States of Matter The Behavior of Gases What do you think? Read the two statements below and decide whether you agree or disagree with them. Place an A in the Before column if you agree with the statement or a D if you disagree. After you ve read this lesson, reread the statements to see if you have changed your mind. Before Statement After 5. Changes in temperature and pressure affect gas behavior. 6. If the pressure on a gas increases, the volume of the gas also increases. Key Concepts How does the kinetic molecular theory describe the behavior of a gas? How are temperature, pressure, and volume related in Boyle s law? How is Boyle s law different from Charles s law? Understanding Gas Behavior Pilots do not worry as much about solids and liquids at high altitudes as they do gases. That is because gases behave differently than solids and liquids. Changes in temperature, pressure, and volume affect the behavior of gases more than they affect the behavior of solids and liquids. In the previous two lessons, you learned about how the particles of matter in different states behave how they are arranged, how they move, how forces affect them, and how changes in energy affect them. The explanation of particle behavior in solids, liquids, and gases is based on the kinetic molecular theory. The kinetic molecular theory is an explanation of how particles in matter behave. Some basic ideas in this theory are small particles make up all matter; these particles are in constant, random motion; the particles collide with other particles, other objects, and the walls of their container; when particles collide, no energy is lost. Make an outline as you read to summarize the information in the lesson. Use the main headings in the lesson as the main headings in your outline. Use your outline to review the lesson. ACADEMIC VOCABULARY theory (noun) an explanation of things or events that is based on knowledge gained from many observations and investigations 1. Explain How does the kinetic molecular theory describe the behavior of a gas? You read about most of these when you learned about all three states of matter. However, the last two statements are important in explaining how gases behave. Reading Essentials States of Matter 109
Greatest volume, least pressure 10 g Pressure Increases as Volume Decreases Less volume, more pressure Least volume, most pressure 20 g 50 g 2. Confirm that the number of gas particles is the same in each cylinder by counting them and writing the number below each one. Fold a sheet of notebook paper to make a three-tab Foldable to compare two important gas laws. Boyle s Law Both Charles s Law What is pressure? Particles in gases are always moving. As a result of this movement, gas particles are always bumping into other particles and into their container. When particles collide with their container, pressure results. Pressure is the amount of force applied per unit of area. For example, a cylinder like the one shown in the figure above might hold trillions of gas particles. These particles exert forces on the cylinder each time they hit it. These forces make up the pressure exerted by the gas. The figure above shows that gases are compressible, which means they can be squeezed into a smaller volume. When the plunger moves down because of the weight on it, the space between gas particles decreases. The gas is compressed. The empty spaces between particles make gases compressible. Pressure and Volume The figure above also shows the relationship between pressure and volume of gas at a constant temperature. Notice that when the volume is greater, as in the cylinder on the left, the particles have more room to move. This bigger space results in fewer collisions within the cylinder. There is less pressure. The gas particles in the middle cylinder have less volume and more pressure. In the cylinder on the right, the pressure is greatest because the particles have the least volume. The particles collide within the container more often and the pressure is greater. 110 States of Matter Reading Essentials
Boyle s Law You read that the pressure and volume of a gas are related. Robert Boyle (1627 1691), a British scientist, was the first to describe this property of gases. Boyle s law states that pressure of a gas increases if the volume decreases and pressure of a gas decreases if the volume increases, when temperature is constant. This law can be expressed mathematically as shown in Math Skills in the margin on the right. Boyle s Law in Action You have probably felt Boyle s law in action if you have ever traveled in an airplane. While on the ground, the air pressure inside your middle ear and the pressure of the air surrounding you are equal. As the airplane takes off and rises quickly, the air pressure of the air in the plane decreases. However, the air pressure inside your middle ear stays the same. Because the air pressure in your middle ear is greater than the pressure in the cabin, air in your middle ear increases in volume. The pressure on your eardrum can cause pain. These pressure changes also occur as the plane is landing. During the flight, the pressure in your ears will have equalized with the cabin pressure. The cabin air pressure increases as the plane descends while the pressure in your middle ear remains the same. This can cause pain. You can equalize this pressure difference by yawning or chewing gum. Graphing Boyle s Law The graph below shows that as pressure increases, volume decreases when gas is at a constant temperature. Pressure is on the x-axis. Volume is on the y-axis. Notice that the line is a curve that decreases in value. As pressure increases along the x-axis, the volume decreases along the y-axis. Volume (L) 600 500 400 300 200 100 0 Volume v. Pressure for a Fixed Amount of Gas at Constant Temperature 50 100 150 200 250 300 350 Pressure (kpa) 400 450 500 3. Relate What is the relationship between pressure and volume of a gas if temperature is constant? Math Skills Boyle s law can be stated by the equation = P V 1 1 P 2 P 1 and V 1 represent the pressure and volume before a change. P 2 and are the pressure and volume after a change. Pressure is often measured in kilopascals (kpa). What is the final volume of a gas with an initial volume of 50.0 ml if the pressure increases from 600.0 kpa to 900.0 kpa? a. Replace the terms in the equation with the values. (600.0 kpa) (50.0 ml) = (900.0 kpa) b. Cancel units, multiply, and then divide. = (600.0 kpa) (50.0 ml) (900.0 kpa) = 33.3 ml 4. Solve Equations What is the final volume of a gas with an initial volume of 100.0 ml if the pressure decreases from 500.0 kpa to 250.0 kpa? 5. Label the left and right sides of the graph as showing low or high pressure and large or small volume. Reading Essentials States of Matter 111
