Boyle's Law: Pressure vs. Volume of a Gas at Constant Temperature
AbstractThis is a modern version of a classic experiment by Robert Boyle on the compressibility of gases. Boyle discovered the relationship between pressure and volume of gases that now bears his name. This project shows you a simple method for re-creating this famous experiment.
- Gabel, Dorothy, 1996. "Learning Sequence Item 929: Gas Laws" in Scope, Sequence and Coordination: A National Curriculum Project for High School Science Education. Arlington, VA: National Science Teachers Association. Available online at: http://dev.nsta.org/ssc/pdf/v4-0929s.pdf.
- Gardner, Robert, 1990. Famous Experiments You Can Do. New York, NY: Franklin Watts (pp. 61–65).
- Blauch, D., 2004. "Gas Laws: Pressure", Department of Chemistry, Davidson College. [accessed December 13, 2005] http://www.chm.davidson.edu/ChemistryApplets/GasLaws/Pressure.html.
The goal of this project is to measure the relationship between the volume of a gas and its pressure, when the temperature of the gas is held constant.
This project re-creates a study begun in 1662 by Robert Boyle. Now that's a classic! Unlike liquids, gases are compressible. Boyle systematically studied the compression of air, sealed in a glass tube with a U-shaped curve. The air was trapped by a column of mercury, added to the open end of the tube. By changing the amount of mercury in the tube, Boyle could change the pressure exerted on the trapped air. Boyle's apparatus was an example of a manometer, a device used to measure pressure.
The following diagram and description, from Prof. David N. Blauch, of Davidson College, explain how a manometer works.
"A manometer is a device employed to measure pressure. There are a variety of manometer designs. A simple, common design is to seal a length of glass tubing and then bend the glass tube into a U-shape. The glass tube is then filled with a liquid, typically mercury, so that all trapped air is removed from the sealed end of the tube. The glass tube is then positioned with the curved region at the bottom. The mercury settles to the bottom (see the picture at the left).
"After the mercury settles to the bottom of the manometer, a vacuum is produced in the sealed tube (the left tube in the picture). The open tube is connected to the system whose pressure is being measured. In the sealed tube, there is no gas to exert a force on the mercury. In the tube connected to the system, the gas in the system exerts a force on the mercury. The net result is that the column of mercury in the left (sealed) tube is higher than that in the right (unsealed) tube. The difference in the heights of the columns of mercury is a measure of the pressure of gas in the system.
"In the example at the left, the top of the left column of mercury corresponds to 875 mm on the scale. The top of the right column of mercury corresponds to 115 mm. The difference in heights is 875 mm − 115 mm = 760. mm, which indicates that the pressure is 760. mm Hg or 760. torr." (Blauch, 2004).
You can learn more about how manometers work, and even run a simulated Boyle's Law experiment by visiting the Chemistry Applet website (see Bibliography). This would be excellent preparation for doing the experiment on your own, so we highly recommend it.
You can repeat Boyle's experiments with an inexpensive, modern apparatus based on a disposable plastic syringe. Mercury is a dangerous neurotoxin, so we'll avoid working with it. Instead, you will compress the air in the syringe with . . . bricks!
Pressure is force exerted over a unit area, so the units are those of force divided by area. The larger area of a syringe (compared to a narrow glass tube) means that you will need a larger force to compress the gas. Bricks, which are stackable and weigh about 1 kg apiece, will do the job nicely.
Terms and ConceptsTo do this project, you should do research that enables you to understand the following terms and concepts:
- Boyle's Law,
- ideal gas,
- atmospheric pressure,
- What assumption is made about the temperature of the gas in this experiment?
- Pressure is measured in many different units. For example, blood pressure is typically expressed in mm of Hg (mercury), as in Boyle's experiments. In the U.S., pressure for car tires is typically expressed in pounds per square inch. The SI unit for pressure is the pascal (Pa). How are all of these different units related? How can you convert from one to another?
- Here is the sequence of three Chemistry Applet webpages mentioned in the Introduction. These will really help your understanding of Boyle's Law if you take the time to do the virtual experiments!
- Blauch, D., 2004. "Gas Laws: Pressure", Department of Chemistry, Davidson College. [accessed December 13, 2005] http://www.chm.davidson.edu/ChemistryApplets/GasLaws/Pressure.html,
- Blauch, D., 2004. "Gas Laws: Boyle's Law", Department of Chemistry, Davidson College. [accessed December 13, 2005] http://www.chm.davidson.edu/ChemistryApplets/GasLaws/BoylesLaw.html, and
- Blauch, D., 2004. "Gas Laws: Boyle's Law Calculations", Department of Chemistry, Davidson College. [accessed December 13, 2005] http://www.chm.davidson.edu/ChemistryApplets/GasLaws/BoylesLawCalc.html.
- The Sizes.com website has an exhaustive index of units of measure, including the SI definition for the pascal, and a link to a calculator to convert between various units of pressure:
Editor, Sizes.com, 2000. "pascal" [accessed December 13, 2005] http://www.sizes.com/units/pascal.htm
Materials and Equipment
- Syringe that can hold at least 30 mL. If the syringe does not come with a tight-fitting cap, you will also need epoxy or silicone sealant. A suitable syringe that comes with a cap is available from Amazon.com.
