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Gases

Chapter 5

Substances That Exist as Gases (5.1)Pressure of a Gas (5.2)The Gas Laws (5.3)The Ideal Gas Equation (5.4)Dalton’s Law of Partial Pressure (5.5)The Kinetic Molecular Theory of Gases (5.6)Deviation from Ideal Behavior (5.7)

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Single ideal gases – (5.1-5.4)◦ Properties of a gas (5.1, 5.2)◦ Experimental behaviors of gases (5.3)◦ Ideal gas law (5.4)

STPCalculations involving the ideal gas law

◦ Combined gas law (5.3-5.4)◦ Stoichiometry (5.4)Mixture of gases – (5.5)◦ Dalton’s Law of Partial Pressures◦ Wetting of a gasKinetic Molecular Theory – (5.6)◦ Energy◦ Molecular speed (rms)◦ Diffusion and effusionReal gases – (5.7)◦ van der Waals equation

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5.1 Substances That Exist as GasesRepresentation of matter:

Macroscopic versus particle

What are four properties of gases?

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• Gases assume the volume and shape of their containers.

• Gases are the most compressible state of matter.

• Gases will mix evenly and completely when confined to the same container.

• Gases have much lower densities than liquids and solids.

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5.1 Substances That Exist as Gases

Margin Figure, p. 138

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5.1 Substances That Exist as Gases

Margin Figure, p. 138

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5.1 Substances That Exist as Gases

p. 138

5.1 Substances That Exist as GasesGases molecules do not interact with other molecules (if they do collide, it is elastic)

Gas molecules themselves have no volume (not true but consider the vast space between each molecule)

There is no attraction between molecules (all gases are the same)

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5.2 Pressure of a Gas

Key Questions:What is pressure? How is pressure measured?What is pressure? ◦ On a particle level◦ On a macroscopic level

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5.2 Pressure of a Gas

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Figure 5.3, p. 141Figure 5.2, p. 140

5.2 Pressure of a Gas

Key Questions:What is pressure? How is pressure measured?What is pressure? ◦ On a particle level◦ On a macroscopic level

What are the standard units for pressure?

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5.3 The Gas Laws

Key Questions:How do we represent a proportionality?How do we convert this to an equality?What is the relationship between◦ Pressure and volume◦ Temperature and volume◦ Amount and volume

How do these combine?

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13Figure 5.6, p. 145

5.3 The Gas Laws

Figure 5.5, p. 144

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14Figure 5.8, p. 145

5.3 The Gas Laws

Figure 5.5, p. 144

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15Figure 5.8, p. 145

5.3 The Gas Laws

Figure 5.5, p. 144

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Figure 5.5, p. 144

5.3 The Gas Laws

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Figure 5.9, p. 147

5.4 The Ideal Gas Equation

5.4 The Ideal Gas Equation

Key Questions:What is “R”?What are the units on RWhat is STP?What is the value of R

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Figure 5.10, p. 148

5.4 The Ideal Gas Equation

Key Questions:When can a gas be assumed to be ideal (when can we use this equation)?What can be calculated directly from the ideal gas law?What can be calculated indirectly from the ideal gas law?How can the properties of a gas (P, V, T) be useful in a reaction?

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Gases and Stoichiometry

When 3.1 atm of carbon monoxide reacts with 2.7 atm of oxygen at a constant temperature in a closed rigid container, what is the theoretical yield (in atm) of carbon dioxide?

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Figure 5.12, p. 152

What is the pressure (in atm) of 24.0 g of nitrogen in a 25.0 L container at 25 oC?A. 1.7 atm B. 0.84 atmC. 0.14 atm D. 0.070 atm

What is the molar mass of an ideal gas which has a density of 0.901 g·L–1 at STP?A. 24.5 g·mol–1 B. 22.4 g·mol–1

C. 20.2 g·mol–1 D. 0.901 g·mol–1

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5.5 Dalton’s Law of Partial Pressures

Key Definitions:partial pressure◦ The pressures of individual gas components in a

mixtureDalton’s law of partial pressures◦ Total pressure of a mixture of gases is just the

sum of the pressures that each gas would exert if it were present alone

mole fraction◦ Dimensionless quantity that expresses the ratio

of the number of moles of one component to the number of moles of all components present

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Dalton’s Law of Partial Pressures

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Figure 5.13, p. 154

The reaction of oxygen and hydrogen to form water is utilized in fuel cells. In the figure below the volume of the rigid container is 10.0 L, the temperature is constant at 55oC and each symbol represents 0.050 mol of gas. Water molecules are not explicitly shown in any phase.

If the total pressure is 1243 mmHg, what are the partial pressures of all gases?

If the reaction continues to completion, what is the resulting partial pressure of oxygen and hydrogen?

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5.5 Dalton’s Law of Partial Pressures

Key Questions:Does partial pressure change with container size?◦ with temperature?

What is wetting of a gas?◦ Why is this a useful

experimental technique?◦ Why does Dalton’s Law of

Partial Pressures apply?

