Boyle’s Law
Objectives
Determine the effect of volume on the pressure of a closed system containing a fixed amount of
molecules at a constant temperature. Through this investigation students will

Show that an inverse relationship exists between pressure and volume for a
gas at a constant temperature.

Apply Boyle’s law PV = k and P1V1 = P2V2.

Differentiate between real and ideal gases.
Materials and Equipment
For each student or group:
 data collection system
 rubber tubing1, 1.5cm long
 absolute pressure sensor
 quick-release connector1
 syringe1, 20mL
 glycerin2, 2 drops
Background
The kinetic molecular theory explains that the particles in all forms of matter are in constant
motion. In solids and liquids, the atoms or molecules are moving and are positioned very close to
each other. In gases, the atoms or molecules are also moving, but they are positioned very far apart
from each other and thus have properties very different from those of solids or liquids.
The kinetic molecular theory of gases makes a few basic assumptions. First, it assumes that gases
are made up of small, hard particles that are very far apart from each other. Because the particles
are so far apart, their volume is considered insignificant and there are no attractive or repulsive
forces between the gas particles. The large amount of empty space between the gas particles
explains why gases, unlike solids or liquids, are compressible. The lack of attractive or repulsive
forces explains that gas particles take the shape and volume of containers they occupy.
The second assumption is that gas particles are in constant, random motion. The gas particles
move independently from one another in straight lines and only change direction when they collide
with other particles or the walls of a container. Gas pressure is related to how often and how hard
gas molecules collide into surfaces.
The third, and final, assumption is that the collisions between gas particles are elastic. This means
that no energy is lost when particles collide. The total kinetic energy remains the same before and
after collisions. A gas that behaves according to all of the assumptions is called an ideal gas.
Although there is no such thing as an ideal gas, at many conditions of temperature and pressure
real gases behave ideally.
There are four variables that are used to describe a gas. These variables are volume (V), pressure
(P), temperature (T) and number of moles (n).
Robert Boyle discovered the mathematical relationship between gas pressure and volume. Boyle’s
law states that for a given number of gas molecules at constant temperature, the volume of the gas
varies inversely with pressure. Because it is an inverse relationship, the product of the pressure
(P) and volume (V) is constant (k); as one variable increases, the other must decrease. Boyle’s law
can be represented by the following two equations:
1) PV = k
2) P1V1 = P2V2
When a given number of gas molecules at constant temperature are forced into a smaller volume
the pressure will increase. The increase in pressure is due to an increase in collisions between the
gas particles and the container. The number of collisions increases because it takes less time for
the particles to travel across a smaller space.
Boyle’s law, like all the gas laws, holds true only for ideal gases. At higher pressures and lower
volumes real gases behave less ideally and therefore do not follow Boyle’s law as well. This is
because the assumption that gas particles are so far apart that their volume is considered
insignificant no longer holds true. The closer the atoms are forced together, the more important
their volume becomes. As the gas molecules become even closer, attractive forces also begin to take
effect. This is what enables gases to condense into liquids.
Lab Safety
 Follow all standard laboratory safety procedures.
 Avoid over-compressing the air in the syringe in order to minimize the risk of injury or
damage to the equipment.
Sequencing Challenge
Procedure with Guided Inquiry
While viewing a
data table display,
connect a syringe
with 20mL of air to
the absolute
pressure sensor.
Connect the
absolute pressure
senor to the data
collection system
and set up manual
sampling.
Calculate the
average pressure at
each volume and
use the calculated
averages to draw
conclusions about
the relationship
between pressure
and volume.
Collect two
additional runs of
absolute pressure
data at each
volume.
Record the
absolute pressure at
20mL, 18mL,
16mL, 12mL,
10mL, 8mL, and
6mL.
After you complete a step (or answer a question), place a check mark in the box () next to that step.
Collect Data
8.
 Make sure your data collection system is in manual mode and you are viewing the table
display. Start a new data set.
9.
 Set syringe volume to 20mL and record the pressure in the column labeled “run 1” in
the table below.
10.
