Boyle s Law: Pressure-Volume Relationship in Gases

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1 Boyle s Law: Pressure-Volume Relationship in Gases Experiment 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. 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 12 and has since been known as Boyle s law. Figure 1 MATERIALS Power Macintosh or Windows PC Vernier computer interface Logger Pro Vernier Gas Pressure Sensor or Pressure Sensor 20-mL gas syringe PROCEDURE AND DATA 1. Prepare the Pressure Sensor and an air sample for data collection. Plug the Pressure Sensor into Channel 1 of the computer interface. a. 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. b. 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 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. Prepare the computer for data collection. Chemistry with Computers - 1

2 Experiment Prepare the computer for data collection by opening the Experiment folder from Chemistry with Computers. Then open the experiment file that matches the sensor you are using. On the Graph window, the vertical axis has pressure scaled from 0 to 250 kpa. The horizontal axis 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 for another to operate the computer. a. Move the piston to position the front edge of the inside black ring (see Figure 3) at the 5.0-mL line on the syringe. Hold the piston firmly in this position until the pressure value stabilizes. Figure 3 b. BE VERY CAREFUL ONLY TO HANDLE THE SYRINGE DURING THE EXPERIMENT AND NOT TO PUT ANY PRESSURE ON OR TWIST THE CONNECTION!! KEEP ONE HAND ON THE PLUNGER AND THE OTHER ON THE BARREL OF THE SYRINGE. YOU WILL FIND IT WILL TAKE SOME EFFORT TO KEEP THE SYRINGE AT A STEADY VOLUME WHEN YOU GET TO THE HIGHER VOLUMES. c. When the pressure reading has stabilized, click Keep or the blue round flower-like button and type the volume in the edit box that will appear. Press the ENTER key to keep this data pair. (Note: You can choose to redo a point by pressing the ESC key (after clicking Keep, but before entering a value). d. Continue the procedure for volumes near 7.5, 10.0, 12.5, 15.0, 17.5, and 20.0 ml. e. Click Stop when you have finished collecting data. 5. In the data table, record the pressure and volume data pairs displayed in the Table window. - 2 Chemistry with Computers

3 Boyle s Law: Pressure-Volume Relationship in Gases Name Date Data Table Trial Pressure ( kpa) Volume ( ml) Calculations 1. Based on your data, when the volume is doubled from 5.0 ml to 10.0 ml, by what factor did the pressure change? (That is, did it triple, double, change by one half or one third or what)? 2. Based on your data, when the volume changes by one half, from 20.0 ml to 10.0 ml, by what factor did the pressure change? 3. Based on your data, when the volume is tripled from 5.0 ml to 15.0 ml, by what factor did the pressure change? 4. Refer to your graph on the computer and use it to predict what your think the pressure would be if the volume were 8.0 ml. Sketch your graph of P versus V Chemistry with Computers - 3

4 Experiment 5. Do you think the relationship between pressure and volume is a direct or inverse relationship? Explain your choice. To see if you made the correct choice for the relationship between P and V, you will let the computer draw a best fit curve for your data and determine the equation for this curve. To do this: Click the Curve Fit button on the tool bar, your graph and press Try Fit. Choose the equation that best fits A best-fit curve will be displayed on the graph. If you made the correct choice, the curve should match up well with the points. If the curve does not match up well, try a different equation and click Try Fit again. When the curve has a good fit with the data points, then click OK. ) Write the equation for your graph that is given on the computer using the variables x, y and include the numerical value for the constant in the equation. Rewrite this equation replacing the letters, x and y, with the letters P and V. Keep the value of the constant: 7) a) Use your equation that relates P and V to calculate the pressure ( P) when the volume (V) is 8.0 ml b) How does this compare to the value you estimated from the graph in question (4) that was based on your experimental data? 8) a) Refer to your graph on the computer and predict what the pressure would be if the volume of the syringe was 12.5 ml. b) Use your equation in () to calculate the pressure (P) when the volume(v) is 12.5 ml c) How do these values compare? - 4 Chemistry with Computers

5 Boyle s Law: Pressure-Volume Relationship in Gases 9) The mathematical relationship between pressure and volume is called Boyle s Law after the scientist, Robert Boyle, who first found it. One of the things it predicts about gases is that for a given gas when the pressure is multiplied by the volume you will always get the same number. See if your data verifies this, multiply the pressures and volumes for each set of data you collected and show your results in the table below. If you always get the same, or close to the same, number the equation is verified. The value for k would be the constant for air and should be the same for each lab group. Trial P x V Do your data verify Boyle s Law ( does PV = a constant value)? 10) Boyle s law is more useful when it is written : P 1 V 1 = P 2 V 2, where the subscript 1 represents initial conditions and the subscript 2 represents the new conditions. Use this equation to solve the following problem: A gas has a pressure of 10.5 atm and a volume of 0L. What is its new pressure if the volume changes to 13 L? 11). A gas must be described using its pressure, temperature, volume and the amount of the gas in the container. Which of these conditions was kept constant in this experiment? (There may be more than one) Boyle s law is valid to use only when these conditions are kept constant. If they change in an experiment, the value of the constant will be different. Chemistry with Computers - 5

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