Chemistry
Notes and Practice Problems: Gas Laws
Chapter 14
Shuster
Section 14.1 Lecture Notes
The Gas Laws – Kinetic Molecular Theory and Boyle’s Law
Kinetic Molecular Theory



Gas particles behave differently than those of
liquids and solids.
The kinetic molecular theory provides a model
that is used to explain the properties of solids,
liquids, and gases in terms of particles that are
always in motion and the forces that exist
between them.
The kinetic molecular theory assumes the
following concepts about gases are true:
1. Gas particles do not attract or repel
each other
 Gases are free to move within
their containers without
interference from other
particles
2. Gas particles are much smaller than
the distances between them; this is
why gases are compressible
 Gas particles themselves have
virtually no volume
 Almost all the volume of a gas
is empty space
 Gases can be compressed by
moving gas particles closer
together because of this low
density of particles
3. Gas particles are in constant, random
motion and they quickly become
thoroughly mixed in a closed
container – this phenomena is called
dispersion
 Gas particles spread out and
mix with each other because
of this motion
 The particles move in straight
lines until they collide with
each other or with the walls of
their container
4. Collisions between gas particles or the
sides of their containers are
completely elastic; there is no kinetic
energy lost
 Such collisions are completely
elastic
 As long as the temperature
stays the same, the total
kinetic energy of the system
remains constant
5. All gases have the same average
kinetic energy at a given temperature
a. As temperature increases, the
total energy of the gas system
increases
b. As temperature decreases,
the total energy of the gas
system decreases
The Nature of Gases
The assumptions of the Kinetic Molecular Theory are
based on 4 variables:
1.
2.
3.
4.
These four variables work together to determine the
behavior of gases, and when one variable changes it
affects the other three. The explanations as to what
happens when one of the variables changes is
explained by the Gas Laws
The Gas Laws
There are five gas laws that we will study:
1.
2.
3.
4.
5.
Boyle’s Law
Charles’ Law
Gay-Lussac’s Law
Combined Gas Law
Graham’s Law of Diffusion
#1 – Boyle’s Law

Boyle’s Law states that the volume of a gas
varies inversely with the pressure, provided
the temperature and number of air particles
do not change


Boyle’s Law explains why we wear oxygen
masks at high elevations and why our ears pop
when we go up in an airplane:
Air pressure is measured using several
different systems which are all based on the
pressure the atmosphere exerts at sea level,
which is the atmosphere (atm).
1. psi –
2. kPa –
3. inHg –
4. mmHg –
Standard Temperature and Pressure (STP)
STP ensures uniformity worldwide in the
measurement and calibration of pressure, and has
been established as ________atm @ ________°C
Pressure System Measurements:
@STP, one atmosphere = ________ psi
@STP, one atmosphere = ________kPa
@STP, one atmosphere= ________inHg
@STP, one atmosphere = ________mmHg
Boyle’s Law Calculations
Boyle’s Law is an inverse relationship: increase the
pressure, decrease the volume.
The formula is:
A typical Boyle’s Law Problem would look like this:
EXAMPLE: If a gas occupies 2 L at 1 atm, what will be
the volume of this gas at 4 atm?
P1V1 = P2V2
(2 L)(1atm) = (4 atm)(V2)
= V2
The greatest difficulty students have with Boyle’s Law is moving from one pressure system to another. Look at the
following problem. Notice that there are two different pressure systems (kPa and psi). The system must have the
same unit on each side of the equation, so you must change either kPa or psi.
EXAMPLE: A gas occupies a volume of 5 L at 100 kPa. What volume will it occupy at 100 psi?
100 psi x 101.3 kPa = 689.1 kPa
14.7 psi
P1V1 = P2V2
(5 L)(100 kPa) = (689.1 kPa)(V2)
.752 L = V2
Boyle’s Law Practice I
1.
Convert 202.6 kPa to psi.
2.
Convert 500 mmHg to kPa.
3.
Convert 100 psi to mmHg.
4.
Convert 3 atm to mmHg.
5.
Convert 50 psi to mmHg.
6.
If a gas occupies 2.56 L at 1 atm, what will be the volume of this gas at 2 atm?
7.
If 600 mL of a gas is at a pressure of 9 atm, what will be the volume at 3 atm?
8.
If 200 ml of O2 is collected at a pressure of 5 atm, what volume will this gas occupy at STP?
9.
A gas occupies a volume of 500 mL at 101.3 kPa. What volume will it occupy at 400 kPa?
10. A gas occupies one liter at STP. How much pressure (atm) would be required to decrease the volume to 100 mL?
11. If a gas occupies 1500 mL at 303.9 kPa, how many atmospheres of pressure will be needed to reduce its volume to 500
mL?
12. If the pressure on 500 mL of a gas changes from 800 mmHg to 120 psi, what will be the new volume?
Boyle’s Law Practice II
1.
Convert 890 mmHg to psi. (17.2 psi)
2.
Convert 500 kPa to atm. (4.94 atm)
3.
Convert 100 psi to mmHg. (5170 mmHg)
4.
If a gas occupies 2 L at 1 atm, what will be the volume of this gas at 4 atm? (.5L)
5.
If 500 mL of a gas is at a pressure of 6 atm, what will be the volume at 3 atm? (1000 mL)
6.
If 100 mL of O2 is collected at a pressure of 920 mmHg, what volume will this gas occupy at STP? (121 mL)
7.
A gas occupies a volume of 5 L at 100 kPa. What volume will it occupy at 100 psi? (.725 L)
8.
A gas occupies one liter at STP. How much pressure would be required to decrease the volume to 500 mL? (2 atm)
9.
If a gas occupies 4.2 L at 303.9 kPa, how many atmospheres of pressure will be needed to reduce its volume to 500 mL?
(25.2 atm)
10. If the pressure on 2 L of a gas changes from 800 mmHg to 120 psi, what will be the new volume? (.26 L)
Section 14.2 Lecture Notes
Charles’ Law , Gay-Lussac’s Law, Avogadro’s Principle and Molar Volume of Gases
Charles’ Law
States that if the pressure of a gas is held constant,
the volume of the gas will increase as the temperature
is increased




