Science with Handhelds 14 - 1

Experiment

14Boyle’s Law: Pressure-VolumeRelationship in Gases

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 Gas 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 Gas 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 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. Historically, this relationship was first established by Robert Boyle in 1662 and has since been known as Boyle’s law.

Figure 1

OBJECTIVES

In this experiment, you will

Use a Pressure Sensor and a gas syringe to measure the pressure of an air sample at several different volumes.

From the results, determine the relationship between pressure and volume of the gas. Describe the relationship between gas pressure and volume in a mathematical equation. Use the results to predict the pressure at other volumes.

MATERIALS

LabPro interface Data Pro programPalm handheld 20 mL gas syringeVernier Gas Pressure Sensor or Pressure Sensor

PROCEDURE

1. Prepare the Pressure Sensor and an air sample for data collection.

a. Plug the Pressure Sensor into Channel 1 of the LabPro interface. Connect the handheld to the LabPro using the interface cable. Firmly press in the cable ends.

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) is positioned at the 10.0 mL mark.

c. Attach the 20 mL syringe to the valve of the Pressure Sensor.

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Experiment 14

Newer Vernier Gas Pressure Sensors have a white stem protruding from the end of the sensor box—attach 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 attach the syringe directly to the remaining open stem of the 3-way valve.

2. Press the power button on the handheld to turn it on. To start Data Pro, tap the Data Pro icon on the Applications screen. Choose New from the Data Pro menu or tap to reset the program.

3. Set up the handheld and interface for a Pressure Sensor.

a. On the Main screen, tap .b. If the handheld displays PRESS(kPa) in CH 1, proceed directly to Step 4. If it does not,

continue with this step to set up your sensor manually.c. Tap to select Channel 1. d. Press the Scroll buttons on the handheld to scroll through the list of sensors. e. Choose the correct pressure sensor (in units of kPa) from the sensor menu.

4. Set up the data-collection mode

a. On the Setup screen, tap the button, then choose Events with Entry.b. Enter the x-axis label (Volume) and unit (mL). You can enter this information using the

onscreen keyboard (tap “abc”), or by using the Graffiti writing area.c. Tap twice to return to the Main screen.

5. You are now ready to collect pressure and volume data. It is easiest if one person takes care of the gas syringe and another operates the handheld.

a. Tap 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 handheld screen stabilizes.

c. Tap and enter “5”, the gas volume (in mL) on the handheld screen (using the numerical keyboard displayed on the screen). Tap 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, tap and enter “7.5” as the volume. Tap .

e. Continue with this procedure using volumes of 10.0, 12.5, 15.0, 17.5, and 20.0 mL.

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Boyle’s Law: Pressure-Volume Relationship in Gases

f. Tap when you have finished collecting data, then tap to view a graph of pressure vs. volume.

6. To examine the data pairs on the displayed graph, tap or any data point. As you move the examine line, the pressure and volume values of each data point are displayed to the right of the graph. Record the pressure and volume data values in your data table.

7. Based on the graph of pressure vs. volume, decide what kind of mathematical relationship exists between these two variables, direct or inverse. To see if you made the right choice:

a. Tap , then tap .b. From the Fit Equation menu, choose Power. The curve fit statistics for these two data

columns are displayed for the equation in the formy = 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. Note: The relationship between pressure and volume can be determined from the value and sign of the exponent, b.

c. To display the regression curve on the graph of pressure vs. volume, tap . If you have correctly determined the mathematical relationship, the power regression line should very nearly fit the points on the graph (that is, pass through or near the plotted points).

8. (optional) If directed by your instructor, proceed directly to the Extension that follows Processing the Data.

DATA AND CALCULATIONS

Volume(mL)

Pressure(kPa)

Constant, kP / V or P • V

CONCLUSION

1. 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 = P•V. Is the relationship between pressure and volume direct or inverse? Based your answer on your calculations in the third and fourth columns of your data table.

2. How constant were the values for k you obtained in Question 1? Good data may show some minor variation, but the values for k should be relatively constant.

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Experiment 14

3. Using P, V, and k, write an equation representing Boyle’s law. Write a verbal statement that correctly expresses Boyle’s law.