Kinetic Molecular Theory (College Board AP® Chemistry)
Study Guide
Written by: Oluwapelumi Kolawole
Reviewed by: Stewart Hird
Kinetic Molecular Theory
All of the gas laws and the ideal gas equation describe how gases behave but not why they behave the way they do on the molecular level
For example:
Why does a gas expand when heated at constant pressure?
Why does the pressure increase when a gas is compressed at a constant temperature?
In the nineteenth century, several physicists, notably James Clerk Maxwell and Ludwig Boltzmann, found that the physical properties of gases can be explained in terms of the motion of individual molecules
This observation resulted in a number of basic assumptions about gas behavior that have since been known as the kinetic molecular theory of gases
The Basic Assumptions of Kinetic Molecular Theory
Kinetic molecular theory is based on five basic assumptions:
Gases are composed of molecules whose size is negligible compared with the average distance between them
These molecules are considered to be “points” which means they possess mass but have negligible volumes
It also explains why gases are easily compressed
Gas molecules move randomly in straight lines in all directions and at various speed
Hence, the properties of a gas which depend on the motion of the molecule, such as pressure, will be the same in all directions
The forces of attraction or repulsion between two molecules in a gas are very weak or negligible, except when they collide
Basically, gas molecules will continue moving in a straight line with undiminished speed until they collide with another gas molecule or with the walls of the container
When molecules collide with one another, the collisions are elastic
Elastic collisions are collisions in which the total kinetic energy is conserved
Hence, gas molecules will forever move with the same average kinetic energy per molecule unless the kinetic energy is removed from them, for example as heat
The average kinetic energy of a molecule is proportional to the absolute temperature
This means the higher the temperature, the greater the average kinetic energy of the molecules
For more information about the particulate model and its graphical representations, see Solids, Liquids and Gases and Graphical Representations of the Gas Laws
Average Kinetic Energy
The kinetic molecular theory explains both pressure and temperature at the molecular level
Gas pressure is caused by collisions of its molecules with the walls of the container
The magnitude of the pressure is determined by how often and how forcefully the molecules strike the walls
The absolute temperature of a gas is a measure of the average kinetic energy of its molecules
If two gases are at the same temperature, then their molecules have the same average kinetic energy
An increase in temperature is an increase in average kinetic energy and an increase in the molecular motion of the particles
The average kinetic energy of a molecule is given as:
KE = ½ mv2
m represents the mass of the molecule measured in grams
v represents its average speed measured in ms-1
KE represents kinetic energy measured in Joules
It is important to note that:
Average kinetic energy is dependent on temperature
Average velocity is dependent on the temperature and mass of the molecules
Hence, while two different gases at the same temperature will have the same average kinetic energies, they will not have the same average velocities because of their different masses
Worked Example
Two identical flasks, X and Y, containing 2 moles samples of N2 (g) are shown below. Which of the following statements is true?
The rate of collision of N2 gas molecules with the walls of the flask in X and Y are the same
The pressure exerted by N2 gas molecules is less in flask X than in flask Y
The average kinetic energy of N2 gas molecules is the same in flasks X and Y
The average kinetic energy of N2 gas molecules is less in flask Y than in flask X
Answer:
The correct answer to this question is D because:
The average kinetic energy of gas molecules is directly proportional to its absolute temperature
Since the gas molecules in flask Y are at a lower temperature, the average kinetic energy of the molecules is less than in flask X
Option A is incorrect because
The rate of collision of N2 molecules with the flask walls is dependent on the number of gas molecules and the average speed of the molecules
Both flask X and flask Y contain the same number of molecules
However, the molecules in flask X have higher average kinetic energy given its higher temperature
Hence, flask X has a higher rate of collision
Option B is incorrect because
The pressure exerted by a gas is dependent on the frequency and intensity of collision with container walls
In this case, both flask X and flask Y contain the same number of molecules
However, the molecules in flask X have a higher average kinetic energy due to the higher temperature
Hence, the molecules in flask X have a higher average speed and will collide more frequently and with more average force, resulting in greater pressure
Option C is incorrect because
The gas molecules in both flasks are at different temperatures and so do not have the same average kinetic energy.
Kelvin Temperature
According to the kinetic theory, the average kinetic energy of gas particles is indicated by the magnitude of its absolute temperature, T
The term absolute temperature is also known as thermodynamic temperature
Based on the relationship between average kinetic energy and temperature, we can say that:
K.E ∝ T
Average Kinetic Energy-Temperature Graph
A graph showing the linear relationship between average kinetic energy and absolute temperature of a gas.
The absolute temperature of an object is its temperature on a scale where the object is at the lowest possible energy
On the Kelvin scale, one Kelvin (K) has the same magnitude as one degree Celsius
The main differences are:
The zero position is shifted, so 0 K is equivalent to -273.15 ℃
Temperatures, in Kelvin, are not reported in degrees like the Celsius scale
The Celsius scale is a relative scale based on the melting and boiling points of water
Conversion from the Celsius scale to the Kelvin scale is given by the relationship:
K = ℃ + 273.15
Important points on the Kelvin and Celsius scales are given below:
| Kelvin (K) | Celsius (℃) |
|---|---|---|
Absolute Zero | 0 | -273.15 |
Melting point of water | 273.15 | 0 |
Boiling point of water | 373.15 | 100 |
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