GS_Kinetic Molecular Theory Lesson

Kinetic Molecular Theory

Despite the numerous gas laws that had been developed that explained the mathematical relationships between gases, scientists still were searching for a more theoretical explanation of gases. The  kinetic theory of gases was born. The postulates of the kinetic molecular theory of gases, sometimes referred to as KMT, are outlined below. These should be familiar to you from the earlier lesson on the ideal gas law.

Kinetic Theory of Gases A gas consists of a large amount of particles that are extremely tiny. They are in constant, rapid, random motion. The gas particles themselves occupy a volume so small that it can be considered to be zero. The gas particles collide with each other and the walls of the container in perfectly elastic collisions. They move in straight lines between collisions with no attractions or repulsions.

The kinetic molecular theory, can be used to explain each of the laws and concepts previously discussed in this module.   Here are two examples of this explaining Boyle's Law and Charles' Law.   You should practice using the postulates of the kinetic molecular theory to explain the other laws on your own.

Boyles Law (P ∝1/v)

gif of Boyles LawGases 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. 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.

Charles Law (V ∝T)

Charles Law gifThe 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.

Real Gases

When using Boyle's law, it has been noted that not all gases follow the law. For gases at very high pressures or very low temperatures, Boyle's law does not work. This same phenomena has been found to be true for other gas laws as well. Recall that in ideal gases:

  • There are no intermolecular attractive forces (IMA).
  • All the collisions between atoms or molecules are perfectly elastic, meaning that no kinetic energy is lost.
  • The gas particles do not take up any space, meaning their actual volume is completely ignored. This is why we only consider the volume of the container.
  • The gas particles are in constant, random, straight-line motion.

When gases don't behave "ideally," we call them real gases. It is important for you to understand the circumstances in which gases do not behave ideally and why. Let's begin by explaining the circumstances where gases behave ideally and why.

Gases behave ideally at room temperature and standard atmospheric pressure because:

  1. The space between the actual molecules is so large compared to the size of the molecules themselves that the size of the molecule itself.
  2. The molecules move rapidly enough and are far apart enough that the intermolecular attractions between the molecules are insignificant.

Real gases do follow the gas laws during normal conditions. This is why we can use the gas laws without having to make any corrections for intermolecular attractions under most conditions.

Gases deviate from ideal at very high pressures or very low temperatures because

  1. Real gas molecules do actually have volume.
  2. Real gases do experience weak intermolecular attractions.

Identifying a Real Gas

A different way to describe an ideal gas and to show how much a real gas differs from this is to describe it mathematically. If we use the ideal gas law as shown to the right, an ideal gas will always equal 1.  

LaTeX: \frac{PV}{nRT}=1PVnRT=1

The further away from 1, the greater the deviation from ideal behavior or the more real the behavior of the gas. This relationship is shown in the following graph of one mole of several gases. The graph is a plot of PV/RT versus pressure. The dotted horizontal line represents ideal behavior.

Real Gas Graph

Intermolecular attractions, IMA, cause the pressure of a real gas to be slightly lower than the pressure of an ideal gas. This is because the molecules are pulled off of their normal straight-line path, causing them to take longer to travel before they hit the walls. This therefore decreases the overall pressure.

Ideal Gas (straight lines) versus Real Gas (curvy lines)

Van der Waals corrected the ideal gas equation to take into consideration factors that would affect the gas behavior.

Remember to work on the module practice problems as you complete each section of content.  

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