CHAPTER 3 States of Matter 4 Behavior of Gases SECTION KEY IDEAS As you read this section, keep these questions in mind: What are some properties of gases? How do changes of pressure, temperature, or volume affect a gas? What Are Some Properties of Gases? Particles in a gas move rapidly in all directions. Some of the unique properties of gases are listed below: expand to fill their containers easily mix with one another have low densities can be compressed are mostly empty space GASES AND THEIR CONTAINERS Gases exert pressure on their containers. For example, as helium molecules inside a balloon move, they bump into each other and the walls of the balloon. One molecule alone does not have a large effect. However, millions of molecules create a steady force. If too many gas molecules are in the balloon, the total pressure they exert can cause the balloon to break. READING TOOLBOX Organize As you read, make a table that lists all of the gas laws discussed in the section. For each law, identify which factor must stay constant, which variables change, and the relationship between the variables. 1. Predict What would happen to pressure if you removed some of the gas particles from the balloon? Gas particles exert pressure on the walls of a balloon. A gas under pressure will escape its container if possible. For example, if you open the end of a balloon, gas will rush out of the balloon. For this reason, gases in pressurized containers, such as propane tanks or helium tanks, can be very dangerous. Interactive Reader 61 States of Matter
What Are the Gas Laws? Gases behave differently than solids or liquids do. For example, the volume of a gas can change due to pressure, but the volume of a solid or liquid generally cannot. The gas laws describe how variables such as pressure, volume, and temperature affect the behavior of gases. The gas laws will help you understand and predict the behavior of gases in specific situations. READING CHECK 2. Identify Boyle s law describes the relationship between which two variables? PRESSURE AND VOLUME A diver is swimming at a depth of 10 m below sea level. An air bubble escapes from her mouthpiece. As the bubble rises to the surface, it gets bigger. When the bubble reaches the water s surface, its volume is double its original size. This example shows the relationship between the volume and pressure of a gas, also known as Boyle s law. Boyle s law is true for almost any gas, if temperature and amount of gas are constant, or unchanged. Boyle s Law For a certain amount of gas at a constant temperature, the volume of a gas decreases as the gas s pressure increases. Likewise, the volume of a gas increases as the gas s pressure decreases. In mathematical terms: Boyle s Law (initial pressure)(initial volume) = (final pressure)(final volume) P 1 V 1 = P 2 The figure below illustrates Boyle s law. Both pistons contain the same amount of gas at the same temperature. 3. Identify What happens to volume as pressure decreases? If you lift the piston, pressure decreases. The gas particles spread farther apart, and the volume increases. If you push the piston, pressure increases. The gas particles are pushed closer together, and the volume decreases. Interactive Reader 62 States of Matter
APPLYING BOYLE S LAW You can use Boyle s law to predict changes in the pressure or volume of a gas. Remember that Boyle s law is true only when the temperature and amount of gas do not change. A balloon has a volume of 7.5 L at 100.0 kpa. As the balloon rises in the atmosphere, the gas inside expands to a volume of 11 L. Assume the balloon is at a constant temperature and the amount of gas does not change. What is the pressure when the volume is 11 L? READING CHECK 4. Identify Under what conditions does Boyle s law apply? The ballon on the left has a volume of 7.5 L and a pressure of 100 kpa. As the balloon rises, it becomes larger. The balloon s new volume is 11 L. The temperature and number of molecules inside the balloon stay the same. Step 1: List the given and unknown values. Step 2: Write the equation and rearrange to solve for the unknown. Given: V 1 = 7.5 L P 1 = 100.0 kpa = 11 L P 1 V 1 = P 2 P 2 = _ P V 1 1 Step 3: Insert the known values and (100.0 kpa)(7.5 L) solve for the unknown value. P 2 = 11 L P 2 = 68 kpa Unknown: P 2 Math Skills 5. Calculate A 300 ml sample of hydrogen gas is at a pressure of 0.500 kpa. If the pressure increases to 0.750 kpa, what will be the final volume of the sample? Assume that temperature stays constant. PRESSURE AND TEMPERATURE Recall that temperature is a measure of the average kinetic energy of particles. As the particles of a substance move faster, the substance s temperature increases. The particles bump into each other and the sides of the container more often, which increases pressure. Thus, as temperature increases, pressure increases. This is known as Gay-Lussac s law. Interactive Reader 63 States of Matter
Gay-Lussac s Law When volume is constant, the pressure of a gas increases as temperature increases. Pressure decreases as temperature decreases. In other words, the pressure and temperature of a gas are directly related. As one changes, the other changes in the same direction. 6. Compare How are the relationships between variables described in Gay-Lussac s law and Charles s law similar? TEMPERATURE AND VOLUME Like the temperature and pressure of a gas, the temperature and volume of a gas are directly related. This relationship is described in Charles s Law. Charles s Law When the amount of a gas and pressure are constant, the volume of a gas increases as its temperature increases. Likewise, as volume decreases, temperature decreases. The figure below illustrates Charles s Law. Both pistons have the same amount of gas at the same pressure. When temperature decreases, the gas particles move more slowly and volume decreases. When temperature increases, the gas particles move faster and volume increases. The following experiment also illustrates Charles s law. 7. Identify What two factors did not change during the experiment? Air-filled balloons are put into liquid nitrogen. The low temperature of the liquid nitrogen makes the volumes of the air in the balloons smaller. When the balloons are removed from the liquid nitrogen, their temperature increases. The volume of each balloon increases to its original volume. Interactive Reader 64 States of Matter
How Can Graphs Illustrate the Gas Laws? You can use graphs to show how temperature, pressure, and volume affect gases. A graph can show the relationship between two factors. For example, the graph can show if a relationship is direct or inverse. In a direct relationship, the two variables change in the same direction. In an inverse relationship, the variables change in opposite directions. In the graph below, temperature and volume have a direct relationship. Volume (L) Volume versus Temperature for a Gas at a Constant Pressure 0.700 0.600 0.500 0.400 0.300 0.200 Graphing Skills 8. Analyze Is the relationship shown in this graph direct or inverse? How do you know? 0.100 0.000 0 100 200 300 Temperature (K) The shape of the line in a graph also describes the relationship. If a graph is a straight line, such as the graph above, one variable is directly or inversely proportional to the other. In a proportional relationship, the variables stay in the same ratio to each other as their values change. If a graph is a curve, one variable is not proportional to the other. This means that the variables do not stay in the same ratio to each other as their values change. Volume (L) Volume versus Pressure for a Gas at a Constant Temperature 0.500 0.400 0.300 0.200 0.100 9. Analyze Is this relationship proportional? Explain your answer. 10. Identify Which gas law does this graph represent? 11. Infer Is the relationship between the variables direct or inverse? Explain your answer. 0.000 0 100 200 300 400 Pressure (kpa) Interactive Reader 65 States of Matter
Section 4 Review SECTION VOCABULARY gas laws the laws that state the mathematical relationships between the volume, temperature, pressure, and quantity of a gas 1. Identify How do gas particles exert pressure on their container? 2. Apply Concepts Chandra notices that her bicycle tires have higher pressure during the hot summer than during the cold winter. Which gas law explains her observation? Explain your answer. 3. Predict What would happen eventually to a balloon sitting in a sunny window? Which gas law predicts this? 4. Describe In Boyle s law, what is the relationship between pressure and volume? 5. Graph Relationships In the space below, create a graph showing the proportional relationship between temperature and pressure described by Gay-Lussac s law. Be sure to label the axes of your graph and give your graph a title. Interactive Reader 66 States of Matter