Kinetic Molecular Theory and Gas Law Unit Packet
Kinetic Molecular Theory notes
Before you begin your studies of Kinetic Molecular Theory, you need to know what the
word means. Kinetic refers to things in motion; molecular deals with molecules; a theory is
a hypothesis that has been supported with experimental evidence. Now, we need to define
terms. You know what these terms are, but for the discussion of this unit, we will define
them differently than normal.
Temperature is a measure of the average kinetic energy of the molecules in a sample.
Since KE = ½ mv2, the change in temperature of a sample is caused by a change in
velocity (speed) of the molecules in that sample.
Volume of a sample is the space that the particles take up (not much differently than it is
normally thought of).
Pressure of a gas sample is caused by the molecules of that sample colliding with the
walls of the container. Pressure = Force / Area, so in order for a gas to exert more pressure
on its container, there must be more collisions or more forceful collisions.
Kinetic Molecular Theory is guided by the following assumptions:
1. The molecules of an ideal gas (an ideal gas is a gas that follows the assumptions of
kinetic molecular theory) are in constant, random, straight-line motion. Gas molecules
are constantly moving very, very fast and their direction is completely random. They
move in straight lines within their container.
2. The molecules in an ideal gas can be considered dimensionless points. This
assumption can be made because molecules are very, very small compared with the
empty space in a gas sample. Therefore, you can assume that the volume of a gas
sample is equal to the size of the container that it is held.
3. The collisions between molecules in an ideal gas with each other and the walls of its
container are completely elastic. Elastic collisions mean that no energy is lost or gained
when the molecules collide.
4. There are no attractive or repulsive forces in an ideal gas. This means that the
molecules of an ideal gas do not like or hate each other, they are indifferent. If they
pass by another gas molecule, they don’t even notice them, they just go about their
business. This assumption is totally false, but as long as the molecules of the gas have
plenty of space, they really won’t interact with each other.
Consequences of KMT (Kinetic Molecular Theory)
When gas molecules follow these rules, the gas is said to be “ideal”. Most gases are
ideal and will follow these rules. The only conditions under which these assumptions fail
is when the gas sample is either under high pressure or at low temperatures. When a
gas is compressed under high pressure, the gas is no longer mostly empty space, so
assumption number 2 fails and the gas will condense to a liquid. When a gas is at low
temperature, the molecules are moving slowly enough that they notice each other and
assumption number 4 fails. Once the gas molecules realize that they are not alone, they
start to feel attractive and/or repulsive forces and they will condense to a liquid.
Scientists and Gas Laws
Scientists started to conduct experiments with gases and they came up with
equations to describe the relationships between the variables, temperature, volume,
pressure, and moles of gas. Once you understand the assumptions of KMT and the
definitions of the variables, the relationships make sense. Here are the scientists and
their laws:
Boyle’s law – If you hold temperature and the amount of molecules in a gas sample
constant, the pressure of a sample of gas is inversely proportional to the volume. In
equation form this law is P x V = Constant number.
In English: If the speed of the molecules in a gas doesn’t change (Temperature
constant), if you change the amount of space the molecules have, you will change the
amount of times they collide with the walls of the container. If you have less space, you
have more collisions and vice versa.
Charles’ Law – If you hold the pressure and amount of molecules in a gas sample
constant, the volume of a sample of gas is directly proportional to the temperature. In
equation form this law is V/T = Constant number.
In English: If the frequency of the molecules collisions with the walls doesn’t change
(Pressure constant), a change in the speed of the molecules requires a change in the
amount of space they take up. If the molecules move faster, they need more room and
vice versa.
Gay-Lussac’s Law – If you hold the volume and amount of molecules in a gas sample
constant, the pressure of a sample of gas is directly proportional to the temperature. In
equation form this law is P/T = Constant number.
In English: If the amount of space doesn’t change (Volume constant), a change in the
speed of the molecules will result in a change in the collisions with the walls of the
container. If the molecules move faster, they will hit the walls more often and with more
force and vice versa.
Avogadro’s Law – If you hold the temperature and pressure of a gas sample constant,
the volume of a gas sample is directly proportional to the number of molecules. In
equation form this law is V/n = Constant number.
In English: If the speed of the molecules and the number of collisions with the walls of
the container doesn’t change, when you change the amount of molecules, the amount
of space they take up will change. If you add more molecules, they take up more space
and vice versa.
Can you combine them?
If you combine all of the gas laws together, you get a gas law for all situations, as
long as the gas behaves ideally. Strangely, chemists refer to this law as the ideal gas
law.
PxV=nxRxT
Pressure times Volume = amount of moles times the Ideal Gas Constant times Kelvin
Temperature. The Ideal Gas Constant is located on the back of your periodic table. In
fact, a summary of gas laws is located on the back of the periodic table.
R = 0.0821 L atm/mol K
OR
8.31 J/mol K
L = Liters, atm = atmospheres, mol = moles, K = Kelvin,
J = Joules = Liters x kilopascals
The key for gas law calculations is to keep the units the same. So, you need to know
what the different units for each variable are and how to convert between them.
Pressure

