Activity 4 Hot-Air Balloons [Catch art: xxxxxxxxxxxxxxxxxx] GOALS In this activity you will: Investigate the relationship between temperature and volume of a gas. Understand why the Kelvin scale is used for temperature relationships. Apply Charles s Law to launch a hot-air balloon. Safety goggles and a lab apron must be worn at all times in a chemistry lab. What Do You Think? A young child takes a helium-filled balloon outside the store on a cold, wintry day and the balloon seems to deflate. How might a decrease in temperature affect an inflated balloon? Record your ideas about this question in your log. Be prepared to discuss your responses with your small group and the class. Investigate In this activity, you will explore the effects of temperature on a gas s volume under constant pressure. You will then invent a toy that can be based on this relationship. Part A: Volume and Temperature of a Gas 1. Completely fill an empty pipette with water. 2. Count and record the number of drops it takes to empty the pipette. a) This number represents the volume of the pipette. It also represents the volume of gas at room temperature in the empty pipette in this activity. Record this as the volume of the empty pipette. 3. Half-fill a 600 ml-beaker with H 2 O (approximately 20ºC). 379
Ideal Toy 4. Half-fill a second 600 ml-beaker with water and place it on a hot plate. Place a thermometer in the beaker. Do not allow the thermometer to rest on the bottom of the beaker. Do not turn the hot plate on until the entire setup is ready to go. (Your teacher may supply you with pre-heated water instead of the hot plate.) 5. Turn the hot plate on and begin heating. Continue heating until the water reaches the temperature assigned to your group by your teacher. 6. Use tongs to hold the bulb of the pipette under water in the beaker being heated. The stem of the pipette should be above the water level. Keep the pipette immersed for 2 minutes. After 2 minutes, squeeze and seal the tip of the pipette with tweezers. Then lift the pipette out of the water. 250 ml 200 ml 150 ml 100 ml 50 ml This traps the hot air in the pipette. Quickly transfer the pipette to your room temperature water bath and, removing the tweezers, completely submerge the pipette bulb and stem. Hold it in place with your tongs. 7. Notice that water is entering the pipette. Keep the pipette submerged until no further changes are noted (about 1 minute). 8. Remove the pipette from the water and dry the outside. Count the number of drops of water that were drawn into the pipette. This number allows you to calculate the volume of the air in the pipette when the pipette is at room temperature (20ºC). Subtracting the number of drops of water from the total volume of the pipette (found in Step 2) gives you the volume of the air at 20ºC. a) Complete this calculation and record the volume of the 20ºC air in the pipette in your log. b) When the hot air in the pipette cooled in the room temperature (20ºC) water, it took up less space and water got sucked into the pipette. Write a statement summarizing this observation using the terms temperature and volume. 9. Repeat these measurements three times. a) Calculate and record the average. b) Your class will now share the data and complete the first three columns of the following data chart: 380
Activity 4 Hot-Air Balloons Temperature of hot air (equal to the temperature of the heated water bath) Volume of hot air (equal to the total volume of the pipette from Step 2) Volume of room temperature 20ºC air Ratio of volumes (hot air to room temperature 20ºC air) Volume of hot air corresponding to 100 drops of room temperature 20ºC air c) What is the relationship between the volume of hot air and the volume of room temperature 20ºC air for different temperatures of hot air? d) It would be very helpful to compare the volume of hot air if each group had an identical amount of room temperature 20ºC air. This is not possible with one size pipette and your procedure. However, a bit of math can help you. You can calculate what the volume of hot air would have been for any volume of room temperature 20ºC air. For example, if your volume of hot air was 200 drops and your volume of room temperature 20ºC air were 80 drops, you can see that the volume of hot air is 200/80 or 2.5 times larger than the volume of room temperature air. Calculate the ratio of your hot air to room temperature 20ºC air and place this in the class data chart. e) Use the ratio to calculate what the volume of hot air would be if the volume of room temperature 20ºC air was 100 drops. Record this in the class data chart. 10. Prepare a graph of your class data, with temperature (in degrees Celsius) on the horizontal axis (x-axis) and the volume of hot air corresponding to 100 drops of room temperature 20ºC air on the vertical axis (y-axis). Although your temperature data goes from 0ºC to 100ºC, the x-axis should be numbered from 350ºC to 150ºC for reasons that will be clear soon. Draw the line with the best fit through all the data points. Answer the following questions in your log: a) What is the relationship between the volume and the Celsius temperature as shown on your graph? b) Based on the graph, at what temperature would the volume be zero? What would a zero volume look like? c) Your temperature estimate was probably close to 273ºC. If you created a new temperature scale where the volume becomes zero at a temperature of zero, what would 0ºC be on this new scale? This presumes that both temperature scales have the same scale units. 381
