Boyle’s Law
Inquiry Lab Kit for AP® Physics 2
Materials Included In Kit
Syringes with plungers, 6 Syringe tip caps, 6
Wooden bases with large (23mm diameter) predrilled holes, 6 Wooden tops with medium (20mm diameter) predrilled holes, 6
Additional Materials Required
Books
Ruler
Safety Precautions
Wear appropriate safety eyewear. Do not aim the pressurized syringe at anyone or anything as the syringe tip cap could shoot off. Check the syringe, plunger and tip cap before using and replace any parts that are damaged or worn.
Disposal
All materials may be saved and stored for future use.
Lab Hints
 This laboratory activity can be completed in two 50minute class periods. It is important to allow time between the Introductory Activity and the GuidedInquiry Activity for students to discuss and design the guidedinquiry procedures. Also, all studentdesigned procedures must be approved for safety before students are allowed to implement them in the lab. Prelab Questions may be completed before lab begins the first day.
 Enough materials are provided in this kit for 24 students working in groups of 4 or for 6 groups of students.
 Any kind of mass or object (e.g., books or reams of paper) can be used as the pressure load for this experiment. Be aware that stacking masses too high or unevenly on the top wooden block may cause the syringe to tip over and necessitate further data collection. If the mass is not marked, make sure students measure the mass of the object using a balance and record this in a data table.
 It may be necessary to grease the plunger prior to each trial to minimize friction in the syringe.
 Volume measurements, in mL and with a ruler, were recorded using the first leading edge of the syringe plunger as a marker. Advise students to be careful when they record the syringe volume because it is easy to record an “upside down” volume.
 Small books were used to apply the measurable force, or pressure, to the syringe plunger. Standard masses, such as those used to calibrate a balance, in the range of 50–200 g, were not sufficient to cause an easily measurable volume change.
 For graphing purposes, remind students that the pressure is not zero when the plunger is in the starting position, rather it is equal to atmospheric pressure. Drawing a freebody diagram, as prescribed by the Prelab Questions, of the prevailing forces may help students realize this.
 The system, without weights added to the top, is in equilibrium. The internal gas pressure exerted on the plunger is equal to the external, atmospheric pressure and so the plunger does not move. With each addition of more mass, the system must be given time to reequilibrate, that is, for the plunger to come to a stop owing to the internal pressure/atmospheric pressure + mg balance.
 Students might need a reminder on how to recognize a hyperbola: the products of the coordinates at all points should be constant. Rearrange PV = nRT to y = mx + b form. Place P on the yaxis so the equation becomes P = (nRT)/V. Assuming the compression is slow enough so that the temperature doesn’t change, the process is isothermal and a graph of P vs. 1/V is linear with the other gas variables constant.
 Students can use graph paper and count squares to get at the area under the curve. Integral calculus may be done, but is not necessary.
 To calculate pressure in kPa:
 Convert grams to kilograms.
 Convert kilograms to newtons (force) = mass x acceleration due to gravity, mass in kg x 9.8 m/sec^{2}.
 Pressure = force/area and is expressed in units of newtons/m^{2}. Area is the area of the syringe opening (use A = πr^{2}, r = 7.5 x 10^{–3} m).
 Convert to kPa.
 Add to each the standard atmospheric pressure; 101.33 kPa.
Teacher Tips
 The guidedinquiry design and procedure section was developed to subtly lead students through the experimental design process. You may decide to provide less or more information than is included, as long as the students are challenged to think critically.
 This laboratory provides a unique opportunity to demonstrate the interdisciplinary nature of science. The ability of the distinct disciplines, chemistry and physics, to inform each other is particularly pronounced in this investigation.
Further Extensions
Opportunities for Inquiry
Explore Charles’s law, the relationship between absolute temperature and volume. Or explore the lesserknown Amonton’s law, which describes the relationship between temperature and pressure. A hole may be drilled in the syringe and a temperature probe inserted to measure temperature as gas is compressed.
