Boyle’s Law in a Bottle
Student Laboratory Kit
Materials Included In Kit
Petroleum jelly, foilpac, 5 g Pressure bottles, 1L, fitted with tire valve, 8
Syringes, 10mL, with rubber septum or syringe caps, 8
Additional Materials Required
Barometer (optional) Bicycle pumps with attached pressure gauges, 5–7, or an electric air pump (see Lab Hints)
Graph paper, 16 sheets Tire gauges, 5–7 (optional)
Safety Precautions
The pressure bottle is safe if used properly. The bottle should not be inflated above 100 psi. Even if the bottle should explode, the plastic construction will only result in a quick release of air, an accompanying loud noise and a hole in the bottle. The bottle will split but will not shatter. Wear eye protection (safety glasses or chemical splash goggles) when working with the pressure bottle. Teachers should inspect the pressure bottles for cracks before setting them out for student use.
Disposal
The pressure bottles and syringes are reusable—no disposal required.
Lab Hints
 The laboratory work for this experiment can reasonably be completed in about 20 minutes. All materials are reusable. This should allow ample time in a normal 50minute class period for students to share equipment, if student groups of two are preferred.
 If the bottle leaks air around the cap when pressurized, remove the cap assembly and put additional petroleum jelly around the inside seal of the cap. Vaseline^{®} may also be used in place of the petroleum jelly.
 Best results are obtained using a bicycle pump with an attached pressure gauge. If enough bicycle pumps cannot be obtained with student help, the experiment may be done using common automobile tire gauges. The teacher should prepare the syringe/bottle assemblies and pressurize the bottles ahead of time. Since the scale maximum on many tire gauges is 50 psi, students may have to bleed off enough air initially to get the pressure below 50 psi. The units shown on some pressure gauges may be psig (gauge pressure per square inch. The correct units for the “total pressures” calculated in the Data and Results Table are psia (pounds per square inch absolute) rather than psi.
 For best results, use a barometer to measure the local barometric pressure. The national weather service site reports corrected, sealevel air pressures. Note that these are not actual barometric pressure readings. Meteorologists convert station pressure values to what they would be if they had been taken at sea level. The following equation can be used to recalculate the barometric pressure (in inches Hg) from the reported sealevel pressure (in inches Hg). Elevation must be in meters.
barometric pressure = sealevel pressure – (elevation/312 m)
On many syringes, the black rubber seals have two “seal lines.” Make sure students are consistent in where they measure the volume! A small amount of pressure is released in step 7 before volume measurements are made—this is to overcome the friction between the rubber seal and the syringe barrel.
 Tire gauges come in many shapes and sizes. The best gauges for this experiment are those with an attached pressure dial or digital readout rather than a “popout” sliding scale.
 Many students may have bicycle pumps or tire gauges they are willing to donate to the classroom for a short time in the interest of science (and, of course, extra credit). Ask your students for assistance.
 Electric air pumps are common items in vocational education or mechanical arts classrooms. If using an electric air pump, the teacher should inflate all of the pressure bottles ahead of time. The students may then use tire gauges to measure the pressure. Flinn Scientific sells a bicycle pump with gauge (Flinn Catalog No. AP6884).
 Students may need to be instructed in the use of a tire gauge. Students usually are too cautious—they tend to press the tire gauge softly against the valve, which allows air to escape and does not give an accurate pressure reading. The best advice is to work quickly and deliberately. There is an obvious value for students in learning to use a tire gauge so that they can inflate their automobile tires to the proper pressure. Maintaining proper tire pressure improves safety, tire wear, and gas mileage.
 Try not to exceed the maximum pressure recommended in the Procedure section. It was found that the graph of P versus 1/V became nonlinear as the pressure bottle was pressurized above about 70 psi (total pressure 85 psi). This can be used as a teaching point—deviations from ideal gas behavior are more important at higher pressures. Many textbooks show graphs of real versus ideal gas behavior as a function of pressure. For many gases, deviations from ideal behavior become significant at pressures greater than about 200 atm. Even at modest pressures, however, small deviations are common in the P x V “constant.” Some of this deviation may also be due to a change in temperature. Compressing the gas will increase the temperature of the gas.