Higher temperature, greater volume Lower temperature, less volume 6. Illustrate Draw an ice cube or a snowflake next to the cylinder that is cooler. Draw a sun or a flame next to the cylinder that is warmer. 7. Apply Would the gases in car tires increase or decrease in volume on a hot day? 8. Contrast How is Boyle s law different from Charles s law? Temperature and Volume Pressure and volume changes are not the only factors that affect gas behavior. Changing the temperature of a gas also affects its behavior. The figure above shows two pictures of the same cylinder holding the same amount of gas. The picture on the left shows the gas in the cylinder at a low temperature. The average kinetic energy of the particles is low, and the particles move close together. The volume is small. When thermal energy is added to the cylinder, as shown in the picture on the right, the gas particles move faster and spread farther apart. The temperature of the gas increases, which means the kinetic energy of its particles increases. The particles hit the cylinder more often. This pressure pushes up the plunger. The volume of the gas in the container is greater. Charles s Law Jacque Charles (1746 1823) was a French scientist who described the relationship between temperature and volume of a gas. Charles s law states that the volume of a gas increases with increasing temperature, if the pressure is constant. Charles was interested in balloons. Charles and his colleague were the first to pilot and fly a hydrogen-filled balloon in 1783. Because of this interest, Charles observed the behavior of gases and had practical experience with them. 112 States of Matter Reading Essentials
Charles s Law in Action You have probably seen Charles s law in action if you have ever taken a balloon outside on a cold winter day. Why does a balloon seem to have less air in it when you take it from a warm place to a cold place? In fact, no air escapes from the balloon. When the balloon is in cold air, the temperature of the gas inside the balloon decreases. Recall that a decrease in temperature is a decrease in the average kinetic energy of particles. As a result, the gas particles slow down. They begin to get closer together. Fewer particles hit the inside of the balloon. The balloon seems to be only partway filled. If the balloon is returned to a warm place, the kinetic energy of the particles increases. More particles hit the inside of the balloon and push it out. The volume of the gas increases. Graphing Charles s Law The relationship described in Charles s law is shown in the graph of several gases below. Temperature is on the x-axis. Volume is on the y-axis. The lines are straight. They slant upward, which means the values increase. The graph shows that the volume of a gas increases as the temperature of the gas increases at constant pressure. Notice that each line in the graph is extrapolated to the same temperature: -273 C. (Extrapolated means the graph is extended beyond the data points that scientists have observed in the lab.) This temperature (-273 C) is referred to as 0 K (kelvin), or absolute zero. It is theoretically the lowest possible temperature that matter can have. At absolute zero, all particles have the lowest possible energy they can have. They d o not move at all. The particles contain a minimal amount of thermal energy (potential energy + kinetic energy). Volume (L) 100 80 60 40 20 Extrapolation Temperature and Volume Temperature v. Volume for a Fixed Amount of Gas at Constant Pressure Reading Check 9. Predict What happens when you warm a balloon? 10. Analyze Which factors must be constant in Boyle s law and in Charles s law? 11. Interpret What do the dashed lines mean? Gas A Gas B Gas C -273-200 -100 0 100 200 300 Temperature ( C) Reading Essentials States of Matter 113
Mini Glossary Boyle s law: states that pressure of a gas increases if the volume decreases and pressure of a gas decreases if the volume increases, when temperature is constant Charles s law: states that the volume of a gas increases with increasing temperature, if the pressure is constant kinetic molecular theory: an explanation of how particles in matter behave pressure: the amount of force applied per unit of area 1. Review the terms and their definitions in the Mini Glossary. Write a sentence that explains how the particles of a gas produce pressure. 2. Use what you have learned about Boyle s law and Charles s law to complete the table. Boyle s Law Charles s Law When as pressure of a gas increases, is constant, as pressure of a gas decreases, When is constant, as temperature of a gas increases, volume 3. How did your outline of the lesson help you better understand the main ideas? What do you think Reread the statements at the beginning of the lesson. Fill in the After column with an A if you agree with the statement or a D if you disagree. Did you change your mind? volume ConnectED Log on to ConnectED.mcgraw-hill.com and access your textbook to find this lesson s resources. volume END OF LESSON 114 States of Matter Reading Essentials