Atmospheres – this unit is abbreviated (atm) and was invented to be the standard
unit for pressure. “Standard pressure” is defined as 1 atmosphere.

Pascals – this unit is abbreviated (Pa) and is the force of 1 ant doing one push-up.
You will see kiloPascals used more often. “Standard pressure” is equal to 101.3 kPa.

Pounds per square inch – this unit is abbreviated (psi) and is commonly used in the
English system. “Standard pressure” is equal to 14.7 psi.

Barometric height – a barometer is used to measure atmospheric pressure. For a
barometer, you measure the height of air supported by a column of mercury.
“Standard pressure” is 760 mm Hg or 29.92 inches Hg.
Volume

Liters – this is pretty much the only unit we will use for volume (L)
Temperature

Fahrenheit – this is what we use in America, but no one else does. Celsius is more
often used. Here’s the equation to convert from Fahrenheit to Celsius:
0

C = 5/9(0F – 32)
Celsius – this is the standard international unit for temperature. If you want to
convert from Celsius to Fahrenheit: 0F = 9/50C + 32

Kelvin – this is the unit you will use for gas law calculations. Kelvin is based on
absolute zero, which is the temperature where all molecular motion will theoretically
stop. A unit of Kelvin is equal to one degree Celsius, but they have different starting
points for the scale. To convert from Celsius to Kelvin: K = 0C + 273.15
So now what to use it for (Sample Gas Law Calculations)
Here are the equations you will use for these problems:
Boyle’s law:
Charles’ Law:
Gay-Lussac’s Law:
Avogadro’s Law:
P1V1 = P2V2
V1/T1 = V2/T2
P1/T1 = P2/T2
V1/n1 = V2/n2
Ideal Gas Law:
Combined Gas Law:
PV = nRT
P1V1/T1 = P2V2/T2
1. A gas sample has a volume of 150 mL when the pressure is 135 kPa. If the
temperature and amount of gas remains constant, what volume will the gas sample
occupy at a pressure of 180 kPa?
In order to do any gas law calculation, you need to identify the variables involved in the
problem. Then you can determine the gas law that applies to the problem. The variables
for this problem are:
V1 = 150 mL
P1 = 135 kPa
P2 = 180 kPa
V2 = ?
Now you can see that you will use Boyle’s law for this problem. Set the unknown equal
to “X” and solve for it, using the algebra you learned in middle school.
P1V1 = P2V2
(135 kPa)(150 mL) = (180 kPa)X  Divide both sides by 180 kPa to get X by itself.
(135)(150)/(180) = X  Punch the numbers into your calculator and you will have the
answer. Only use as many digits (numbers) as you were given in the problem.
X = 113 mL  I rounded the number from 112.5 because there were three digits in the
numbers that were given to me in the problem.
More sample problems
2. A 600 mL sample of gas is collected at a room temperature of 27 0C. What volume
will the sample have at 0.00C assuming the pressure of the gas remains constant?
Start by writing down the variables that were given in the problem:
V1 = 600 mL
T1 = 270C
T2 = 00C
V2 = ?
Now you see two different things. You see that you will be using Charles’ law for this
calculation and the temperature is in Celsius. Right away, you remember that you need
to use Kelvin for gas law calculations! So you convert the Celsius temperatures to
Kelvin:
T1 = 270C + 273 = 300K
T2 = 00C + 273 = 273K
Now you can set the unknown equal to “X” and solve the equation.
V1/T1 = V2/T2
600 mL/300 K = X/273 K  Multiply both sides of the equation by 273 to get X by itself.
(273)(600)/(300) = X  Punch the numbers into your calculator and you will have the
answer. Only use as many digits (numbers) as you were given in the problem.
X = 546 mL  Don’t forget to write the proper units in for your answer!
3. What volume of gas would you expect to get from a 1.0-mole sample at STP?
Start this problem just like any problem, by writing down the variables that are given in the
problem. The challenge is with the term, “STP”. What does it mean? Well, STP stands for
Standard Temperature and Pressure (or Stone Temple Pilots). Standard temperature is
00C (or 273.15 Kelvin) and standard pressure is 1 atmosphere. So now you can write down
the variables in this problem.
P = 1 atm
n = 1.0 mol
T = 273.15 K
V=?
When you look for the equation that corresponds to this problem, it looks like the ideal gas
equation: PV = nRT. But what is R? I gave you 2 possible values for R earlier in the notes.
Use the value of R that has the same units as the problem gives. R = 0.0821 L atm/mol K.
Now you can solve the problem.
PV = nRT
(1 atm)X = (1.0 mol)(0.0821 L atm/mol K)(273.15 K)  Divide both sides by 1 atm to get X
by itself.
X = (1.0)(0.0821)(273.15)/(1)  Punch the numbers into your calculator and you will have
the answer. Only use as many digits (numbers) as you were given in the problem.
X = 22.4 L  Now you’re done!!
Kinetic Molecular Theory and Gas Laws Worksheet
Name:
Use the notes from the KMT packet to fill in the blanks on this worksheet.
1. Temperature is a measure of the ______________ ______________ energy of the
molecules in a sample.
2. A gas exerts pressure on its container because the molecules ___________ with the
walls.
3. Pressure = ______________ / _______________.
4. According to the assumptions of KMT…