Ideal Toy Be careful not to let the plastic touch the hot plate. 11. You are now going to graph your class data on the Kelvin temperature scale where the lowest possible temperature is 0 K (called absolute zero). To do so, you need to add 273 to your Celsius temperatures. K ºC 273 a) Set up a graph in your Active Chemistry log with volume on the y-axis and temperature (in K) on the x-axis from 0 to 400 K. Draw the line with the best fit for the class data points. b) Determine the slope of the line, making sure to include the units on the slope value. The slope intercept equation of a straight line is: y mx b, where b is the y-intercept and m is the slope. You can use this form of the equation to calculate the slope: m y x y b x 0 y b x c) In your graph, the y-values are volume and the x-values are temperature. Using the Kelvin scale, the y-intercept or b in the equation is 0. The equation for your straight line is V mt. This relationship is identical to the one expressed in Charles s Law. Part B: Hot-Air Balloon Challenge In this part of the investigation, you will apply your understanding of the relationship between temperature and volume by constructing a hot-air balloon, and competing to find the balloon that can lift the most mass. 1. For your first trial with a hot-air balloon, use a plastic dry-cleaning bag or a light-weight trash bag. Place about 12 regular sized paper clips, evenly spaced, around the opening of the bag. This added weight will help to maintain stability in the hot-air balloon. 2. As shown in the picture, use at least three people to hold the bag over a hot plate turned to High. Be careful not to let the bag touch the hot surface of the hot plate. 3. Within a minute or two, you can release the hot-air balloon and it will drift slowly to the ceiling. a) In your log, use the change in air volume with respect to temperature to explain how your hot-air balloon worked. 4. You can experiment with more weight, taping the holes in the dry cleaning bag, or a variety of other options. Use your imagination! a) What variables do you think will affect the performance of your hot-air balloon? 5. If your teacher permits a competition in lifting power between groups, design a balloon that you think will win. After your teacher s approval, build your hot-air balloon and let the event begin! 382
Activity 4 Hot-Air Balloons CHARLES S LAW Charles s Experiment Was Similar to Boyle s In France, in the early 1800s, there were many advances made in the understanding of gases and their behavior. Hot-air balloons were becoming popular at that time and scientists were challenged to improve the performance of these balloons. A French scientist, Jacques Charles, made many observations and measurements on how the volume of a gas was affected by changes in temperature. Charles discovered that a quantity of gas kept at a constant pressure expands as it warms and contracts as it cools. The equipment used by Charles was very similar to that employed by Boyle. A quantity of gas was trapped in a glass tube that was sealed at one end. This tube was immersed in a water bath. By changing the temperature of the water, Charles was able to observe the change in volume of the gas. The pressure was held constant by adjusting the height of mercury so that the two columns of mercury had equal height, and so the pressure was always equal to the atmospheric pressure. This allowed Charles to examine the effect of only one variable, temperature, on the volume of a gas. Through repeated experimentation with many different gases, Charles found that there was a relationship between the volume of a gas and the temperature of that gas. Your class s graph from the activity demonstrated this direct relationship. Relationship between the Temperature and the Volume of a Gas Charles s Law states: the volume of a gas varies directly with the temperature (measured in kelvins) for a given amount of gas at a constant pressure. volume a constant temperature volume temperature a constant Expressed mathematically: V kt or V T k, where k is a constant Jacques Charles Chem Words Charles s Law: a gas law that states that for a given amount of gas at a constant pressure, the volume of the gas varies directly with the temperature. V kt 383
Ideal Toy Chem Words absolute zero: a theoretical temperature at which molecular motion is minimal. 0 K, or 273ºC You can compare the volumes of the same gas at two different temperatures: V 1 T1 V 2 T2 Kinetic Theory of Matter and Charles s Law A mass weighing 10 N (newtons), approximately 2 lb, is supported by a column of air in a piston. The air must be supplying a force of 10 N to keep the mass from falling down. When the air is heated to a higher temperature, the mass rises due to the increase in volume of the air. The piston stops moving when once again, the air is supplying a force of 10 N to keep the mass from falling. The Kinetic Theory of Matter provides a way to understand this relationship between the temperature and the volume of a gas at the nanoscopic or molecular level. The particles of a gas are moving about with a range of speeds and corresponding kinetic energy. These particles can collide with the walls and the moveable piston. These collisions create the pressure, or force per area, on the piston. The particles hit the piston so that the average force on the piston is 10 N. When you increase the temperature of the air, you are increasing the speed and kinetic energy of the air molecules. These molecules hit the piston more often and with a greater force. If the average increased force is 12 N, then the mass will move up. When the piston moves up, it increases the volume. As the volume increases, these energetic air particles don t hit the piston as often because of the extra distance they must travel. The average force of the energetic particles once again becomes 10 N and the piston remains in its elevated position. When the air cools, the particles have a decrease in their kinetic energies. They hit the piston less often and the average force is now less than 10 N and the mass descends again. Absolute Zero and the Kelvin Temperature Scale If a decrease in temperature results in a decrease in volume, what happens if the temperature is lowered to a point where the volume drops to zero? A negative volume is impossible, so the temperature at which the volume drops to zero must be the lowest temperature that can be achieved. This temperature is called absolute zero. Absolute zero is the lowest possible temperature. It is 0 K, or 273ºC. Whenever determining the effect of a temperature change on the volume of a gas, you must first convert from the 384