 This lab provides excellent data and is a great way to introduce the use of computer spreadsheet or graphical analysis programs. Using these programs, it is possible with just a “click of the mouse” to draw bestfit, straight or curved lines (trendlines) through data and obtain regression equations. High school students are not expected to do the math involved in generating a bestfit straight line (linear regression). It is worthwhile, however, for students to learn how this important statistical tool is used to evaluate the reliability of results.
 See the Further Extensions for an example of how the data from this experiment can be analyzed to extrapolate the value of the atmospheric pressure in units of psi.
 For convenience in shipping and handling, the kit contains eight 1L plastic soda bottles. Pressure bottles may also be prepared using more readily available 2L soda bottles. See the Further Extensions section for instructions on how to prepare homemade pressure bottles. If you are constructing homemade pressure bottles, it will be necessary to cut or saw off the flanges on the top of the syringes. Otherwise, the syringes will not fit inside the pressure bottles.
Teacher Tips
 What does a pressure of 14.7 psi feel like? The Atmosphere Bar available from Flinn Scientific (AP5882) is a 52inch steel bar that weighs 14.7 lbs. The base of the bar is one inch square. The resulting pressure of 14.7 pounds per square inch certainly feels impressive!
 If necessary, review the definition of the average deviation with your students. The average deviation is obtained by finding the difference between each individual value (X_{i}) and the average value (Ẋ), taking the sum (Σ) of their absolute values and dividing by the number of measurements.
average deviation =
{12729_Tips_Equation_1}
 Does Boyle’s law depend on the nature of the gas? The experiment can be extended to test the behavior of gases other than air by filling the syringes with pure gases such as helium, hydrogen, and nitrogen. Any source of gas may be used. Call or write Flinn Scientific to obtain a complimentary copy of Publication No. 10527, Construction of a Simple Gas Delivery Apparatus.
 The approaches shown here may be conceptually challenging for students but they lead to some interesting discussions. Are negative pressures possible? Why or why not?
 Boyle’s law can also be demonstrated with every breath you take! When you inhale, your diaphragm moves down, and the volume of the body cavity surrounding the lungs expands. As the volume increases, the pressure decreases, and the outside air, which is at a higher pressure, rushes into the lungs. The opposite occurs when you exhale—the diaphragm moves upward, the lung cavity contracts, and the pressure increases relative to the outside air, pushing air out of the lungs. See the Functioning Lung Model (Catalog No. FB1110) available from Flinn Scientific for a large, demonstrationsize model of the pressure–volume relationship involved in breathing.
 The great 17th century physicist Isaac Newton was a contemporary of Robert Boyle, and Boyle’s results prompted Newton to propose an explanation for the pressure of a gas. Newton assumed that the particles in a gas were motionless (static) and that the pressure of a gas was due to the mutual repulsion of gas particles. That no less a person than the “father of physics” and the discoverer of the calculus proposed this model might serve as a cautionary tale for all teachers—our modern, obvious explanations for gas behavior may not always be obvious to students.
 The foundation of the modern kineticmolecular theory of gases is usually attributed to Daniel Bernoulli. In 1734 Bernoulli proposed that a gas was composed of “hard” (inelastic) particles that were in constant and random motion. The force exerted by these particles as they collided with the walls of their container was the source of the gas pressure. Using this model, Bernoulli derived a mathematical equation for the pressure of a gas. His mathematical treatment correctly “predicted” the inverse pressure–volume relationship that had been observed empirically by Robert Boyle. The development of the kinetic theory culminated in the mid1800s with the definition of temperature and the relationship between temperature and kinetic energy.
Further Extensions
Construction of a Pressure Bottle
Cut off the top portion of a 2L soda bottle. This will be used as a base or cap handle to hold the bottle caps that must be drilled. Screw one bottle cap securely onto the bottle top. Using a ½inch drill and drill press, drill a hole through the center of the cap, as shown in Figure 5. (Notice you are drilling through the bottom of the cap.) Remove the cap from the bottle top, add rubber cement to the lip of the valve stem, and use pliers to pull the valve stem through the hole from the inside, as shown. The tire valve will stick out of the top of the bottle cap when it is placed on the soda bottle. Clear away any burrs that may remain in the drilled hole. They will cause the seal to break.