The molecules of an ideal gas are in _____________, _____________,
_______________ - _______________ motion.

The molecules of an ideal gas can be considered ________________ points
because most of the volume of a gas is _____________ space.

Collisions in an ideal gas are completely _____________.

There are no attractive or repulsive __________ in an ideal gas.
5. The assumptions of KMT fail under high ____________________ or low
_______________.
6. _______________ law relates pressure and volume in an equation.
7. _______________ law relates volume and temperature in an equation.
8. _______________ law relates pressure and temperature in an equation.
9. PV = nRT is referred to as the ____________ gas law.
10. Standard pressure is equal to _________ atmospheres, _________ kPa, ________ psi,
____________ mm Hg, or ____________ in Hg.
11. Standard temperature is equal to ___________ 0C or _________ K.
12. Explain the “Crushing Can” demo by using gas laws.
13. Use a metaphor to explain any of the relationships described by the gas laws.
14. According to KMT, if 2 different gas molecules were at the same temperature and
pressure, but one was large and the other small, who would win in a race?
Gas Laws Study Guide
Name: ___________________
Define the following terms as they apply to Kinetic Molecular Theory:
Pressure –
Volume –
Temperature –
n (moles) -
Calculations
1. A gas sample has a volume of 150 mL when the pressure is 175 kPa. If the temperature
and amount of gas remains constant, what volume will the gas sample occupy at a
pressure of 120 kPa?
2. A 650 mL sample of gas is collected at a room temperature of 30 0C. What volume will
the sample have at 0.00C assuming the pressure of the gas remains constant?
3. An aerosol can of hair spray is filled to a pressure of 50.0 psi at a room temperature of
25.00C. Calculate the pressure inside the can if the can is placed in boiling water.
4. A balloon has a volume of 400.0 mL at a pressure of 600.0 mm Hg. Calculate the
volume the balloon would have at standard atmospheric pressure if the temperature
remains constant.
5. A car tire has a pressure of 30.0 psi at a temperature of 27.00C. Calculate the extremes
of pressure caused by temperatures ranging from –20.00C (-4.000F) on a cold winter
day to 50.00C (1220F) while being driven on a hot summer day.
6. A gas sample has a volume of 480 mL at a temperature of 37 0C and a pressure of 95.5
kPa. What volume would the gas occupy at STP?
7. If you collect 1.75-L of Hydrogen gas during a lab experiment, when the room
temperature is 230C and the barometric pressure is 105 kPa, how many moles of
hydrogen will you have?
8. What volume of gas would you expect to get from a 1.5-mole sample at 350C and 1.12
atm?