Chemistry Unit 6:States of Matter & Basic Gas Laws Name Lab Partner Lab #12:Boyle s Law, Dec. 20, 2016 Pressure-Volume Relationship in Gases Purpose: The primary objective of this experiment is to determine the relationship between the pressure and volume of a confined gas. The gas we use will be air, and it will be confined in a syringe connected to a pressure sensor (see Figure 1). When the volume of the syringe is changed by moving the piston, a change occurs in the pressure exerted by the confined gas. This pressure change will be monitored using a pressure sensor connected to a CBL. It is assumed that temperature will be constant throughout the experiment. Pressure and volume data pairs will be collected during this experiment and then analyzed. From the data and graph, you should be able to determine what kind of mathematical relationship exists between the pressure and volume of the confined gas. You should be able to calculate the PV product constant (k) for your gas sample, both graphically and for each individual trial. Historically, this relationship was first established by Robert Boyle in 1662 and has since been known as Boyle s law. Materials CBL System TI Graphing Calculator Vernier Pressure Sensor Vernier adapter cable 20-mL gas syringe TI-Graph Link Pressure Sensor or Figure 1 Procedure 1. Prepare the Pressure Sensor and an air sample for data collection. a. Plug the Pressure Sensor into one of the channels on the LabQuest. Firmly press in the cable ends. 1
b. With the 20-mL syringe disconnected from the Pressure Sensor, move the piston of the syringe until the front edge of the inside black ring (indicated by the arrow in Figure 1, see above) is positioned at the 10.0 ml mark. c. Attach the 20-mL syringe to the valve of the Pressure. Newer Vernier Gas Pressure Sensors have a white stem protruding from the end of the sensor box screw the syringe directly to the white stem with a gentle half-turn. Older Vernier Pressure Sensors have a 3-way valve at the end of a plastic tube leading from the sensor box. Before attaching the 20- ml syringe, align the blue handle with the stem of the 3-way valve that will not have the syringe connected to it, as shown in the figure at the right this will close this stem. Then screw the syringe directly to the remaining open stem of the 3-way valve. 2. Turn on the LabQuest. 3. Select Sensor from the top of the screen. a. Select sensor setup. Using the drop down arrow on channel 1 select pressure sensor, then select gas pressure sensor. b. Select kpa for the corresponding units from the drop down arrow off to the right. c. Select OK in the bottom right corner. 4. Set up the data-collection mode. a. To select MODE from the right side of the screen. b. Select EVENTS WITH ENTRY. c. Enter the Event Name (Volume) and Units (ml), then select OK. 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 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. Tap Keep and enter 5 as the gas volume (in ml) on the calculator. Select OK to store this pressurevolume data pair. Figure 2 2
d. Continue with this procedure using volumes of 7.5, 10.0, 12.5, 15.0, 17.5, and 20.0 ml. e. Stop data collection. 6. To examine the graph of pressure vs. volume, tap any data point. The pressure and volume values for that data pair will be displayed to the right of the graph. Record the pressure and volume values for your data. At this point you may also go to the table and write down your data. Then using a TI-83 enter your data into list 1 and list 2. 7. Draw a graph representing Pressure vs. Volume, this is graph 1. On the TI-83 use power regression to find the line of best fit. This uses the following y = ax^b where x is volume, y is pressure, a is a proportionality constant, and b is the exponent of x (volume) in this equation. On graph #1 make certain to state the equation of your line, your corresponding R value, and label two places on the line of best fit (think about sigs). 8. Draw a graph representing Pressure vs. Inverse Volume, this is graph 2. On the TI-83 use linear regression to find the line of best fit. On graph #2 make certain to state the equation of your line, your corresponding R value, and label two places on the line of best fit (think about sigs). On the graph publish your slope value and y-intercept value with units. Data/Calculations: Data Calculated Values Volume ( ) Pressure ( ) Constant, k Inverse Volume ( ) ( ) Average k value = 3
Graph #1: ** Label two points on the line (x,y). R 2 = Equation of the line = Graph #2: ** Label two points on the line (x,y). R 2 = m = b = 4
Processing the Data: 1. Label Graph #1 correctly and sketch in the result of the power regression you created of volume versus pressure. The independent variable is the volume, the dependent variable is the pressure. State your R 2 value on Graph 1, this is your correlation coefficient. The close R 2 is to 1 or -1 the better your data fits your predicted line of best fit. 2. To confirm that an inverse relationship exists between pressure and volume, a graph of pressure vs. reciprocal of volume (1/volume or volume -1 ) should be plotted on Graph #2. To do this using your calculator, it is necessary to create a new data list, reciprocal of volume, based on your original volume data. First, press ENTER to return to the MAIN MENU and select QUIT. Then follow this procedure for your calculator: To view the lists, press STAT to display the EDIT menu and then select Edit. Move the cursor up and to the right until the L3 heading is highlighted. Create a list of 1/volume values in L3 by pressing 2nd [L1] x 1 ENTER. L1 is volume, L 2 is pressure, and L3 is 1/volume. 3. Once you have L2 (pressure) and L3 (inverse volume) follow the normal steps for creating a line graph using linear regression between these two variables. 4. Label Graph #2 correctly, use a ruler and draw in a straight line. Use the trace feature on your graph and label two points (x,y). The independent variable is the inverse volume, the dependent variable is the pressure. Discussion Questions: 1. If the volume is doubled from 5.0 ml to 10.0 ml, what does your data show happened to the pressure? State your experimental pressure values in your answer and what it should be theoretically (assuming that the 5.0mL pressure value is accurate). Explain how you know what the theoretical should be. 5
2. From your answer to the first question and the shape of the curve in the plot of pressure versus volume, do you think the relationship between the pressure and volume of a confined gas is direct or inverse? Explain your answer. 3. What experimental factors (variables) are assumed to be constant in this experiment? 4. How constant were the values for k you obtained for each trial (on the data table)? Good data may show some minor variation, but the values for k should be relatively constant. State the range of your k values and the average k value. Compare these k values to the slope of graph #2. 6
5. What was your y-intercept for Graph #2. What does this y-intercept represent (in relation to the two variables)? What should the value of the y-intercept really be? Explain. 6. A balloon with a volume of 2.00 L is filled with a gas at 3.20 atmospheres. If the pressure is reduced to 0.550 atmospheres without a change in temperature, what would be the volume of the balloon? Law? 7. A 600.0 ml sample of nitrogen is heated from 27.88 C to 77.25 C at constant pressure. What is the final volume? Law? 7
8. A 6.33 L sample at 25.50 C and 2.00 atm of pressure contains 0.5723 moles of a gas. If an additional 0.255 moles of gas at the same pressure and temperature are added, what is the final total volume of the gas? Law? Conclusion: State Boyle s law. State both of your k values, use the average k value to represent your data table. Explain how the k value from your data table and the slope of graph two compare and how these values relate to Boyle s law. 8