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5A. BOYLE’S LAW: PRESSURE-VOLUME RELATIONSHIP IN GASESMany important scientific studies have been carried out on the behavior of gases. Some of theimportant properties of gases include pressure, volume, temperature, and amount (moles). In the firstexperiment, you investigated the relationship between the pressure of a gas (air) in a bottle and themass of the gas sample using graphical methods. The mathematical relationship between any two ofthese variables may be examined while the values of the other two are held constant.The primary objective of this experiment is to determine the relationship between the pressure andvolume of a confined gas. The gas we use will be air, and it will be confined in a syringe connected to aPressure Sensor (see Figure 1). When the volume of the syringe is changed by moving the piston, achange occurs in the pressure exerted by the confined gas. This pressure change will be monitoredusing a Pressure Sensor. 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 thedata and graph, you should be able to determine what kind of mathematical relationship exists betweenthe pressure and volume of the confined gas. Historically, this relationship was first established byRobert Boyle in 1662 and has since been known as Boyle’s law. Figure 1. Syringe attached to Pressure SensorMATERIALSWindows PC Vernier Gas Pressure SensorVernier computer interface 20-mL gas syringeLoggerPro softwarePROCEDURE1. Prepare the Pressure Sensor and an air sample for data collection.a. Plug the Pressure Sensor into Channel 1 of the computer interface. b. With the 20-mL syringe disconnected from the Pressure Sensor, move the piston of the syringeuntil the front edge of the inside black ring (indicated by the arrow in Figure 1) is positioned atthe 10.0 mL mark.c. Attach the 20-mL syringe to the valve of the Pressure Sensor. Newer Vernier Gas PressureSensors have a white stem protruding from the end of the sensor box—attach the syringedirectly to the white stem with a gentle half-turn.2. Prepare the computer for data collection. • Open the Experiment 6 folder from Chemistry with Computers. Then, if necessary, open theexperiment file that matches the sensor you are using.2• On the Graph window, the vertical axis has pressure scaled from 0 to 250 kPa. The horizontalaxis has volume scaled from 0 to 20 mL.3. Click COLLECT to begin data collection.4. Collect the pressure vs. volume data. It is best for one person to take care of the gas syringe and foranother to operate the computer.a. Move the piston of the syringe to position the front edge of the inside black ring (see Figure 2)at the 5.0-mL line on the syringe. Hold the piston firmly in this position until the pressure valuestabilizes. Figure 2. Reading the first volume on the syringeb. When the pressure reading has stabilized, click KEEP. Type “5.0” in the edit box. Press theENTER key to keep this data pair. Note: You can choose to redo a point by pressing the ESCkey (after clicking KEEP, but before entering a value).c. Continue the procedure for volumes of 7.5, 10.0, 12.5, 15.0, 17.5, and 20.0 mL.d. Click STOP when you have finished collecting data.5. In your data table, record the pressure and volume data pairs displayed in the Table window (or, ifdirected by your instructor, print a copy of the Table window).6. Examine the graph of pressure vs. volume. Based on this graph, decide what kind of mathematicalrelationship you think exists between these two variables, direct or inverse. To see if you made theright choice:a. Click the Curve Fit button, . b. Choose Variable Power (y = Ax^n) from the list at the lower left. Enter the value of n in theDegree/Exponent edit box that represents the relationship shown in the graph (e.g., type “1” ifdirect, “-1” if inverse). Click TRY FIT.c. A best-fit curve will be displayed on the graph. If you made the correct choice, the curve shouldmatch up well with the points. If the curve does not match up well, try a different exponent andclick TRY FIT again. When the curve has a good fit with the data points, then click OK . 7. Once you have confirmed that the graph represents either a direct or inverse relationship, print acopy of the Graph window, with the graph of pressure vs. volume and its best-fit curve displayed.Enter your name(s) and the number of copies you want to print.3DATA AND CALCULATIONSVolume(mL)Pressure(kPa)Constant, k(P / V or P ! V)PROCESSING THE DATA (Answer the following in your report.)1. If the volume is doubled from 5.0 mL to 10.0 mL, what does your data show happens to thepressure? Show the pressure values in your answer.2. If the volume is halved from 20.0 mL to 10.0 mL, what does your data show happens to thepressure? Show the pressure values in your answer.3. If the volume is tripled from 5.0 mL to 15.0 mL, what does your data show happened to thepressure? Show the pressure values in your answer.4. From your answers to the first three questions and the shape of the curve in the plot of pressureversus volume, do you think the relationship between the pressure and volume of a confined gas isdirect or inverse? Explain your answer. 5. Based on your data, what would you expect the pressure to be if the volume of the syringe wasincreased to 40.0 mL? Explain or show work to support your answer.6. Based on your data, what would you expect the pressure to be if the volume of the syringe wasdecreased to 2.5 mL? Explain or show work to support your answer.7. What experimental factors are assumed to be constant in this experiment? 8. One way to determine if a relationship is inverse or direct is to find a proportionality constant, k,from the data. If this relationship is direct, k = P/V. If it is inverse, k = PAV. Based on your answerto Question 4, choose one of these formulas and calculate k for the seven ordered pairs in your datatable (divide or multiply the P and V values). Show the answers in the third column of the Data andCalculations table. 9. How constant were the values for k you obtained in Question 8? Good data may show some minorvariation, but the values for k should be relatively constant. Are any trends evident? 10. Using P, V, and k, write an equation representing Boyle’s law. Write a verbal statement that correctlyexpresses Boyle’s law.4EXTENSION1. To confirm the

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