Deviations from Ideal Gas Law Behavior

Deviations Due to Raising Pressure: Ideal gas behavior is most closely approximated at low pressure. There are two factors that cause real gas behavior to deviate from ideal gas behavior as pressure is increased. One is the attraction that exists among gas particles, which becomes significant at medium pressure; and the other is the volume of the gas particles themselves, which is significant at high pressure. The ideal gas law assumes that these two factors are insignificant, which is generally true at low pressures. As you start raising the pressure to a medium level, the gas particles begin to attract one another. This causes them to "stick" together and contracts the volume of the gas overall below what would be expected if no attraction were occurring. As you continue to raise the pressure, the volumes of the individual gas particles begin to occupy a significant portion of the volume of the container. This causes the volume of the gas to be larger than expected, because the ideal gas law does not take into account the volumes of the gas molecules. (According to the ideal gas law, the molecules have no volume, as well as no intermolecular interactions.)

Deviations Due to Lowering Temperature: Ideal gas behavior is most closely approximated at high temperatures. Remember that temperature is a measure of the average kinetic energy of the molecules in the gas. As the temperature is decreased, the molecules move more and more slowly. This makes the intermolecular attractions among them more significant. If the temperature is decreased enough, the gas will reach its vaporization point (boiling point), and turn into a liquid (or possibly a solid if the pressure is below the triple point pressure). As explained above, intermolecular interactions cause the gas’s volume to be smaller than what is predicted by the ideal gas law.

Correcting for Deviations in Pressure and Temperature: The ideal gas law works fairly well as long as the pressure is kept low and the temperature is kept high. However, under conditions of high enough pressure and low enough temperature, it breaks down. The van der Waals equation of state is one example of a modified gas law equation that attempts to correct for the effects of particle volume and intermolecular attractions. It looks similar to the ideal gas law, but it has two extra terms:

van der Waals equation of state: [P + (n^2)(a)/(V^2)](V-nb) = nRT

The a-term is to compensate for attractive forces among the molecules, and it will be lowest for nonpolar molecules and higher for polar ones. The b-term compensates for molecular volume, and it will be lowest for small molecules and higher for larger ones. Note that if a = b = 0, the van der Waals equation reduces down to the ideal gas law:

[P + (n^2)(0)/(V^2)][V-n(0)] = nRT
[P][V] = nRT