Alignment to the Curriculum Framework for AP^{®} Physics 2
Enduring Understandings and Essential Knowledge The energy of a system is conserved. (5B) 5B5: Energy can be transferred by an external force exerted on an object or system that moves the object or system through a distance. This process is called doing work on a system. The amount of energy transferred by this mechanical process is called work. Energy transfer in mechanical or electrical systems may occur at different rates. Power is defined as the rate of energy transfer into, out of, or within a system. (A piston filled with gas getting compressed or expanded is treated in Physics 2 as part of thermodynamics.) 5B7: The first law of thermodynamics is a specific case of the law of conservation of energy involving the internal energy of a system and the possible transfer of energy through work and/or heat. Examples should include P–V diagrams—isovolumetric processes, isothermal processes, isobaric processes, and adiabatic processes. No calculations of internal energy change from temperature change are required; in this course, examples of these relationships are qualitative and/ or semiquantitative.
Learning Objectives 5B5.4: The student is able to make claims about the interaction between a system and its environment in which the environment exerts a force on the system, thus doing work on the system and changing the energy of the system (kinetic energy plus potential energy). 5B5.5: The student is able to predict and calculate the energy transfer to (i.e., the work done on) an object or system from information about a force exerted on the object or system through a distance. 5B5.6: The student is able to design an experiment and analyze graphical data in which interpretations of the area under a pressurevolume curve are needed to determine the work done on or by the object or system. 5B7.1: The student is able to predict qualitative changes in the internal energy of a thermodynamic system involving transfer of energy due to heat or work done and justify those predictions in terms of conservation of energy principles. 5B7.2: The student is able to create a plot of pressure versus volume for a thermodynamic process from given data. 5B7.3: The student is able to use a plot of pressure versus volume for a thermodynamic process to make calculations of internal energy changes, heat, or work, based upon conservation of energy principles (i.e., the first law of thermodynamics).
Science Practices 1.1 The student can create representations and models of natural or manmade phenomena and systems in the domain. 1.4 The student can use representations and models to analyze situations or solve problems qualitatively and quantitatively. 2.2 The student can apply mathematical routines to quantities that describe natural phenomena. 4.2 The student can design a plan for collecting data to answer a particular scientific question. 4.3 The student can collect data to answer a particular scientific question. 5.1 The student can analyze data to identify patterns or relationships. 6.4 The student can make claims and predictions about natural phenomena based on scientific theories and models.
Correlation to Next Generation Science Standards (NGSS)^{†}
Science & Engineering Practices
Asking questions and defining problems Developing and using models Planning and carrying out investigations Analyzing and interpreting data Using mathematics and computational thinking Obtaining, evaluation, and communicating information Engaging in argument from evidence
Disciplinary Core Ideas
MSPS3.C: Relationship between Energy and Forces HSPS3.C: Relationship between Energy and Forces
Crosscutting Concepts
Patterns Stability and change Cause and effect Scale, proportion, and quantity Systems and system models
Performance Expectations
MSPS35. Construct, use, and present arguments to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object. HSPS31. Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. HSPS32. Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motion of particles (objects) and energy associated with the relative position of particles (objects).
Answers to Prelab Questions
 When you use a bicycle pump to inflate a bicycle tire, are you doing work on the gas or is the gas doing work on the environment? Explain.
You are doing work on the gas. In order to compress the gas, you must exert a force to move the bicycle pump over a distance.
 If you inflate a bicycle tire to nearbursting using a bicycle pump, and then release the pump handle, the handle will rise against gravity.
In this case, is work done on or by the gas? In this case, work is done by the gas on the bicycle pump handle. The internal pressure exerted by the gas molecules in the pump is greater than the external atmospheric pressure and exerts a force against gravity over a distance.
 One summer saw gasoline prices fall significantly from the previous summer. The falling gas prices were attributed, in part, to a glut, or huge supply of oil on the market. In this simplified model, is the relationship between oil supply and gas prices an inverse or direct relationship? Explain.
This model describes an inverse relationship between oil supply and gas prices. That is, as one increases, the other decreases.
 Explain why the pressure exerted by gas molecules against their container walls increases as the container size, or volume, decreases.
