Ideal Gas Law Activity
This worksheet will take you through an exploration of the properties of an ideal gas:
temperature, pressure, and microscopic representation. It will build on what you have
been learning in class about collisions, forces, and energy, and on the following model of an
ideal gas.
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


Ideal Gas Model:
The molecules move in random directions in straight lines until they hit the container
walls or each other. The collisions with the wall are responsible for the pressure of the
gas.
The gas molecules do not interact with each other except when they collide. Because
the molecules are very small (almost point particles), the molecules only very rarely
collide with each other.
The temperature of the gas is proportional to the average kinetic energy of the gas:
2 𝐾
1
2
𝑇 = 3 𝑘𝑎𝑣𝑒 = 3 𝑚𝑣𝑟𝑚𝑠
where kB=1.38 x 10 -23 J/K is the Boltzmann constant and vrms is
𝐵
essentially a gas molecule’s average speed.
Lastly, we give you a table with some typical values of kinetic energy (KE), average speed
(vrms), and change in gravitational potential energy at y=3m (Ug) for hydrogen and oxygen:
Gas
Mass (kg)
40 C = 104 F= 313 K
-20 C = - 4 F = 253 K
Hydrogen
3.2 x 10 – 27
KE= 6.48 x 10 -21 J
Vrms= 2010 m/s
KE= 5.24x10-21 J
Vrms= 1810 m/s
Oxygen
5.25 x 10 -26
KE= 6.48 x 10 -21 J
Vrms= 497 m/s
KE= 5.24x10-21 J
Vrms= 447 m/s
Ug at y=
3m
9.4 x 10-26 J
Boiling
point
-252 C
1.5 x 10-25 J
-182 C
1. Role of gravity in an ideal gas
Consider the following conversation (but do NOT respond yet!):
Natalie “This ideal gas model must be wrong. It says that gas molecules move in
straight lines – they are ignoring gravity that would pull the molecules back down.
When gases get colder, the molecules will fall to the bottom of the container because of
gravity.”
Veronica “But look at those velocities - hydrogen moves at 1810 m/s which is over
4000 mph. Gravity is not important if you are moving that fast.”
Dan Young and Dawn Meredith 11/2014
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a. Your group agrees that both Natalie and Veronica have a point. To see if gravity
matters, use conservation of energy to find out how much smaller the kinetic energy
is at the top of a 3 m room for hydrogen at T=40 oC. (Use the data in the table.)
b. Do the same calculation, but at T=-20oC, to see how much change there is at the
colder temperature.
c. Finally, find out at what temperature the kinetic energy decreases by half at the top
of the room (assuming the gas remains a gas at this temperature).
i.
Given the question, what is the kinetic energy at the bottom compared
to the gravitational potential energy at the top?
ii.
Given the kinetic energy, what is the temperature?
d. Given your calculations, how would you respond to Natalie and Veronica?
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Ideal Gas Law Activity
2. Pressure and Collisions
a. Play with the beach ball/bouncy ball demo to investigate how collisions of the small balls
against the larger ball affect the motion of the larger ball.
i.
Using the demo, what factors (e.g. velocity of the bouncy balls) would change the net
collisional force on the beach ball?
ii.
Given the demo, which of the following equations best describes the force due to the
collision (m is mass of the small ball, v = velocity of small ball)
a. F=m
b. F=v
c. F=mv
d. F=m/v
e. F=v/m
f. Something else:
iii.
Using the demo, describe and sketch a situation where four bouncy balls hit the
beach ball, but the beach ball remains stationary. What is the net force on the beach
ball in this case (to the left, to the right, or zero)?
iv.
Using the demo, describe and sketch a situation where four bouncy balls hit the
beach ball and make the beach ball move to the left fairly quickly (without hurting
people!!). What is the net force on the beach ball in this case (to the left, to the right,
or zero)?
Key Idea: Ideal gas molecules exert pressure (pressure=force/area) on their containers by
colliding with the walls of the container (just as the bouncy balls collided with the beach
ball). Increasing the force of the collisions and the frequency of collisions will increase the
pressure on the walls.
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Ideal Gas Law Activity
b. For each of the following instances, draw the new situation described in the box
provided, circle the appropriate answer, and discuss how the strength and frequency of the
collisions against the chamber walls will change. The length of the arrow represents the
velocity where longer arrows indicate a larger velocity.