{12729_Extension_Figure_5}
Graphical Analysis and the Value of the Atmospheric Pressure
As observed in PostLab Question 6, the graph of total pressure versus 1/V is a straight line that passes through the origin ( yintercept equal to zero). This graph corresponds to an equation of the form P _{total} = m x 1/V, where m is the slope of the line. If instead of the total pressure, students plot the gauge pressure (P _{gauge} = P _{total} – P _{air}) versus 1/V, they will obtain a straight line of the form P _{gauge} = (m x 1/V) – P _{air} (where the yintercept is equal to –P _{air}). The value of P _{air} can be estimated by extending the bestfit straight line backwards to “negative ” gauge pressures. The best estimate we were able to obtain using this method was about 12 psi (18% error).
{12729_Discussion_Figure_8}
Algebraic Determination of the Value of the Atmospheric Pressure
It is also possibe to use the gauge pressure–volume measurements to estimate a value for the atmospheric pressure in psi. This is a nice algebraic challenge for students. According to Boyle's law, multiplying any two sets of P–V data should give the same result (P _{1}V _{1} = P _{2}V _{2}). This is only true if the pressures are total pressures rather than relative gauge pressures (P _{total} = P _{gauge} + x, where x = value of atmospheric pressure in psi). The following equation is obtained by combining the equations for Boyle ’s law and the total pressure:
(P_{gauge, 1} + x)(V_{1}) = (P_{gauge, 2} + x)(V_{2})
Substituting the raw data for 17 psi and 1 psi (see Sample Data) into this equation gives:
(17 psi + x)(3.8 mL) = (1 psi + x)(8.4 mL)
64.6 + 3.8x = 8.4 + 8.4x
56.2 = 4.6x
x = 12 psi
Answers to Prelab Questions
 According to our modern understanding of the gas laws, there are four measurable properties (variables) of a gas. These variables are P (pressure), V (volume), T (temperature) and n (number of moles). In Boyle’s experiment, which two variables were held constant?
Both the temperature (T) and the number of moles of gas (n) were held constant in Boyle’s Jtube experiment.
 Fill in the blanks to summarize the relationship among the gas properties in Boyle’s experiment:
For a fixed number of moles of gas at constant temperature, the pressure of a gas increases as the volume of its container decreases.
 Pressure is defined in physics as force divided by area (P = force/area). According to the kineticmolecular theory, the particles in a gas are constantly moving and colliding with the walls of their container. The pressure of the gas is related to the total force exerted by the individual collisions. Use the kinetic theory to explain the results of Boyle’s experiment.
In Boyle’s experiment, the pressure of air increased when it was compressed into a smaller volume container. According to the kinetic theory, confining the gas particles in a smaller volume will increase the number of collisions and hence the total force of the collisions with the container walls. (The distance the particles must travel between collisions decreases as the volume is reduced.)
 The pressure scale on a tire gauge is marked in units of pounds per square inch (psi). The scale starts at zero when the gauge is exposed to the surrounding air. This means that the total pressure is equal to the gauge pressure plus the pressure of the surrounding air. Standard atmospheric pressure (1 atm) is equal to 14.7 psi. Assume that you have just inflated the tire on your bicycle to 82 psi using a bicycle pump. What is the total pressure of air in the tire in psi? In atmospheres?
Relative (gauge) pressure = Total pressure – Atmospheric pressure 82 psi = Total pressure – 14.7 psi Total pressure = (82 + 14.7) psi = 97 psi (two significant figures)
{12729_Answers_Equation_2}
Sample Data
{12729_Data_Table_1}
*See PostLab Question 2. †See PostLab Question 5.
Results Table
{12729_Data_Table_2}
Answers to Questions
 Convert the local barometric pressure to psi units and enter the value to the nearest psi in the Data and Results Table. Some appropriate conversion factors are shown.
