Kinetic Molecular Theory

Introduction

The Kinetic Molecular Theory underlies our understanding of how the variables of pressure, temperature, amount, and volume influence gas behavior. Theory allows for the creation of models. Models may be correct or incorrect, but the intent is to give our brains a way to envision what is happening to cause the behaviors observed.

In order to simplify our understanding there are certain assumptions that kinetic molecular theory makes. Note: These assumptions are really properties that we ignore or neglect in order to have a working model.

Gases are composed of a large number of particles that behave like hard, spherical objects in a state of constant, random motion.
These particles move in a straight line until they collide with another particle or the walls of the container.
These particles are much smaller than the distance between particles. Most of the volume of a gas is therefore empty space.
The attractive forces (IMFs) between gas particles are negligible.
Collisions between gas particles or collisions with the walls of the container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container.
The average kinetic energy of a collection of gas particles is dependent upon the temperature of the gas and nothing else.

How The Kinetic Molecular Theory Explains Gas Laws

The kinetic molecular theory can be used to explain each of the experimentally determined gas laws.

The Link Between P and n

The pressure of a gas results from collisions between the gas particles and the walls of the container. Basic physics informs us that pressure is simply force divided by area (P = F/A). Each time a gas particle hits the wall, it exerts a force on the wall over a certain surface area. The total pressure a gas exerts is therefore equal to the sum total of the forces exerted by each particle divided by the sum total of the area. An increase in the number of gas particles in the container increases the frequency of collisions with the walls and therefore the pressure of the gas.

Charles' Law (V directly proportional to T)

The average kinetic energy of the particles in a gas is proportional to the temperature of the gas. Because the mass of these particles is constant, the particles must move faster as the gas becomes warmer. If they move faster, the particles will exert a greater force on the container each time they hit the walls, which leads to an increase in the pressure of the gas. If the walls of the container are flexible, it will expand until the pressure of the gas once more balances the pressure of the atmosphere. The volume of the gas therefore becomes larger as the temperature of the gas increases.

Avogadro's Hypothesis (V directly proportional to n)

As the number of gas particles increases, the frequency of collisions with the walls of the container must increase. This, in turn, leads to an increase in the pressure of the gas. Flexible containers, such as a balloon, will expand until the pressure of the gas inside the balloon once again balances the pressure of the gas outside. Thus, the volume of the gas is proportional to the number of gas particles.

Amontons' Law ( Gay-Lussac's law) (P is directly proportional to T)

The last postulate of the kinetic molecular theory states that the average kinetic energy of a gas particle depends only on the temperature of the gas. Thus, the average kinetic energy of the gas particles increases as the gas becomes warmer. Because the mass of these particles is constant, their kinetic energy can only increase if the average velocity of the particles increases. The faster these particles are moving when they hit the wall, the greater the force they exert on the wall. Since the force per collision becomes larger as the temperature increases, the pressure of the gas must increase as well.

Boyle's Law (P = 1/V)

Gases can be compressed because most of the volume of a gas is empty space. If we compress a gas without changing its temperature, the average kinetic energy of the gas particles stays the same.

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There is no change in the speed with which the particles move, but the container is smaller. Thus, the particles travel from one end of the container to the other in a shorter period of time. This means that they hit the walls more often. Any increase in the frequency of collisions with the walls must lead to an increase in the pressure of the gas. Thus, the pressure of a gas becomes larger as the volume of the gas becomes smaller.

Real Gases Experience Real Forces...Intermolecular Forces!

Under certain conditions, gases demonstrate different behaviors than what would be predicted by gas laws. Atoms and molecules DO take up space. As that is true, the opportunity to collide with the walls of the container - which is an expression of pressure, reduces as the space in which the particles are free to move is reduced. As a result, the number of collisions increases showing an elevated pressure than expected.

Collisions are NOT perfectly elastic because real molecules have dipoles- either permanent or temporary creating Dispersion or Dipole-Dipole forces. And that alters the ideal behavior.

If a great pressure is applied to a gas, far beyond the normal few atmospheres we usually find in chemistry, the particles move closer under that pressure. And the closer they come to each other, the more likely they are to interact with each other due to IMFs. This is how gases condense into liquids. As well, with the particles attracted to one another, the number of collisions with the walls of the container decreases reflecting a lower pressure than expected for that amount of that gas at that temperature. In addition, when the molecules do collide with the wall of the container they collide with a lesser force which in turn causes a lower than predicted pressure.

From the viewpoint of temperature, gases show the most ideal behavior at high temperatures. As the temperature drops, the KE of gases decreases. Since mass is constant, this means the velocity of the particles slow. And when they slow, the opportunity to experience the IMFs increases. So at low temperatures, gas behavior is non-ideal.

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