CHEMISTRY 30S – MODULE 2
GASES AND THE ATMOSPHERE
LESSON 3 – Pressure and Volume
OUTCOMES: The student will be able to:

Describe the relationship between the pressure and volume of a confined gas at a
constant temperature using graphed data.

Describe the contribution of Robert Boyle to our understanding of gas behaviour.

Describe the relationship between pressure of a gas and its volume.

Solve problems involving pressure-volume relationships.

Describe some practical applications of Boyle’s Law.
Mathematical relationships are often described as direct or inverse. Give an example of a
direct relationship and an inverse relationship.
PRESSURE & VOLUME ASSIGNMENT
Follow the link below for a simulation of a syringe and a pressure gauge. This simulation
uses a moveable syringe with a maximum volume of 30 mL. The pressure is measured in
psi (pounds per square inch). Remember from our discussion of pressure that 14.7 psi = 1
atm. The starting volume of 30.0 mL is at standard pressure, 1 atm or 14.7 psi. We will
examine how pressure changes as the volume in the syringe is decreased.
Link to site:
http://www.chem.iastate.edu/group/Greenbowe/sections/projectfolder/flashfiles/gasla
w/boyles_law.html
The volume of the tube leading to the pressure gauge is about 5 mL. This is added to the
total volume when it is recorded in the table.
Procedure:
1. Start collecting data drag the plunger to various volumes. The pressure will read on
the gauge and be recorded in the accompanying table.
2. Collect the pressure values for at least 6 distinctly different volumes.
Analyzing the Data
1. Draw a graph of pressure vs. volume (pressure on y-axis and volume on the x-
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axis). Include a title and labels (including units) on the axis.
2. Examine the graph of pressure vs. volume. Based on this graph, decide what
kind of mathematical relationship you think exists between these two
variables, direct or inverse.
Questions
Answer the following questions refering to the data and the graph.
1. How does the pressure change when the volume of the gas was decreased?
Is this a direct or inverse relationship?
2. Using the graph of your data with the best-fit curve, answer the following
questions:
a. If the volume is doubled from 10.0 mL to 20.0 mL, what does your
data show happens to the pressure? Show the pressure values in
your answer.
b. If the volume is halved from 10.0 mL to 5.0 mL, what does your
data show happens to the pressure? Show the pressure values in
your answer.
c. If the volume is tripled from 5.0 mL to 15.0 mL, what does your
data show happens to the pressure? Show the pressure values in
your answer.
3. From your answers to question #2 and the shape of the curve in the plot of
pressure versus volume, do you think the relationship between the pressure
and volume of a confined gas is direct or inverse? Explain your answer.
4. One way to determine if a relationship is inverse or direct is to find a
proportionality constant, k, from the data. If this relationship is direct, k =
P/V. If it is inverse, k = P•V. Based on your answer to Question #2,
choose one of these formulas and calculate k for the pressure-volume pairs
in your data table (divide or multiply the P and V values). If you choose
correctly, the calculated values should be similar. Show the answers in a
separate table.
Method of Evaluation:
This assignment will be worth 10 marks. Evaluation will be based on presentation of data,
interpretation of the data and accuracy of the answers to questions.
In the activity, you observed that there is an inverse relationship between pressure and
volume. That is, decreasing the volume of a gas will cause an increase in pressure at a
constant temperature. This relationship was first described by Robert Boyle (1627 – 1691)
in 1662 and is commonly called Boyle’s Law
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BOYLE’S LAW
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You have likely noticed Boyle’s Law when you squeezed a balloon or sat on an air
mattress. When you decreased the volume by squeezing, the air in the balloon or air
mattress pushes back harder.
The experiment that Boyle used to study the relationship
between pressure and volume involved filling a closedended tube, called a J-tube, with mercury, trapping
gases in the closed end.
The more mercury he added, the smaller the height of
the gas at the end of the tube. He determined that the
more mercury meant greater force or pressure on the
gas.
A practical example of Boyle’s Law is drawing liquid
into a syringe. Pulling on the plunger increases the volume of the gas in the syringe. The
increased volume decreases the pressure inside the syringe. As a result, the pressure on the
surface of the liquid (air pressure) is larger, forcing the liquid into the syringe. Pushing on
the syringe reduces the volume of trapped gas, increasing its pressure. The pressure inside
the syringe is greater than the air pressure and the liquid is forced out of the syringe.
Explaining Boyle’s Law
We can use the kinetic molecular theory to explain Boyle's Law works. Decreasing the
volume of a sample of gas, while keeping the temperature constant, would result in the
same number of molecules squeezed into a smaller space. This will increase the number
collisions of the gas molecules with the sides of the container. Imagine trying to fit a room
full of people into a closet. If the people continue to try and move around they will be
bumping into the walls more frequently. The increased frequency will result in a higher
force, or pressure, on the walls of the closet than the walls of the room. An increased
number of collisions means an increased pressure
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Now, take the people out of the closet. This is like increasing the volume of a sample of
gas at a constant temperature. Increasing the volume reduces the number of collisions of
the gas molecules with the sides of the container.
According to the kinetic molecular theory, we should be able to compress a gas down to a
volume of zero. A gas that behaves in this way is called an ideal gas. Ideal gases do not