 Repeat step 9, but set the syringe volumes to 18mL, 16mL, 14mL, 12mL, 10mL,
8mL, and 6mL.
Data Table
Volume
Pressure (kPa)
run 1
run 2
run3
20mL
18mL
16mL
14mL
12mL
10mL
8mL
6 mL
11.
 Stop the data collection.
12.
 Remove the syringe from the absolute pressure sensor using the quick-release
connector. Set the syringe plunger to 20mL and re-connect the syringe to the absolute
pressure sensor. Start a new data set and record the pressure at each of the indicated
volumes in the next run column in the table above.
13.
 Stop the data set. Repeat step 12 so that you have three sets of collected data.
14.
 Explain when and why it becomes difficult to depress the syringe.
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15.  Why is it important to collect more than one set of data?
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16.
 Save your data file and clean up your lab station according to the teacher’s instructions.
Data Analysis
Note to Editor: Erase the teacher tips in the student versions.
1. Calculate the average pressure for each volume. Use the average pressure to
calculate the constant “k” for each run of data (PV=k). Use the table below to
show your work.
Volume × Pressure = k
V
20mL
18mL
16mL
14mL
12mL
10mL
8mL
6mL
P
P
P
▬
Run
Run
Run
P
1
2
3
(Average)
(kPa) (kPa) (kPa)
(kPa)
▬
V×P= k
(kPa•mL)
2. What is the average value of “k” for all volumes?
3. Graph average pressure versus volume.
This graph should be titled average pressure versus volume. The x-axis should be
labeled volume (mL) and the y-axis should be labeled average pressure (kPa).
4. What does this graph tell you?
Analysis Questions
1. Are pressure and volume directly proportional or inversely proportional? How
do you know?
2. Does your data support Boyle’s law that PV = k (pressure × volume = constant)?
Explain any discrepancies in your data.
3. What region of the pressure versus volume graph does air behave like an ideal gas? Like a
real gas? What is the difference between an ideal and a real gas?
4. What is the constant (k) for air? (hint: look at question #2 above)
5.
Calculate the pressure you would expect at 15.0 mL. Show your work.
Synthesis Questions
1. Explain why it is possible to write Boyle’s law as both PV = k and P1V1 = P2V2.
2. How could you change the experimental design to get results more consistent
with an ideal gas?
3. A helium balloon is released into the atmosphere. As it rises, atmospheric pressure
decreases. What do you expect will happen to the volume of the balloon?
4.
A cylinder containing 250 mL of a gas has a pressure of 350 kPa. If the gas was
compressed to a volume of 45 mL what would the pressure change to?
Multiple Choice Questions
Select the best answer or completion to each of the questions or incomplete statements below.
1. What conditions will cause the volume of a gas to decrease?
A. An increase in the amount of gas.
B. An increase in temperature.
C. An increase in pressure.
D. A decrease in pressure.
2. At constant temperature the relationship between the volume (V) of a gas and its
pressure (P) is
A. V= (constant)P.
B. P = (constant)V.
C. PV = constant
D. V/P = constant
3. Which graph shows the relationship between the pressure and volume of nitrogen
gas at a constant temperature?
A.
B.
C.
D.
4. At room temperature, air behaves like an ideal gas at
A. low pressures
B. high pressures
C. all pressures
D. air never behaves ideally
5. A gas contained in a 3.0 L cylinder has a pressure of 120 kPa. What will the new
volume be if the pressure is increased to 240 kPa?
A. 1.5 L
B. 3.0 L
C. 4.5 L
D. 6.0 L
Key Term Challenge
Fill in the blanks from the list of randomly ordered words in the Key Term Challenge Answers section.
Gases are able to be _____________ into smaller volumes because there is _____________ space
between gas particles. Solids and liquid, on the other hand, have fixed _____________ and cannot be
compressed. When a fixed amount of gas is forced into a smaller volume the pressure of the gas
will _____________. This happens because volume is _____________ proportional to pressure. This
relationship is known as _____________ law.
An ideal gas is composed of a collection of perfectly hard _____________ that are so far apart that
their _____________ is assumed to be insignificant. The gas particles move in constant
_____________ motion and only change direction when they _____________ with another particle or
the walls of the container. The collision of gas particles with a surface creates _____________. Real
gases can behave ideally at certain temperatures and pressures. However, real gases are not ideal
because they actually do have volume. Their volume cannot be considered insignificant at
_____________ pressures.
Key Term Challenge Word Bank
Paragraph 1
Paragraph 2
a lot of
high
very little
low
Boyle’s
spheres
Avogadro’s
pressure
volumes
volume
increase
temperature
decrease
ordered
indirectly
random
directly
collide
compressed