EXPERIMENT. Boyle s Law

Transcription

1 EXPERIMENT Boyle s Law Hands-On Labs, Inc. Version Review the safety materials and wear goggles when working with chemicals. Read the entire exercise before you begin. Take time to organize the materials you will need and set aside a safe work space in which to complete the exercise. Experiment Summary: You will investigate Boyle s law, the relationship between pressure and volume of a contained gas. You will use a syringe apparatus to determine the change in volume of the syringe based on pressure. You will then extrapolate the data to determine the atmospheric air pressure. 1 Hands-On Labs, Inc.

2 Learning Objectives Upon completion of this laboratory, you will be able to: Describe the relationship between pressure and volume of a contained gas. Explain Boyle s law using PV=k. Explain how data on force (m/s 2 ; N), mass (kg), and area (m 2 ) can be used to calculate pressure (N/m 2 ; Pa) in a closed system. Determine the relationship in volume of a gas sample and pressure using a syringe apparatus. Create scatter plots from experimental data to illustrate Boyle s law. Analyze data to determine the atmospheric air pressure. Calculate k from Boyle s law using experimental data. Time Allocation: 2 hours 2 Hands-On Labs, Inc.

3 Materials Student Supplied Materials Quantity Item Description 1 Bathroom scale (optional) 1 Calculator 5 Hardcover text books; approx. equal in weight 1 Optional: small marshmallow HOL Supplied Materials Quantity Item Description 1 Boyle s law apparatus 1 Metric ruler Note: To fully and accurately complete all lab exercises, you will need access to: 1. A computer to upload digital camera images. 2. Basic photo editing software, such as Microsoft Word or PowerPoint, to add labels, leader lines, or text to digital photos. 3. Subject-specific textbook or appropriate reference resources from lecture content or other suggested resources. Note: The packaging and/or materials in this LabPaq kit may differ slightly from that which is listed above. For an exact listing of materials, refer to the Contents List included in your LabPaq kit. 3 Hands-On Labs, Inc.

4 Background Boyle s Law Imagine four people in a large elevator. Most likely, these people would be standing on opposite sides of the elevator, spaced as far apart as possible. If the elevator were much smaller and the individuals had to touch elbows, they would still most likely be spaced evenly throughout the elevator. In the smaller elevator, the likelihood that they would bump into each other is much higher. This analogy is similar to gas in a closed system, though the gas particles are in constant motion. In a closed system, gas molecules are spaced apart as far as possible. When the volume of a container decreases, there is less space between particles, and more opportunities for collisions between particles and also against the sides of a container. The increased number of collisions creates the rise in pressure. See Figure 1. Figure 1. When volume of gas in a closed system decreases, the pressure of the gas in the system increases and creates more opportunities for collisions between particles and also against the sides of a container. Boyle s law describes the relationship between pressure and volume of an ideal gas, where mass and temperature are held constant. Boyle s law is written as: If the value k is a constant (the amount of gas and the temperature both remain constant), then if the volume of the container is decreased, the pressure of the gas increases. Likewise, if the volume of the container is increased, the pressure of the gas decreases. The relationship is therefore an inverse relationship between the volume and pressure. When a fixed amount of an ideal gas is kept at a constant temperature, pressure (P) and volume (V) are inversely proportional (when one increases, the other decreases). Figure 2 shows the relationship between pressure and volume. When pressure is plotted against volume, the relationship is inversely proportional, and therefore nonlinear. When volume is plotted against the inverse of pressure (1/pressure) or when pressure is plotted against the inverse of volume (1/volume), the relationship is linear. 4 Hands-On Labs, Inc.

5 Figure 2. The relationship between pressure and volume for an ideal gas. As SCUBA divers ascend from a deep underwater dive, they must remember not to hold their breath. Because the water is much heavier than air, the air that the diver breathes during a deep underwater dive is compressed, so the diver breathes more air at depth. During the ascent, the amount of water above the diver decreases, so the air pressure in their lungs decreases and volume increases. If they hold their breath while ascending, the air in their lungs expands beyond capacity, which can cause painful internal injuries. Calculating Pressure In this laboratory, you will be using an apparatus for calculating pressure. The apparatus consists of a syringe mounted between two boards, much like a piston. The syringe has a spout cap to keep gas from escaping as books are placed on the top of the apparatus, compressing the piston and applying pressure. See Figure 3. The books have a specific mass, but the pressure that will be exerted on the gas is not only based on mass, but also based on acceleration due to gravity and the surface area of the piston. 5 Hands-On Labs, Inc.

6 Figure 3. Complete setup for laboratory. Pressure (P) is a ratio of the amount of force (F) applied per a unit of area (A). In order to calculate pressure, you must know the force and the area of the applied force. If the mass of an object is known, and the mass is the only force pushing an object downward, then the force can be calculated by multiplying the mass by the acceleration of gravity. Force (F) equals mass (m) times acceleration (a). The International Standard System unit of force is the Newton (N). One Newton is equal to 1 kg m/s 2. If you know the mass of the books, then you can obtain units of force in Newtons. Multiply the mass of the books in kg times the acceleration due to gravity. The acceleration due to gravity is: Therefore, to find the force in Newtons, you find the product of the mass, in kilograms, times 9.81 m/s 2. Since it is optional to use a bathroom scale for this exercise, you may not know the mass of the books. However, by using books of similar sizes, you can measure the mass in book units rather than kg. Therefore, you will simply substitute the number of books for the mass in the equation to calculate the force. 6 Hands-On Labs, Inc.

7 To determine the area of the tip of the piston (the portion that is pressing on the gas), use the formula for calculating the surface area of a conical shape (without the base). You will measure the diameter of the piston at the base and the slant height. The slant height is measured from the tip of the cone to the side of the base. See Figure 4. The area of a conical surface is Pi (π) times the radius of the base (r) times the slant height (s): Figure 4. A. Measurements that are required for determining the surface area of a conical shape: radius, r, and slant height, s. B. Slant height is shown for the piston that is used in this laboratory. The S.I. unit for pressure is a Pascal (Pa). One Pascal is equal to one Newton per square meter (N/ m 2 ). You will have to use these calculations to determine the pressure caused by the weight of the books and the area of the plunger in this laboratory. For example (if you have a bathroom scale): if one book weighs 3 kg, and the diameter of the syringe piston is 2 cm (radius is 1 cm), and the slant height is 1.2 cm, then the pressure of the one book would be: 7 Hands-On Labs, Inc.

8 For example (if you do not have a bathroom scale): one book is 1 book unit, and the diameter of the syringe piston is 2 cm (radius is 1 cm), and the slant height is 1.2 cm, then the pressure of one book would be: 8 Hands-On Labs, Inc.

9 Exercise 1: Observing Boyle s Law In this exercise, you will increase the pressure on a gas sample confined in a syringe and observe the resulting changes in volume. While air is a mixture of gases, the air will exhibit the same behavior as a gas sample composed of a single, homogenous gas. Procedure 1. Select 5 large hardcover textbooks of roughly equal weight. 2. Optional: If a bathroom scale is available, determine the mass of each book in kilograms and record each mass in Data Table 1 of your Lab Report Assistant. 3. Calculate the total force for each number of books and record in Data Table 1. Note: The total mass for 1 book is the mass of the first book. The total mass for 2 books is the mass of the first book + the mass of the second book. If you are using book units then the mass for 1 book is 1 book unit and the total mass for 2 books is 2 book units. Part 1: Determine the Unit of Area 4. Use the metric ruler to measure the inside diameter of the syringe in millimeters (measure the inside of the rim to the inside of the rim at the widest part). See Figure 5. Record the diameter in Data Table 2 of your Lab Report Assistant. Figure 5. Measuring the diameter of the syringe from inside rim to inside rim (shown in red). 5. Convert the diameter from millimeters to meters and record in Data Table Use the diameter of the syringe (m) to determine the radius of the syringe in meters. Record the radius in Data Table Hands-On Labs, Inc.

10 7. Measure the slant height of the piston in millimeters. See Figure 6. Record the slant height in Data Table 2. Figure 6. Measuring the slant height (s) of the piston (shown in red). 8. Convert the slant height from millimeters to meters and record in Data Table Calculate the surface area of the syringe tip in meters and record in Data Table Calculate the pressure (in Pa) for each number of books by dividing the force (F) generated by the book(s) in Data Table 1, by the surface area (A) of the syringe tip as calculated in Data Table 2. Record the pressure for each number of books in Data Table 1. Note: Refer to the Background section as necessary for help with calculations. Part 2: Calculating the Volume 11. Remove the end cap of the syringe spout and pull the piston approximately to the 60-mL position. See Figure 7. Figure 7. Removing the end cap of the syringe and pulling the piston approximately to the 60- ml position Hands-On Labs, Inc.

11 12. Replace the end cap onto the syringe spout and push down on the piston with your hand slowly and steadily until the volume of the trapped gas is reduced to approximately 20 ml. 13. Release the piston and note whether it returns to the initial volume. Perform this test at least 3 more times. Note: The starting position of the piston will be where it returns consistently. The gas trapped in the syringe is at approximately the same pressure as the ambient surroundings. 14. Place the Boyle s law apparatus on a flat, steady surface, such as a sturdy table or the floor. The syringe should be pointing downward. See Figure Place one book onto the board above the piston and record the resulting gas volume in the Volume Trial 1 column and the 1 Book row in Data Table 3 of your Lab Report Assistant. Note: In order to read the volume of trapped gas, always read the measurement on the lowest portion of the piston (the part that is in contact with the gas). See Figure 8. Note: Ensure that the book is balanced. The books may tip, and it might be optimal to have a partner help to ensure that the books do not fall over as you are recording the data. Alternatively, you may want to place the apparatus near a wall to help hold the books on top. Figure 8. Boyle s law apparatus on a steady surface with books stacked on top. 16. Place a second book onto the first book, allow the books to settle on the piston, and record the resulting gas volume in Data Table Continue adding books and recording the resulting volumes until all 5 books are resting on the board. Remember to steady the books, especially when the apparatus is being read Hands-On Labs, Inc.

12 18. Remove all the books from the piston. The volume of the syringe should reset the apparatus to the initial volume. Note: If the piston does not return to the original position, gently nudge the piston until it does. 19. Repeat Steps two additional times to complete the data for a total of 3 trials. 20. Calculate the average volume (ml) for each number of books and record in Data Table Calculate the inverse volume (1/V avg ) for each of the average volumes (1/mL) and record in Data Table Use the data in Data Table 1 and Data Table 3 to create a scatter-plot graph of Average Volume vs. Pressure; with Average Volume (ml) on the x-axis and Pressure (Pa) on the y-axis. 23. Resize and insert an image of the graph into Data Table 4 of your Lab Report Assistant. Refer to the appendix entitled Resizing an image for guidance. 24. Use the data in Data Table 1 and Data Table 3 to create a scatter-plot graph of 1/Average Volume vs. Pressure; with 1/Average Volume (ml -1 ) on the x-axis and Pressure (Pa) on the y-axis. 25. Add a linear trend-line to the scatter-plot, and display the equation of the line on the graph (this is a typical function of graphing programs). 26. Resize and insert an image of the graph into Data Table Use the equation of the line to determine atmospheric pressure; As the trend-line equation is displayed as y=mx + b, b is the value where y is 0, thus the absolute value of b is roughly representative of atmospheric pressure. Record the atmospheric pressure into Data Table 5 of your Lab Report Assistant. 28. For each number of books calculate the total pressure, by adding the atmospheric pressure to the pressure values in Data Table 1. Record the total pressure for each number of books in Data Table Calculate the product of Total Pressure multiplied by the Average Volume for each number of books and record in Data Table 5. Relating this back to the information presented in the Background section, Boyle s law is written as PV = k, therefore the values calculated in this step represent the constant (k) in Boyle s law. Part 3: Optional Exercise: Remove the syringe spout cap. Take the syringe apart. Place 1 mini-marshmallow into the syringe. Replace the piston. Push the plunger down until it barely touches the marshmallow. Place the end cap onto the syringe spout. Pull the plunger and observe the marshmallow. Release the plunger and observe the marshmallow. Repeat this process several times. Remove the end cap, pull the syringe apart, and remove the marshmallow. Observe the marshmallow and record your observations. Pulling the plunger almost all of the way out of the syringe creates low pressure a partial vacuum inside the syringe Hands-On Labs, Inc.

13 Cleanup: 30. Return all items to the kit for future use. Questions: A. Describe the relationship of pressure versus the volume of a confined gas. B. Would you expect your experimental results would change if a different gas, such as CO 2, were used instead of air? Explain your answer. C. Use a reliable source to determine the atmospheric pressure at your location (atmospheric pressure at sea level is Pa and atmospheric pressure in Denver, Colorado is Pa). Use the equation below to calculate the percent difference between your experimental value for atmospheric pressure and the theoretical value (actual atmospheric pressure). Show all work. What are some possible sources of errors in your experiment? D. As stated by Boyle s law, the products PV should equal a constant, k. Did your results of P t V avg come out approximately the same for k? 13 Hands-On Labs, Inc.