26Table 5.2, p. 157

27Figure 5.14, p. 157

5.5 Dalton’s Law of Partial Pressures

More Practice:Hydrogen peroxide (H2O2) decomposes into water and oxygen. This process can be sped up through the use of a catalyst.

If a 1.50 mL sample of a hydrogen peroxide solution is decomposed with a catalyst and 79.0 mL of gas is collected over water at 22.5ºC and under 1.015 atmof pressure, what is the concentration of hydrogen peroxide (in water solution) (%v/v)?

The vapor pressure of water at 22.5ºC is 20.20 mmHg and the density of hydrogen peroxide is 1.46 g·mL–1.

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5.5 Dalton’s Law of Partial Pressures

Hydrogen peroxide (H2O2) decomposes into water and oxygen. This process can be sped up through the use of a catalyst. If a 1.50 mL sample of a hydrogen peroxide solution is decomposed with a catalyst and 79.0 mL of gas is collected over water at 22.5ºC and under 1.015 atm of pressure, what is the concentration of hydrogen peroxide (in water solution) (%v/v)? The vapor pressure of water at 22.5ºC is 20.20 mmHg and the density of hydrogen peroxide is 1.46 g·mL–1.

1. What is the total pressure in mmHg?2. What is the partial pressure of oxygen?3. How many moles of oxygen were produced?4. What is the balanced chemical equation?5. How many moles of peroxide were present?6. What volume of peroxide was present?7. What is the %v/v concentration?

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More Practice:The reaction N2O4(g) 2NO2(g) does not actually go to completion at all temperatures. If 35.0 g of N2O4 is originally placed in a 2.0 L container at 100°C and allowed to react, the final pressure in the container is 10.6 atm. What is the partial pressure of NO2 and N2O4 at equilibrium and what is the percent yield of the reaction under these conditions?

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5.5 Dalton’s Law of Partial Pressures

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The reaction N2O4(g) 2NO2(g) does not actually go to completion at all temperatures. If 35.0 g of N2O4 is originally placed in a 2.0 L container at 100°C and allowed to react, the final pressure in the container is 10.6 atm. What is the partial pressure of NO2 and N2O4at equilibrium and what is the percent yield of the reaction under these conditions?

1. How many moles of N2O4 are present initially?2. How many total moles of gases were present after

the reaction ended?3. How can the completion of the reaction be

modeled using a variable (“x”) and the correct mole ratios (remember, the reactants are consumed (or decreasing number of moles) and the products are formed (or increasing number of moles)?

4. How many moles of NO2 were experimentally formed?

5. What is the percent yield?6. What are the partial pressures of both gases?

5.6 The Kinetic Molecular Theory of GasesKey Questions:

(Review) What do we assume when we say a gas is “ideal”?How are average kinetic energy and temperature related for an ideal gas?◦ Will all ideal gases, regardless of type have the

same average kinetic energy at the same temperature?

How are molecular speed and temperature related for an ideal gas?

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5.6 The Kinetic Molecular Theory of Gases

Figure 5.15, p. 161

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5.6 The Kinetic Molecular Theory of Gases

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5.6 The Kinetic Molecular Theory of Gases

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5.6 The Kinetic Molecular Theory of Gases

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5.6 The Kinetic Molecular Theory of Gases

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5.6 The Kinetic Molecular Theory of Gases

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5.6 The Kinetic Molecular Theory of Gases

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5.6 The Kinetic Molecular Theory of Gases

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5.6 The Kinetic Molecular Theory of Gases

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5.6 The Kinetic Molecular Theory of Gases

5.6 The Kinetic Molecular Theory of GasesKey Questions:

What do we assume when we say a gas is “ideal”?How are average kinetic energy and temperature related for an ideal gas?◦ Will all ideal gases, regardless of type have the

same average kinetic energy at the same temperature?

How are molecular speed, temperature and gas identity related for an ideal gas?

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Will the speed of all gases be the same at one temperature?

44Figure 5.15, p. 161

Diffusion/Effusion

Key Definition:Diffusion◦ Gradual mixing of molecules of one gas with

molecules of another by virtue of their kinetic properties

Key Question:Why does a gas, traveling so fast, take such a long time to diffuse?

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46Figure 5.16, p. 163

Diffusion/Effusion

Key Definition:Effusion◦ The process by which

a gas under pressure escapes from one compartment of a container to another by passing through a small opening.

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Figure 5.18, p. 164

5.7 Deviation from Ideal Behavior

Under what conditions can a gas be assumed to be ideal?

48Figure 5.20, p. 165 and Table 5.3, p. 166

5.7 Deviation from Ideal Behavior

Under what conditions can a gas be assumed to be ideal?

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Figure 5.19, p. 165

Which ideal gas will have the greatest average kinetic energy at STP?A. H2 B. He C. NeD. All ideal gases have the same average kinetic

energy for a given temperature.

What is the root mean square speed of fluorine at room temperature (25 oC)?A. less than 50 m·s–1

B. between 50 m·s–1 and 275 m·s–1

C. between 275 m·s–1 and 500 m·s–1

D. greater than 500 m·s–1

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