According to the kinetic molecular theory of gases, gas molecules exhibit constant, random motion. Gas molecules exert pressure by bumping into, or colliding with, their container walls. If the container size is decreased while the number of gas molecules stays the same, then the number of collisions between the gas molecules and container walls will increase, and so too will the pressure.
 The apparatus used in this experiment consists of a plunger inserted in a syringe held upright by two wooden blocks. Mass is added to the top wooden block and resulting volume changes are measured. What prevents the plunger from rising up and out of the syringe housing, when no books or masses are kept on top of it?
Atmospheric pressure, or the force air molecules exert in their collisions with the plunger, prevent it from rising in the absence of an additional external force. When the plunger is static, the internal pressure of the gas molecules must be equal to the external, atmospheric pressure.
 Given your answer to Question 5, how will this impact your calculation of the pressure, or, the first point on a PV graph?
The first point on the PV graph will have a pressure value equal to atmospheric pressure. As books are added to the top of the plunger, new pressures attributable to the addition of new mass will be calculated and added to the atmospheric pressure.
 Draw a freebody diagram of the forces on the piston to show that the total force on the top block (mg + atm) is in direct opposition to the internal pressure of the gas in the syringe.
{14009_PreLabAnswers_Figure_3}
 Calculation of the amount of work done on or by a gas requires integral calculus, or graphical analysis. Describe how you might use graphical analysis to determine the area under a curve like the one shown in Figure 1 by using graph paper composed of small squares or blocks.
If graph paper composed of small squares is used, the area of one square may be calculated by measuring the side length and squaring to determine the area of a single square. The squares under the curve can then be counted. The total number of squares multiplied by the area of one square will provide an estimate of the area under the curve. Some squares will have only a portion of their areas fall under the curve, so some level of approximation is required. Alternatively, a triangle can be outlined (as best as possible) under the curve and the sides measured to enable calculation of the triangle’s area using the formula A = ½ x base x height.
Sample Data
Discussion for Introductory Activity As the plunger is depressed, the volume of the container, or syringe, decreases. Since the syringe is capped, the amount of gas in the syringe remains constant. Therefore, as the volume decreases, the pressure of the gas inside the syringe increases because the number of collision between the gas molecules and their container walls increases. As the plunger is depressed, the gas is being worked upon. It takes a force (i.e., the push of your hand) to move the plunger over a distance. When you release your hand from the plunger, it rises as the gas expands to fill a larger volume. In this case, the gas is performing work on the plunger by moving it over a distance.
Analyze the Results
 How do your measured values describing the volume changes with pressure changes compare to the theoretical, calculated values? Account for differences.
Recall that Boyle’s law can be expressed as P_{1}V_{1} = P_{2}V_{2} to convey the fact that as volume decreases, pressure must necessarily increase to keep the product PV constant. You may use atmospheric pressure and the initial syringe volume to calculate the constant PV product. As mass is added to the syringe, the pressure exerted may be calculated and plugged into the equation P_{1}V_{1} = P_{2}V_{2}, which may be rearranged to solve for a theoretical V_{2} value. The theoretical V_{2} value may be compared to the experimental V_{2} value, or the volume change attributable to the addition of increased mass.
Remember we are assuming that the gas inside the syringe is ideal and thus has negligible volume and molecules that do not attract each other. As the volume decreases, we would expect deviations from ideal behavior to become more pronounced because the gas molecules assume more significant volumes relative to the container volume and their proximity increases the strength of the attractive forces the experience amongst themselves.
 The process by which data is manipulated and graphed to yield a straight line, as opposed to a curve, is called linearization. How can you manipulate your P–V data to convert your curve into a straight line?
This can be done by taking the inverse of all volume measurements, that is, by dividing the measured volumes into 1. This has been done and the results reported in the sample data.
The linearization of the PV data is based on rearrangement of the ideal gas law so that pressure and volume are on opposite sides of the equation: P = nRT/V. The term nRT is a constant and can be omitted from the equation to yield the direct relationship P = 1/V.