Explained by the Kinetic Molecular Theory – as
gas molecules are heated they move faster
Gas molecules strike the sides of the container
more often and increasing the volume;
provided the temperature is held constant
The formula is:
The relationship between temperature and
pressure is __________________
Charles’ Law Calculations
The difficulty with Charles’ Law problems is that since the
law is based on molecular motion, there is only a direct
proportion if the Kelvin scale is used.
The Kelvin scale is based on absolute zero, which is the
temperature that all molecular activity stops.
Therefore, if the temperatures in a Charles’ Law problem
are given in Celsius, they must be converted to Kelvin.
A typical Charles’ Law Problem looks like this:
EXAMPLE: A gas sample at 40°C occupies a volume of 2.32
L. If the temperature is increased to 75°C, what will the
volume be assuming the pressure remains constant.
***The first thing that has to happen is the Celsius
temperatures must be changed to Kelvin.
40°C + 273 = 313 K
75°C + 273 = 348 K
Then substitute the formula:
V1 = V2
T1 T2
2.32 L = V2
313 K 348 K
V2 = 2.58 L
Charles’ Law Practice I
1. Convert 40°C to Kelvin. (313 K)
2. Convert 75°C to Kelvin. (348 K)
3. Convert 451 Kelvin to °C. (178°C)
4. Calculate the temperature (°C) that will decrease 2.0 L of a gas at 20°C to 1.0L. (-126.5°C)
5. A gas occupies 900 mL at a temperature of 27°C. What is the volume at 132°C? (1215 mL)
6. What change in volume results if 60 mL of a gas is cooled from 33°C to 5°C? (54.5 mL)
7. Given 300 mL of a gas at 17°C, what is its volume at 10°C? (54.5 mL)
8. A gas occupies 1.0 L at standard temperature. What is the volume at 333°C? (2.2 L)
9. At 27°C, a gas has a volume of 6.0 L. What will the volume be at 150°C? (8.46 L)
10. At 225°C a gas has a volume of 8.0 L. What is the volume of this gas at -23°C? (4 L)
Boyle’s and Charles’ Law Review I
1. Boyle’s Law: When ____________________ is held constant, the pressure and volume of a gas are
____________________ proportional.
2. Mathematically, Boyle’s Law is stated as P1V1 = _______________.
3. At a pressure of 405 kPa, the volume of a gas is 6.00 mL. Assuming the temperature remains constant, at
what pressure will the new volume be 4.00 mL? (607.5 kPa)
4. A volume of gas at 1.10 atm was measured at 326 mL. What will be the volume if the pressure is adjusted to
1.90 atm? (188.7 mL)
5. If 36.5 L of a gas are collected at a pressure of 755 mmHg, what volume will the gas occupy if the pressure is
changed to 632 mmHg? (43.6 L)
6. Charles’ Law: When ____________________ is held constant, the volume and temperature of a gas are
____________________ proportional.
7. Mathematically, Charles’ Law is stated V1 = _______________
T1
8. The _______________ temperature scale must be used in all gas law problems.
9. At 189 K, a sample of a gas has a volume of 32.0 cm3. What volume does the gas occupy at 242 K? (40.9 cm3)
10. The gas in a balloon occupies 2.25 L at 30°. At what temperature (°C) will the balloon expand to 3.50 L?
(198°C)
11. A sample of gas has a volume of 852 mL at 25°C. What Celsius temperature is necessary for the gas to have a
volume of 945 mL? (57.5°C)
Boyle’s Law and Charles’ Law Practice II
1. To change a temperature expressed in degrees Celsius to a temperature on the Kelvin scale, what must be
done to the Celsius temperature?
Why must we use the Kelvin scale in gas law problems?
2. The volume of a sample of gas is 2.00 L when the temperature is 11.0C. While the pressure remains
constant, the temperature is changed to a new value, which causes the volume to become 3.00 L. What was
the temperature changed to?
This is an example of ____________________’s Law.
3. The volume occupied by a sample of gas is 480 mL when the pressure is 115 kPa. What pressure must be
applied to the gas to make its volume become 650 mL?
This is an example of __________________’s Law.
4. The volume occupied by a sample of gas is 240.0 mL when the pressure is 1.20 atm. What volume, at
constant temperature, will the gas occupy when the pressure is decreased to 0.860 atm?
5. The volume of a sample of gas is 25.0 mL when the temperature is 270 K. If the temperature is changed to
30.0C, what will be the new volume occupied by the gas assuming that the pressure remains constant?
6. When the volume of a sample of gas is divided by the temperature of the gas, the result is 1.33 mL/K. The
temperature of the gas is changed to a new value, which happens to be 411 K while the pressure is kept
constant. What volume does the sample of gas occupy at 411 K?
Gay-Lussac’s Law
Show the relationship between pressure and
temperature


