Name ___________________________________Chem 161, Section: _______Group Number: ______
ALE 21. Ideal Gases and the Gas Laws
(Reference: Chapter 5 in Silberberg 5th edition)
How are the volume, temperature, and pressure of a gas related?
The Model: Charles’ Law
Charles’ Law: The relationship between the volume and temperature of an ideal gas. Condition: the
pressure and the number of moles of the gas are constants.
Place balloon in
refrigerator.
Balloon filled with gas at
room temperature.
Balloon filled with same amount
of gas in a refrigerator.
An ideal gas is a hypothetical gas consisting of identical particles with zero volume, with no intermolecular
forces. Additionally, the constituent atoms or molecules undergo perfectly elastic collisions with the walls of
the container. An ideal gas can consist of molecules (e.g. carbon dioxide molecules, CO2) or atoms (e.g. neon
atoms, Ne). Real gases do not exhibit these exact properties, although many gases behave as ideal gases at
high temperatures and low pressure. A good way of remembering the four properties that constitute an ideal
gas is the acronym 'PRIE', which stands for:
 Point masses (the volume of a gas particle essentially zero—if infinitely compressed, all the
molecules of an ideal gas would occupy a single point of insignificant volume.
 Random motion (constant random motion of gas particles)
 Intermolecular forces (there are NO intermolecular forces)
 Elastic collisions (all collisions are totally elastic)
Key Questions
1. When the pressure and the number of moles of a gas are constants, is the relationship between volume
and temperature a direct relationship or an inverse relationship?
ALE 21. Ideal Gases and the Gas Laws
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2. The volumes of three
different ideally-behaving
gases (“A”, “B”, and “C”)
are monitored as a
function of their
temperatures. Use a
straightedge to determine
the temperature at which
each gas would have a
volume of 0 L. (Confirm
this temperature with
your instructor or your
textbook.)
3. Gas A, gas B, and gas C all share a common point (ordered pair of T and V coordinates) in the plot in
Question 2. What is this point, and what is the relevance of that point?
The Model: Absolute Temperature
Whenever the temperature of a gas is needed, it ought to be expressed on the absolute
temperature scale. The absolute temperature is defined so that the gas has a volume of zero when the
absolute temperature is 0 K. (The unit of temperature in the absolute scale is called Kelvin, K.) You convert
between the temperature in C and K using the formula:
T (K) = t (C) + 273.15
Key Questions
4. A mathematical way to represent Charles’ Law is
V V
T T
1
2
1
2
where the subscript “1” identifies the initial volume and temperature of the gas and the subscript “2”
identifies the final volume and temperature of the gas.
a. On a mathematical basis, explain why the temperatures in the above equation must be expressed in
Kelvin and not in Celsius. (Hint: What if the temperature was 0 oC or -22 oC?.)
b. Under what conditions may the above equation be used? (Hint: You may need to refer back to The
Model: Charles’ Law—what two factors must not change?)
ALE 21. Ideal Gases and the Gas Laws
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Exercise
A. An ideally-behaving gas has a volume of 18.25 L at a temperature of 15.9 C. The temperature of the gas
is raised to 40.7 C while the number of moles and the pressure of the gas are kept constant. What is the
new volume of the gas (in L)? Show work using units and sig figs. Circle your answer!
The Model: Boyle’s Law
Recall from ALE 20…
P
F
A
Where…
P is pressure (in kPa, kilopascal)
F is force (in N, Newton)
A is the area to which the force is applied (in m2).
Common Units of Pressure: 1 atm = 760 mm Hg = 760 torr = 101.325 kPa = 14.70 lb/in2
Boyle’s Law: The relationship between the pressure and the volume of an ideal gas. Conditions: the
temperature and the number of moles of the gas are constants.
100
kg
1.00 mol of ideal gas in cylinder with one
movable wall (piston) at a temperature of
25.0 C under a pressure of 1 atm
possesses a volume of 24.466 L.
ALE 21. Ideal Gases and the Gas Laws
200
kg
1.00 mol of ideal gas in the same cylinder at the
same temperature possesses a volume of 12.233 L.
Page 3 of 6
Key Questions
5. Does Boyle’s Law describe a direct relationship or an inverse relationship between the pressure and the
volume of an ideal gas? Explain.
6. A mathematical way to represent Boyle’s Law is
P1 V1 = P2 V2
where the subscript “1” identifies the initial volume and pressure of the gas and the subscript “2”
identifies the final volume and pressure of the gas. When would it be inappropriate to use the above
equation to relate an ideal gas’s pressure to its volume—i.e. what two factors must not change?
Exercise
B. An ideal gas has a volume of 10.8 L at a temperature of 25.0 C and a pressure of 1.60 atm. The pressure
of the gas is reduced to 370.0 mmHg, but the temperature and number of moles of the gas are kept
constant. What is the new volume of the gas (in L)? Show work using units and sig figs. Circle your
answer!
The Model: STP and the Combined Gas Law
Standard Temperature and Pressure (STP): T = 0 C = 273.15 K
P = 1 atm
At STP, 1 mole of an ideal gas has a volume of 22.41 L.
When there is a change in more than just two of the variables (P, V, T ), it is appropriate to use the combined
gas law:
P1 V1
P V
T1
T2
2 2
 = 
ALE 21. Ideal Gases and the Gas Laws
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Key Questions
7a. Draw a line from “Charles’ Law” and from “Boyle’s Law” to the correct description of each
gas law:
direct relationship between V and P
Charles’ Law
direct relationship between V and T
inverse relationship between V and P
Boyle’s Law
inverse relationship between V and T
b. Explain in a couple of sentences that the combined gas law is consistent with both Charles’
Law and Boyle’s Law.
8. Prove that when the temperature remains constant, the combined gas law becomes Boyle’s Law.
9. Prove that when the pressure remains constant, the combined gas law becomes Charles’s Law.
Exercises
You have discovered several new mathematical relationships among gases. Now is your chance to practice
using these equations! Show work using units and sig figs. Circle your answers!
C. Determine the temperature (in C) at which 1.00 mole of an ideal gas will have a pressure of 870.0
mmHg when its volume is 14.5 L. Hint: the molar volume of a gas at S.T.P might be useful!
D. At constant temperature, the volume of a gas expands from 4.0 L to 8.0 L. If the initial pressure was 120.
kPa, what is the final pressure?
ALE 21. Ideal Gases and the Gas Laws
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E. At constant pressure, a gas is heated from 250. K to 500. K. After heating, the volume of the gas was
12.0 L. What was the initial volume of the gas? Notice: as the temperature doubled, what happened to
the volume?
F. The volume of a gas was originally 2.5 L; its pressure was 104 kPa and its temperature was 270. K. The
volume of the gas expanded to 5.3 L and its pressure decreased to 95 kPa. What is the temperature of the
gas?
G. At constant temperature, if you increase the volume by a factor of two (doubling the volume), the
pressure _______________ by a factor of ______________.
increases or decreases
what number
H. What is the effect of the following on the volume of 1.00 mol of an ideal gas? The pressure changes from
760. torr to 202 kPa and the temperature changes from 37.0 oC to 155 K (moles of gas remain constant)
Does the volume of the gas change? If it does, by what factor does the volume of the gas increase or
decrease? Show work using units and sig figs. Circle your answer!
ALE 21. Ideal Gases and the Gas Laws
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