- Wood blocks with center holes drilled partway through (2); see the diagram in the Experimental Procedure section.
- The first block will hold the syringe upright, and will need a hole that is just slightly larger than the diameter of the syringe, plus a smaller hole to accommodate the syringe tip. For greater stability, this block can be clamped in place (optional).
- The second block will be placed on top of the syringe plunger, and will act as a shelf for the bricks; the diameter of the hole should fit the top of the syringe plunger snugly.
- A small piece of wire
- Bricks with approximately uniform size and weight of about 1 kg (4 or 5 bricks)
- Scale for weighing bricks; a bathroom scale should be adequate.
- Graph paper
- Optional: "C" clamps (2). These are available at hardware stores and online through suppliers such as Amazon.com.
- Lab notebook
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Diagram of a syringe held vertically in pre-drilled wood block support. A thin wire between the plunger tip and the inner syringe wall allows air to escape from in front of the plunger in order to equalize pressure. A second pre-drilled wood block is placed atop the syringe plunger and acts as a platform to increase the pressure on the plunger.
- Before starting the experiment, do your background research so that you are knowledgeable about the terms, concepts and questions, above.
- With the plunger removed from the syringe, seal the tip of the syringe with a tight-fitting cap. If a suitable cap is not available, you can try epoxy or silicone sealant. Allow the epoxy or silicone the recommended curing time before proceeding with the experiment. (Note: if you seal the tip with the plunger in place, you will probably not be able to remove the plunger unless you destroy the seal. Why?)
- When your sealed syringe is ready for use, insert the syringe firmly, tip down, into the pre-drilled hole in the bottom wood block support, as shown in the diagram. The syringe should fit snugly, so it does not wobble when you load it up with bricks. You may wish to clamp the block in place. (Note: clamp to a workbench, not a piece of fine furniture!)
- Insert the plunger to the 30 ml mark of the syringe along with a thin wire as shown in the diagram. The wire will allow air to escape from beneath the plunger, equalizing the pressure in the syringe with the atmosphere. Use the lower ring of the plunger as your indicator.
- Hold the plunger in place and carefully withdraw the wire.
- Make sure that the plunger can move freely in the syringe, and that the tip of the syringe is well-sealed. Give the plunger a small downward push, and verify that it springs back. If it does not, you may need to lubricate the side of the plunger with a small amount of silicone lubricant or you may not have sealed the tip of your syringe properly.
- When you are satisfied with the results of the previous step, record the initial volume of air in the syringe.
- Place second wood block over the top of the plunger, as shown in the diagram. This wood block will act as a shelf to hold bricks in order to exert downward force on the plunger. Make sure that the shelf is level and well-seated on the plunger.
- Place the first brick on the shelf. You may need to tap on the brick to free the plunger. Note the resulting volume of air in the syringe.
- Repeat the previous step until you have 4 or 5 bricks stacked on the syringe. With each added brick, note the volume of air, and the number of bricks.
- Next, you will remove the bricks, one at a time, noting the volume of air in the syringe each time. Again, you may need to tap on the shelf to free the plunger.
- Take the average of your two values (from loading and unloading) for each number of bricks.
- Remove the plunger and repeat steps 4–12 so that you have at least 5 trials.
- Calculate the average and standard deviation of the volume for each of your data points over the repeated trials.
- At this point, you have measured the volume of air in the syringe as a function of the number of bricks pushing down on the plunger. The next step is to convert from bricks to units of pressure.
- Pressure is defined as force per unit area. The SI unit for pressure is the pascal (Pa), which is defined as the force of 1 newton acting over an area of 1 square meter. So you will need to know the force exerted by the bricks, plus the area of the plunger.
- You can calculate the downward force, F of the brick(s) by multiplying the mass, m, of the brick(s) times the acceleration, a, due to gravity (F = ma), where a = 9.83 N/kg.
- You can calculate the area of the plunger (in units of square meters) by measuring the diameter, and recalling the formula for calculating the area of a circle.
- You can then calculate the pressure, in Pa, by dividing the force, F, generated by each stack of bricks by the area, A, of the plunger.
Boyle found that, when temperature is held constant, the pressure and volume of a gas are inversely related. In mathematical terms, we can write PV = k, where P, naturally, is pressure, and V is volume. Alternatively, we can write P1V1 = P2V2, where the subscripts indicate measurements of different pressure-volume pairs. The equation shows that as pressure increases, volume must decrease, and vice versa.
- Do your results agree?
- What method(s) of graphing your results will show the inverse relationship between pressure and volume? (If you need ideas, check out the virtual experiment links in the Bibliography section.) You should be able to describe in your own words how your graph illustrates an equation for Boyle's Law.
- What is the pressure on the air in the syringe before you start adding weight to the the plunger? Can you extrapolate from your measurements to give a value for this pressure? Can you think of a way to check the results of your extrapolation?
- Was the assumption of constant temperature valid?
- What are the possible sources of error in your experiment?
Ask an Expert
- For a related experiment, see: Proving Charles' Law: Volume vs. Temperature of a Gas at Constant Pressure.
- For a more advanced version of this project, combine it with the Charles's Law project (see above) and do background research on statistical mechanics, and explain your results in terms of molecular motions.
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