Kinetic Molecular Theory (College Board AP Chemistry)

• 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

• 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

• 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: