CBL Lab GAS PRESSURE & VOLUME MATHEMATICS CURRICULUM. High School. Florida Sunshine State Mathematics Standards

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1 MATHEMATICS CURRICULUM High School CBL Lab Florida Sunshine State Mathematics Standards GAS PRESSURE & VOLUME John Klimek, Math Coordinator Curt Witthoff, Math/Science Specialist Dr. Benjamin Marlin Superintendent of Schools

2 Gas Pressure and Volume Gas Pressure and Volume (for the Ti-83) In this simple experiment, you will use a Gas Pressure Sensor and a gas syringe to study the relationship between gas pressure and volume. Temperature and amount of gas will be kept constant. The results will be expressed in words, in a table, with a graph, and with a mathematical equation. These are four methods commonly used by scientists to communicate information. This experiment is similar to one first done by Robert Boyle in 1662 without the use of a calculator, of course. The relationship you will discover is known as Boyle s law. OBJECTIVES In this experiment, you will use a TI Graphing Calculator, a LabPro, a Gas Pressure Sensor, and a gas syringe to measure the pressure of an air sample at several different volumes make a table of the results make a graph of the data predict the pressure at other volumes describe the relationship between gas pressure and volume with words and with a mathematical equation MATERIALS LabPro TI Graphing Calculator DataMate software Vernier Gas Pressure Sensor 20-mL gas syringe Figure 1 Physical Math & Science with Calculators 30-1

3 PROCEDURE Experiment Prepare the Pressure Sensor and an air sample for data collection. a. Plug the Gas Pressure Sensor into Channel 1 of the LabPro. b. A 20-mL syringe is already connected to the sensor and set at the 10-mL mark for you. 2. Turn on the calculator and use steps a-d, to start the DATAMATE software. a. Press APPS. b. Scroll down to the APP labeled DATAMIN1. c. Press ENTER. d. Press CLEAR to reset the software. 3. Set up the calculator and interface for a Gas Pressure Sensor Sensor. a. Select SETUP (# 1) from the main screen. b. Does the calculator display GAS PRESSURE (kpa) in CH 1? YES Go to Step 4. NO Complete parts 3c, 3d, 3e & 3f. c. Press ENTER to select CH 1. d. Select PRESSURE (# 4) from the SELECT SENSOR menu. e. Select the GAS PRESSURE SENSOR (# 1) from the PRESSURE menu. f. Select GAS PRESSURE (kpa) (# 1) for units. 4. Set up the data-collection mode. a. To select MODE, press once and press ENTER. b. Select EVENTS WITH ENTRY (# 3) from the SELECT MODE menu. c. Select OK (# 1) to return to the main screen. Physical Math & Science with Calculators 30-2

4 Gas Pressure and Volume 5. You are now ready to collect pressure and volume data. It is best for one person to take care of the gas syringe and for another to operate the calculator. a. Select START (# 2) to begin data collection. b. Move the piston so the front edge of the inside black ring (see Figure 2) is positioned at the 5.0-mL line on the syringe. Hold the piston firmly in this position until the pressure value displayed on the calculator screen stabilizes. c. Press ENTER and type in 5, the gas volume (in ml) on the calculator. Press ENTER to store this pressure-volume data pair. Figure 2 d. To collect another data pair, move the syringe to 7.5 ml. When the pressure reading stabilizes, press ENTER and type 7.5 as the volume. e. Continue with this procedure using volumes of 10.0mL, 12.5mL, 15.0mL, 17.5mL, and 20.0 ml. f. Press STO when you have finished collecting data. 6. Examine the data pairs on the displayed graph. As you move the cursor right or left, the volume (X) and pressure (Y) values of each data point are displayed below the graph. Record the pressure (round to the nearest 0.1 kpa) and volume data values in your data table. Press ENTER when finished. 7. Select QUIT (# 6). Press ENTER. 8. Sketch or print a graph of pressure vs. volume. Physical Math & Science with Calculators 30-3

5 DATA TABLE Experiment 30 Volume (ml) Pressure (kpa) SKETCH YOUR RESULTS: Sketch the results of one of your trials. Include labels for the X axis and Y axis including the correct units. Scale the graph properly. Title Axis Label (units) Axis Label (units) Physical Math & Science with Calculators 30-4

6 PROCESSING THE DATA Gas Pressure and Volume 1. See the data table and note the pressure when the volume is 10.0 ml, and when the volume is 5.0 ml. What happened to pressure when the volume was halved? 2. See the data table and note the pressure when the volume is 20.0 ml. Compare this pressure to the pressure when the volume is 10.0 ml. What happened to the pressure when the volume was doubled? 3. From your data and graph, what is the pressure when the volume is 16 ml? 8 ml? How do these values compare? 4. What would the pressure be at 40.0 ml? At 2.5 ml? Explain how you determined these values. Physical Math & Science with Calculators 30-5

7 Gas Pressure and Volume 5. What is the relationship between gas pressure and volume (Boyle s law) in words? 6. Direct variation definition: when X increases then Y increases. Inverse variation definition: when X increases then Y decreases. Do gas pressure and volume vary directly or inversely? Explain. 7. Boyle s Law states: P = K, use your data table to find K. V 8. Use your results from question # 7 to check your answers in question # 3. Physical Math & Science with Calculators 30-6

8 Gas Pressure and Volume EXTENSIONS 1. Repeat the experiment using a pure, noncorrosive gas, such as oxygen, butane, or carbon dioxide. Compare the results with your results for air. 2. Plot P versus 1/V and discuss the graph. You can do this using graph paper, the TI Graphing Calculator and TI-Graph Link, or Vernier Graphical Analysis. Physical Math & Science with Calculators 30-7