Pressure is a result of the collisions between
gas particles and the walls of their container
An increase in temperature increases collision
frequency and energy, raising the
temperature and pressure if the volume is not
changed
Joseph Gay-Lussac’s law states that the pressure
of a given mass of gas varies directly with the
Kelvin temperature when the volume remains
constant. This is a direct proportion expressed by:
Just like in Charles’ Law, the temperature has to be in
Kelvin units by using K = 273 + °C
To solve:
1. Covert temperatures into Kelvin units
2. Plug in numbers/cross multiply/solve
P1 = P2
T1 T2
3. Be sure your answer is in the correct units and
you have solved for what you have been asked to
solve.
4. Does your answer make sense? (You should
have a DIRECT proportion)!!
EXAMPLE: Determine the pressure change when a
constant volume of gas at 1.00 atm is heated from
20.0°C to 30.0°C.
Avogadro’s Principle and Molar Volume of Gases


The particles making up different gases can
vary greatly in size. However, according to the
Kinetic Molecular Theory, the particles in a gas
are far enough apart that the size has a
negligible influence on the volume occupied
by a fixed number of particles.
Avogadro’s Principle states, equal volume of
gases at the same temperature and pressure
contain equal numbers of particles.
Molar Volume of Gases
One Mole = 6.02 x 1023 particles
The molar volume for a gas is the volume that one
mole occupies at STP.
The volume of one mole of a gas at STP is 22.4L.
Therefore, the following conversion factor to find the
number of moles, the mass, and even the number of
particles in a gas sample is:
22.4 L = 1 mole OR 22.4 L
1 mole
Molar Volume of Gases Practice I
1. How many moles does 44.8 L of hydrogen gas at STP represent? (2 moles)
2. A sample of oxygen gas occupies 6.2 L at STP. How many moles does that represent? (.28 moles)
3. How many liters will 23.50 g of nitrogen occupy at STP? (18.8Liters)
4. How many liters will 100 grams of oxygen occupy @ STP? (70 Liters)
5. How many grams of oxygen would be required to occupy 11.2 L at STP? (16 grams)
6. A sample of chlorine gas occupies 72.3 L @ STP. How many grams of chlorine gas are present? (225.9 grams)
7. How many moles of hydrogen gas are present in 162.4 liters @ STP? (7.25 moles)
8. How many grams of lithium gas would be required to fill a 50 liter container @ STP? (15.6 grams)
9. A sample of bromine gas occupies 28.3 liters @ STP. How many grams of bromine gas are present? (202 g)
10. What is the mass of 857 liters of nitrogen gas @ STP? (1071.3 grams)
The Combined Gas Law
P1V1 = P2V2
T1
T2
OR
P1V1T2 = P2 V2T1
Of the 3 states of matter, gases may have the most unusual, yet consistent set of properties. For example, we know
that ALL gases occupy approximately the same volume per mole under conditions of STP. The problem comes in
arriving at a volume for a given number of moles or mass of gas if conditions are not at STP.
To Solve Combined Gas Law Problems:
1. Convert temperatures into Kelvin Scale
2. Plug in numbers/solve
P1V1 = P2V2
T1
T2
3. Be sure your answer makes sense and is in the correct units!
Combined Gas Law Practice I
1. A gas at 110 kPa and 30°C fills a flexible container with an initial volume of 2.0 L. If the temperature is raised
to 80°C and the pressure is increased to 440 kPa, what is the new volume? (.5825 L)
2. A helium filled balloon at sea level has a volume of 2.1 L at 0.998 atm and 36°C. If it is released and rises to
an elevation at which the pressure is 0.900 atm and the temperature is 28°C, what will be the new volume of
the balloon? (2.268 L)
3. At STP, a sample of gas occupies 30 mL. If the temperature is increased to 30°C and the entire gas sample is
transferred to a 20 mL container, what will the gas pressure be inside the container? (1.665 atm)
4. A sample of air in a syringe exerts a pressure of 1.02 atm at a temperature of 22°C. The syringe is placed in a
boiling water bath at 100°C. The pressure of the air increased to 1.23 atm by pushing the plunger in, which
reduces the volume to 0.224 mL. What was the original volume of the air? (.2136 mL)