1 atm = 760 mm Hg = 29.92 in Hg = 14.7 psi
{12729_Answers_Equation_3}
 The pressure gauge measures the relative pressure in psi above atmospheric pressure. For each pressure reading in the data and results table, add the local barometric pressure to the gauge pressure to determine the total pressure of air inside the pressure bottle. Enter the total pressure to the nearest psi in the table.
Sample calculation for Trial 1: Total pressure = 42 psi + 15 psi = 57 psi Refer to the data and results table for the results of the other calculations.
 Plot a graph of volume on the yaxis versus total pressure on the xaxis. Note: The origin of the graph should be (0,0). Choose a suitable scale for each axis so that the data points fill the graph as completely as possible. Remember to label each axis and give the graph a title.
{12729_Answers_Figure_5}
 Describe the shape of the graph. Draw a bestfit straight or curved line, whichever seems appropriate, to illustrate how the volume of a gas changes as the pressure changes.
The graph is curved. The volume decreases as the pressure increases. At first, there is a sharp reduction in the volume as the pressure increases. The decrease in volume then becomes more gradual and the volume appears to level off as the pressure increases further. Mathematically, the shape of the curve is described as hyperbolic. A hyperbolic curve of this type is obtained when there is an inverse relationship between two variables (y ∝ 1/x). See the graph for the bestfit curved line through the data.
 The relationship between pressure and volume is called an "inverse" relationship—as the pressure increases the volume of air trapped in the syringe decreases. This inverse relationship may be expressed mathematically as P ∝ 1/V. Calculate the value of 1/V for each volume measurement and enter the results in the data and results table.
Sample calculation for Trial 1: V = 2.0 mL 1/V = 0.50 mL^{–1} Refer to the Sample Data and Results Tables for the results of the other calculations.
 Plot a graph of pressure on the yaxis versus 1/V on the xaxis and draw a bestfit straight line through the data. Note: The origin of the graph should be (0,0). Choose a suitable scale for each axis so that the data points fill the graph as completely as possible.
{12729_Answers_Figure_6}
 Another way of expressing an inverse relationship between two variables (P ∝ 1/V) is to say that the product of the two variables is a constant (P x V = constant). Multiply the total pressure (P) times the volume (V) for each set of data points. Construct a results table to summarize the P x V values.
 Calculate the average value of the P x V “constant” and the average deviation. What is the relative percent error (uncertainty) in this constant?
Relative percent error = (Average deviation/Average value) x 100%
Average value of the (P x V) constant = 120 psi • mL Average deviation = 7 psi • mL Relative percent error = (7 psi • mL/120 psi • mL) x 100% = 6% It appears that the mathematical product (P x V) is a constant within plusorminus 6%.
 At constant temperature, the pressure of a gas is proportional to the concentration of gas particles in the container. When some of the pressure was released from the pressure bottle, the syringe plunger moved up. Why did this happen? Use diagrams and explain in words what happens to the gas particles moving around both inside and outside the syringe before and after the pressure is released.
Initially, the pressure was the same both inside and outside the syringe. This means there were equal concentrations of gas particles colliding with the inside and outside of the plunger, so the plunger stayed in place (A). When some of the pressure from the bottle was released, some air particles escaped, leaving fewer air particles to collide on the outside of the plunger (B). The concentration of particles inside the syringe overpowered those outside the syringe and pushed the plunger outward (the volume increased). As the volume increased, the particle concentration inside the syringe decreased. When the concentration of particles (pressure) inside the syringe was the same as that outside the syringe, the plunger stopped moving (C).
{12729_Answers_Figure_7}
 (Optional) Research the properties of high density PETE on the Internet. What characteristics of PETE make it an ideal plastic for use in soda bottles?
PETE is an ideal plastic for soda bottles for several reasons. It is transparent, crystal clear, pure, tough and unbreakable. PETE also has very low permeability to oxygen, carbon dioxide and water, and excellent chemical resistance to acids and bases. If the PETE does not contain additives, it is relatively easy to recycle.
References
This experiment has been adapted from Flinn ChemTopic™ Labs, Volume 9, The Gas Laws, Cesa, I., ed., Flinn Scientific, Batavia, IL, 2003.