Original situation, an ideal gas in a container:
Increasing the number of gas molecules will (Increase/Decrease/Not Change) the force
of the collisions and will (Increase/Decrease/Not Change) the frequency of the collisions.
Therefore, the pressure will (Increase/Decrease/Not Change). Explain your reasoning.
Increasing the volume of the container will (Increase/Decrease/Not Change) the force of
the collisions and will (Increase/Decrease/Not Change) the frequency of the collisions.
Therefore, the pressure will (Increase/Decrease/Not Change). Explain your reasoning.
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Ideal Gas Law Activity
Increasing the temperature of the gas molecules will (Increase/Decrease/Not Change)
the force of the collisions and will (Increase/Decrease/Not Change) the frequency of the
collisions. Therefore, the pressure will (Increase/Decrease/Not Change). Explain your
reasoning.
Changing the type of gas from oxygen to helium (a lighter gas) will
(Increase/Decrease/Not
Change)
the
force
of
the
collisions
and
will
(Increase/Decrease/Not Change) the frequency of the collisions. Therefore, the pressure
will (Increase/Decrease/Not Change). Explain your reasoning.
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Ideal Gas Law Activity
c. Consider the following conversation between two students who have also been working
through the ideal gas law worksheet:
Nathan: “If we have two containers where everything is the same (volume, temperature and
number of particles) but one is hydrogen and one is oxygen, the pressure in the hydrogen case
must be smaller because they are lighter.”
Robert: “But wait! The ideal gas law says the pressure is the same (P=nRT/V). But something
must be different if the masses are different...”
Do you agree with Nathan, Robert, or neither? How can you make their reasoning more
complete based on your previous answers?
Do your other answers also agree with the ideal gas law?
Case
Number increases
Volume increases
Temperature
increases
Your answer
Ideal gas law
Summary and Preview: In this section, you explored the idea of pressure as collisions of
gas molecules against container walls where both the magnitude and frequency of
collisions matter, and confirmed that this molecular description is consistent with the ideal
gas law. In the next section you will apply these ideas to a situation that includes a vacuum.
3. Vacuums and Partial Vacuums
A vacuum is defined as a region with no molecules whatsoever. Sketch a vacuum in the
chamber provided: ;-)
Vacuum
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Ideal Gas Law Activity
True vacuums do not exist. However, partial vacuums exist, where the number of
molecules is far less than typical. For reference, here is a table with values of particle
densities and pressures at various regions inside and above the Earth.
Location
Gas at standard temperature and pressure
Summit of Mount Everest
Upper atmosphere
Inside a physics experiment
Region between Earth and Sun
Number/cubic
centimeter
2.5x1019
1017
1010
106
11
Pressure
100,000 Pa
33,000 Pa
0.1 Pa
1x10-8 Pa
~0 Pa
a. A movable wall is set up as shown below between two chambers of gas, one has the
density of molecules at standard pressure and temperature and the other had the
density of molecules at Mount Everest, as given in the table. The temperature and
volume of both gases is the same. Consider the following conversation:
STP Molecules
Mount Everest Molecules
Emily: “The wall will move right because vacuums (or partial vacuums) want to be filled.”
Ashley: “But ‘wanting’ doesn’t make it happen, forces make things happen. I’m thinking
about collisions – there are collisions on both sides of the wall, so the wall will not move.”
Henry: “Everyone knows vacuums suck – that’s how they work! Even partial vacuums
suck.”
How would you respond to each of these students? How can you make their reasoning
more complete and correct?
Emily:
Ashley:
Henry:
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Ideal Gas Law Activity
b. This worksheet has been about pressure, but since pressure=force/area, it is about
forces as well. Given the sketch of the box above, draw a free body diagram of the wall,
being sure to get the relative sizes of the forces correct (you only need to draw the
horizontal forces).
c. Given that the wall will begin to move rightward, under what conditions, if at all, will
the wall feel a zero net force?
d. Finally, let’s consider a similar box turned on its side, with unspecified pressures above
and below the moveable wall. If the moveable wall has a mass, in order for the wall to
be stationary, is P1 greater than, equal to, or less than P2? Justify your answer in terms
of the forces on the wall. From your answer to this question – do pressures always
“want to be equal”?
P1
P2
4. Summary
Summarize for yourselves the key ideas of this worksheet.
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Ideal Gas Law Activity