 13-2

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.

Section 13-2

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

1. A
2. B
3. C
4. D

Section 13.2 Assessment

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

Section 13-2

1. A
2. B
3. C
4. D

Section 13.2 Assessment

3.00 mol of O₂ at STP occupies how much volume?

A. 30.0 L

B. 22.4 L

C. 25.4 L

D. 67.2 L

End of Section 13-2

Section 13-3

Section 13.3 Gas Stoichiometry

• Determine volume ratios for gaseous reactants and products by using coefficients from chemical equations.

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

• Apply gas laws to calculate amounts of gaseous reactants and products in a chemical reaction.

When gases react, the coefficients in the balanced chemical equation represent both molar amounts and relative �volumes.

Section 13-3

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.

Section 13-3

Stoichiometry and Volume-Volume Problems

• Coefficients in a balanced equation represent volume ratios for gases.

Section 13-3

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

1. A
2. B
3. C
4. D

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)

A. 1.00

B. 2.00

C. 3.00

D. 4.00

Section 13-3

1. A
2. B
3. C
4. D

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)

A. 2.00

B. 3.25

C. 4.00

D. 6.50

End of Section 13-3

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Study Guide 1

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.

Study Guide 1

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.

Study Guide 2

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

Study Guide 2

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.

Study Guide 3

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.

Chapter Assessment 1

1. A
2. B
3. C
4. D

What does the combined gas law relate?

A. pressure and temperature

B. volume and pressure

C. pressure, temperature, and � volume

D. pressure, temperature, � volume, and amount

Chapter Assessment 2

1. A
2. B
3. C
4. D

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.

B. Temperature will increase.

C. Mass will increase.

D. Mass will decrease.

Chapter Assessment 3

1. A
2. B
3. C
4. D

Equal volumes of gases at the same temperature and pressure contain equal numbers of particles is stated by:

A. Law of conservation of mass

B. Boyle’s law

C. Avogadro’s principle

D. Ideal gas law

Chapter Assessment 4

1. A
2. B
3. C
4. D

What is the volume of 1.00 mol of chlorine gas at standard temperature and pressure?

A. 1.00 L

B. 18.0 L

C. 22.4 L

D. 44.8 L

Chapter Assessment 5

1. A
2. B
3. C
4. D

When do real gases behave differently than ideal gases?

A. high temperature or low pressure

B. high temperature or high pressure

C. low temperature or low pressure

D. low temperature or high pressure

STP 1

1. A
2. B
3. C
4. D

If two variables are directly proportional, what happens to the value of one as the other decreases?

A. increases

B. decreases

C. remains constant

D. none of the above

STP 2

1. A
2. B
3. C
4. D

What conditions represent standard temperature and pressure?

A. 0.00°C and 0.00atm

B. 1.00°C and 1.00atm

C. 0.00°F and 1.00atm

D. 0.00°C and 1.00atm

STP 3

1. A
2. B
3. C
4. D

One mole of gas occupies how much volume at STP?

A. 1.00 L

B. 2.20 L

C. 22.4 L

D. 33.7 L

STP 4

1. A
2. B
3. C
4. D

Which of the following would deviate the most from an ideal gas?

A. gas in a hot-air balloon

B. water vapor from the reaction � of gaseous hydrogen and oxygen

C. upper atmospheric gases

D. gases near absolute zero

STP 5

1. A
2. B
3. C
4. D

What volume will 3.50 mol of Xe gas occupy at STP?

A. 78.4 L

B. 22.4 L

C. 25.9 L

D. 54.4 L

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Figure 13.3 The Gas Laws

Table 13.1 The Gas Laws

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