have any forces of attraction so they do not condense when they are compressed. The
particles of ideal gases do not have any volume, so you would be able to compress them to
a volume of zero. The concept of an ideal gas was used to simplify the relationship
between pressure , volume and other factors. These behaviours general hold at low
pressures and higher temperatures where condensation is not a factor. For the sake of this
course, we will assume that all gases are ideal gases.
Practical Examples:
The action of the diaphragm
during breathing demonstrates
Boyle’s Law. The diaphragm is a
muscle that is located just below
the lungs. When we inhale, the
diaphragm moves downward
allowing the lungs to increase in
volume. (Fig. 1)
The increased lung volume decreases the pressure in the chest cavity so that it is less than
the air pressure. The lower pressure forces air to rush into the lungs to equalize the
pressure in the chest cavity. When we exhale the diaphragm moves upward, decreasing the
volume of the chest cavity (Fig. 2). The decreased volume increases the pressure in the
lungs until the pressure in the lungs is greater than the air pressure. The increased pressure
forces the air out of the lungs. When we get a sudden blow to our abdomen, we say we get
the wind knocked out. What actually happens is the diaphragm is briefly paralyzed,
making us temporarily unable to breathe.
Solving Problems Using Boyle’s Law
In your activity, you determined that the product of pressure and volume, at a constant
temperature, results in a constant value. You also determined that a plot of P versus V
results in a inverse curve. Both of these confirm that pressure and volume changes are
inversely related.
When solving problems involving pressure-volume relationships, we must create a ratio of
pressure to volume that would result in the change we would predict. Essentially we ask
ourselves whether the pressure or volume should increase or decrease and multiply by the
ratio that will produce that change.
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Example 1.
2010
If 3 L of gas is initially at a pressure of 1 atm, what would be the new
pressure to cause the volume of the gas to become 0.5 L?
Solution
Decreasing the volume from 3 L to 0.5 L should result in an increase in
pressure. There are two possible volume ratios:
Only one of these ratios, when multiplied by the pressure,
will result in a higher pressure: the first ratio.
6 atm of pressure will change 3 L of a gas at 1 atm to 0.5 L.
Example 2.
A syringe contains 20 mL of a gas at 100 kPa. The pressure in the syringe is
changed to 25 kPa. What is the new volume of the gas?
Solution -- 80 mL
Boyle’s Law Practice Questions
Answer the following questions. Remember that showing all your work is good practice.
1. Gas is placed into a syringe until the pressure is 45.0 kPa. What is the new pressure
if:
a) the volume in the syringe is doubled?
b) the volume in the syringe is tripled?
c) the volume is one third its original volume?
2. 100.0 mL of gas is placed into a syringe. What is the new volume if:
a) the pressure is doubled?
b) the pressure is tripled?
c) the pressure is one quarter the original pressure?
3. Change the following from the initial conditions to the new conditions:
a) 100.0 mL oxygen gas at 10.50 kPa is changed to 9.91 kPa
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b) b) 50.0 cm helium at 97.3 kPa is changed to 102.5 kPa
c) 25.0 mL nitrogen at 0.990 atm is changed to 0.751 atm
d) 745 torr of hydrogen in 0.550 L is changed to 0.700 L
e) 1.40 atm of carbon dioxide in 1.32 L is changed to 0.705 L
f) 525 mL neon at 49.3 kPa is changed to 845 mL
g) 0.150 L carbon monoxide at 635 mmHg is changed to 895 mmHg
4. A sample of gas under a pressure of 822 kPa has a volume of 312 cm3. The
pressure is increased to 948 kPa. What volume will the gas occupy at the new
pressure, assuming the temperature does not change?
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5. A sample of neon has a pressure and volume of 467 kPa and 150 cm3. If the
pressure is decreased to 300 kPa, what volume will the gas occupy? Temperature
is kept constant.
6. The volume of a gas is 204 cm3 when the pressure is 925 kPa. At a constant
temperature, a change in pressure causes the volume of the sample to change. If
the new volume is 306 cm3, what must the pressure have been changed to?
Answer Key
1. a) Doubling the volume should decrease the pressure by one half. The new pressure
will be one half 45.0 kPa or 22.5 kPa.
b) If the volume in the syringe is tripled, the pressure should decrease to one third
of 45.0 kPa or 15.0 kPa.
c) If the volume is one third its original volume the pressure should increase by
three times or 135 kPa.
2. a) If the pressure is doubled, the volume of the gas should decrease to one half, or
50.0 mL.
b) If the pressure is tripled, the volume should be one-third, or 33.3 mL.
c) If the pressure is one quarter the original pressure, the volume should be four
times the original volume or 400.0 mL.
3. a) The type of gas does not affect the pressure or volume. If the pressure decreases,
the volume should increase. – 106 kPa
b) If the pressure increases, the volume should decrease. 47.5 cm3 (mL)
c) 33.0 mL
d) 948 torr
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e) 2.62 atm
f) 30.6 kPa
g) 0.106 L.
4. V2 = 270.5 cm3
5. V2 = 233.5 cm3
6. P2 = 616.7 kPa
EXTRA QUESTIONS
Question(s):
1. A balloon has1.2 L of a gas is at 1.1 atm. What will be the new volume of the
balloon if the balloon is placed in a partial vacuum with a pressure of 0.35 atm?
(1.5 marks)
2. What is the pressure of 725 mL of a gas at 100.2 kPa if it’s volume is changed to
125 mL? (1.5 marks)
3. Explain why weather balloons are not completely filled with gas before they sail
into the upper atmosphere. (2 marks)
4. The maximum lung capacity of an average adult is about 4-6 L. A scuba diver takes
a breath of about 2.1 L of air at a depth of 30 m where the pressure is 405 kPa. If
the diver holds his/her breath while rising to the surface, where the pressure is 102
kPa, what is the volume of air in the lungs? What is the likely result? (2 marks)
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