Activity 4 Hot-Air Balloons Celsius temperature to the Kelvin temperature. You do this by adding 273 to the Celsius temperature. Applying Charles s Law K ºC 273 The mass of your plastic hot-air balloon is the mass of the plastic plus the mass of the air. To get the balloon to fly, you have to decrease the mass of the air in the balloon. In the hot-air balloon activity that you conducted, you found that the hot air takes up more volume than the cool air. Filling your plastic balloon required less hot air than cool air. With less air in the balloon, the balloon had a smaller total mass and it could fly. Example: A balloon is in a room at 25ºC. The volume of the balloon is 2.0 L. Suppose that the balloon is taken outside at a temperature of 5ºC. What will be the new volume of the balloon? Charles s Law lets you predict what the volume of the balloon will be. V 1 T1 V 2 T2 V 1 2.0 L V 2? T 1 25ºC (298 K) T 2 5ºC (268 K) Notice that temperature in kelvin must be used to solve problems with Charles s Law. Rearrange Charles s Law equation to solve for V 2. V 2 V 1 T 2 T 1 2.0 L (268 K) 298 K 1.8 L Checking Up 1. What is the relationship between the temperature and the pressure of a gas? 2. What is absolute zero on the Kelvin and Celsius temperature scale? 3. What problems would you encounter in your calculations if you did not convert the Celsius temperature to the Kelvin scale? 4. How might the temperature in the gym affect the volume of a basketball and thus its bounce? 5. Determine the effect on the volume of a basketball if the initial volume is 6.4 L at 20ºC and the ball is taken outside to a temperature of 27ºC. What Do You Think Now? At the beginning of this activity you were asked: How might a decrease in temperature affect an inflated balloon? Now that you have investigated Charles s Law, how would you answer this question? How would an increase in temperature affect the balloon? 385
Ideal Toy What does it mean? Chemistry explains a macroscopic phenomenon (what you observe) with a description of what happens at the nanoscopic level (atoms and molecules) using symbolic structures as a way to communicate. Complete the chart below in your log. MACRO NANO SYMBOLIC What variables were you measuring during the investigation? What variables did you assume would remain constant? Describe what happens with the particles of a gas when you heat it up while holding the pressure constant. What equation can express the relationship between the volume of a gas as the temperature of the gas changes? How do you know? Does a change in temperature have a predictable effect on the volume of a gas? Use your data to support your answer. Why must the pressure be held constant to make this prediction? Why do you believe? On a very cold day, you notice that your bicycle tires appear under-inflated. You add air to the tires to fully inflate them. Why is there a danger of the tires bursting if you ride long distances and the tires warm up? Why should you care? You are expected to utilize several chemical principles to develop an exciting new toy to market. How could you use your knowledge of the effects of temperature on a gas s volume in your proposed toy? Reflecting on the Activity and the Challenge In this activity, you determined the relationship between temperature and volume in a gas. The volume of a gas is proportional to temperature (Charles s Law). This relationship is represented by the Charles s Law equation. You then applied that understanding by launching a hot-air balloon. Consider all the examples of this relationship you encounter every day hot air rising in a room, the effect of temperature on inflated tires, and wind patterns, to name a few. You might be able to use this relationship in your proposal for a toy and for your presentation. 386
Activity 4 Hot-Air Balloons 1. If you could install only one thermostat in a two-story toy factory, should it be placed on the first or second floor? Explain. 2. Predict the effect of hot temperatures on car tires. Will they appear fuller or flatter? Predict the effect of cold temperatures on car tires. How will their appearance change? Explain your answer. 3. Why must the temperature measurements used in Charles s Law be in kelvin? Show an example that supports your reasoning. 4. Using Charles s Law, what would the volume of a gas be if 2.8 L at 25ºC were heated to 75ºC? 5. If 5.5 L of a gas at 78ºC were cooled to 25ºC, what would the resulting volume be? 6. To what temperature would you need to heat 750 ml of a gas at 25ºC in order to increase its volume to 2500 ml? 7. In a hot-air balloon, the balloonist may have to light the propane torch for a few minutes. Using Charles s Law, explain why he might need to do this. 8. As the temperature of a given sample of gas decreases at constant pressure, the volume of the gas: a) decreases b) increases c) remains the same 9. Preparing for the Chapter Challenge Think of a toy or a sporting goods product that uses or is affected by the relationship between volume and temperature. Explain how Charles s Law is applied and how temperature changes in the environment could affect the product. Brainstorm ways the designer could minimize the effect of temperature on this product. Inquiring Further 1. The motorists guide to temperature and volume Write a short, practical guide for motorists explaining changes in their automobile tire volume during different seasons. Provide them with tips on how to prolong the life of their tires by keeping them properly inflated. Explain to them why these changes in volume occur. Your article could be publishable as consumer help for your local paper. 2. Balloon storage The prom committee has decided to use lots of balloons in this year s décor. Write a memo to the committee suggesting how the inflated balloons should be stored in order to minimize deflation prior to the prom. They re a hard committee to convince, so back up your suggestions with calculations. 387