{14009_Data_Table_1}
Example Calculation of Pressure
P = F/A P = mg/πr^{2} P = (0.9117 kg x 9.8 m/s^{2})/[π x (0.0103m)^{2}] P = 26830.81 Pa P = 26.83 kPa (the atmospheric pressure, 101.33 kPa, must be added to this value: 26.83 kPa + 101.33 kPa = 128.16 kPa)
{14009_Data_Figure_2}
Answers to Questions
Discussion for GuidedInquiry Activity
 Design an experiment that uses the apparatus provided to derive the mathematical relationship between a gas’s pressure and the volume of the container in which it is held. Use the following questions to guide you as you design your experiment.
 Gather several (5–8) objects of approximately equal or uniform mass. These may be copies of the same textbook, reams of paper, or other heavy objects of equal weight.
 Prepare a data table to record the volume of air in the syringe versus the number of masses added to the apparatus. Note: Create enough columns to record three trials, plus a column for the average volume.
 Before beginning, record the first data point by reading the initial volume of air in the syringe with no masses on the apparatus.
 Stack the first mass on the top block of the apparatus and record the volume of air (in cc) as indicated on the scale of the syringe.
 Continue stacking masses on top of the apparatus, recording the air volume each time. If time allows, repeat the procedure 1–2 times.
 Average the volume data and record in a data table.
 Plot the data on a sheet of graph paper.
 Use P = F/A = mg/πr^{2} to calculate pressure on the plunger as mass is added, where r is the plunger radius.
 What are the two gas variables you will be measuring, and plotting on a graph?
Pressure and volume.
 How can you apply a measurable pressure, or rather calculate the pressure, applied to the syringe plunger?
Objects with mass significant enough to move the plunger in the downward direction—to compress the internal gas—must be selected. Prior to the placement of each object on top of the plunger, or top wooden block, the object should be massed on a toploading balance with a high (appr. 1,000 g) capacity. The measured mass can be used with the formula P = mg/πr^{2}, to calculate the pressure applied to the syringe plunger.
 How can the experimental volume change be measured as the pressure exerted on the plunger changes?
The experimental volume change can be measured directly by observation using the mL markings on the syringe. It is recommended that the leading edge of the syringe be used to most closely approximate the true volume of gas in the syringe. The conical tip of the syringe takes up space, but it does not occupy a significant volume relative to that occupied by the gas.
 According to the kinetic molecular theory of gases very fast compressions of a gas from large volumes to small volumes cause significant temperature changes. Why then, for the purpose of this experiment—to determine the mathematical relationship between the gas variables pressure and volume—is it necessary to compress the gas in the syringe slowly?
We are attempting to derive a relationship between the two variables, pressure and volume. Therefore, we want to control the experiment such that the effects of one of those variables on the other are the only effects we observe. In other words, we want to avoid causing significant temperature changes because if significant temperature changes occur red in conjunction with the pressure and volume changes, it would be difficult to determine how much of the volume change could be attributed to the pressure change and how much of the volume change could be attributed to the temperature change. If we want to measure the effects of one variable on the other, we have to control any external variables such as temperature and moles. In other words, we want to hold those constant. Experiments in which temperature is held constant can be called isothermal with respect to each other.
 Construct a graph of pressure (yaxis) versus volume (xaxis).
 How many data points are necessary?
To some degree, this is a matter of subjectivity on the part of the experimentalist. Two data points can be used to define a line but should not be relied upon as confirmation of a relationship, either direct or indirect, between two variables. The experiment is limited in the sense that only so much mass can be placed on the top wooden block before the syringe is fully compressed. Moreover, objects with masses in the range of approximately 500 g to 1,000 g are needed to cause measurable volume changes. We found that using five small books in this mass range yielded good, reproducible data. Between four and seven data points is recommended as necessary and practical, given the limitations of the apparatus.
 Describe qualitatively what happens to gas pressure as the volume of its container decreases and how this relationship is reflected in your graph.
With respect to a gas held in a container of alterable volume, as the container volume decreases, the gas molecules’ motion is confined to a smaller space, and so the number of collisions between the gas molecules and container walls increases. In turn, the pressure the gas molecules collectively exert against their container walls increases. The graph of our sample data, given below, bears out this relationship. You can see that as volume (xaxis) increases pressure (yaxis) decreases in a nonlinear fashion.
 Recall the introductory demonstration in which you were asked whether the compression of the gas in the syringe entailed doing work on the gas. Did you perform work on the gas when you compressed it or did the gas perform work on the plunger, and your hand indirectly?
Compressing the bicycle pump entailed the exertion of a force over a distance. In other words, you had to use mechanical energy to push down the pump handle. In other words, you performed work to compress the gas.
 Calculate the amount of woek done on or by the gas in your experiment. Hint: The area under a pressure–volume curve is equal to the work done on or by the gas.
The method(s) described in the answer to Prelab Question 8 may be used to determine the amount of work done on or by the gas:
Review Questions for AP^{®} Physics 2
 Why is it necessary to account for atmospheric pressure when carrying out your experiment?
The atmospheric pressure at sea level on any given day is typically about 101.33 kPa. Comparatively, the applied pressure (by the addition of masses such as books) to the syringe plunger necessary to compress the internal gas by an observable volume is calculated to fall approximately in the range of 10–30 kPa. Because pressures in this range are in fact lower than the atmospheric pressure, the atmospheric pressure cannot be considered negligible, but must be considered significant.
Prior to placing an external, nonatmospheric pressure on the syringe plunger, the plunger is kept in a static position (it does not rise or fall) because the internal pressure of the gas is equal to the external atmospheric pressure. The two pressures are said to be in equilibrium, in other words.
 You may or may not have lubricated the syringe prior to carrying out your experiment. How would adding a lubricant, to promote easier movement of the plunger, impact your results?
Any friction between the syringe plunger and the syringe itself must be overcome by the external applied pressure to move the plunger in a downward direction against the internal gas pressure. Of course, the syringe plunger’s rising in the upward direction would also be impeded by friction. It would be difficult to quantify the effects, but it is likely that larger volume changes would be observed as friction decreases, that is, when the system is lubricated.
 Describe two sources of error and the effects each had or may have had on your experimental data.
The system may not be entirely closed. That is, some gas may escape with compression. In this case, the plunger would move further into the syringe and the experimental volume change would be overestimated. Also, there is some random error inherent to reading the volume. Finally, if compression occurred too quickly the internal gas temperature may be raised and the internal pressure raised in direct proportion. As a result, the plunger would not move as far into the syringe and the volume change for a given application of pressure would be underestimated.
 Is it reasonable to neglect the mass of the plunger and top wooden blocks in the calculation of the external pressure, or force, applied to the syringe plunger? Explain.
In order to make this determination, weigh the plunger and calculate the pressure it can exert based on that weight. If the pressure is small compared to the atmospheric pressure and the pressure exerted by the books it can be neglected.
 Explain how you might derive theoretical numbers, or data, to which you can compare your experimental results?
You are applying a pressure and experimentally measuring the volume change. In order to derive theoretical volume changes you must plug the calculated pressure into the simple gas law equation P_{1}V_{1} = P_{2}V_{2}, with the understanding that the P_{1}V_{1} product must remain constant if temperature and the number of moles of gas are held constant. The difference in the volumes V_{1} and V_{2} can be compared to the experimental volume change measured using the syringe.
 How does the assumption that the air in the syringe is an ideal gas impact this experiment?
The kinetic molecular theory assumes that ideal gas molecules have negligible volume relative to their containers and also do not experience intermolecular forces. As container volume increases, gases tend to deviate from ideal behavior because their volume becomes increasingly significant relative to their container and they are able to exert attract forces on each other owing to increased proximity. However, the volume does not become exceedingly small in this experiment and so the deviations from ideal behavior are likely negligible.
References
AP^{®} Physics 1: AlgebraBased and Physics 2: AlgebraBased Curriculum Framework; The College Board: New York, NY, 2014.
