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4.5 Real Gases

So far, we have worked with ideal gases. However, we live and, more importantly, work in a real world with real gases, and real gases like real people can behave badly. When a gas does behave badly, it is said to be nonideal because it does not obey the Ideal Gas Law. All gases do have nonideal behavior at high pressures and/or low temperatures, so the two terms are used interchangeably. However, some gases exhibit nonideal behavior at conditions where other gases exhibit ideal behavior.

Sometimes, as a gas is compressed or cooled before reaching the point at which the volume of the molecules becomes relatively large and thus inhibits a further reduction of volume, there are other attractive or repulsive forces that are generated. Those forces are van der Waals forces, which are caused by dipole moments. These forces affect the volume of a nonideal gas, as shown in Figure 4.4.

Figure 4.4

Figure 4.4 Effect of temperature on the volume of a nonideal gas

A dipole moment is an electrostatic force between molecules. Some of the atoms of a gaseous molecule may hold more of the electron cloud due to their higher electronegativity than will the other atoms, resulting in localized charges on the molecule. Oxygen is such an atom because it becomes the location of a greater negative charge. A part of the remaining molecule becomes more positively charged and these molecules are said to be polar. The negatively charged volume of one molecule is attracted to a positively charged volume of another molecule. The force of attraction causes the volume of the gas to be smaller than that predicted by the Ideal Gas Law. The volumes of the electron cloud with the same charge on two different molecules will repel each other.

In addition to permanent dipoles, there can be induced dipoles caused by the temporary location of the electrons as they move about the atoms in a molecule. The induced dipoles are also called London dispersion forces or, even more loosely, van der Waals forces. Those forces are controlled by quantum mechanics, which is one of the weirdest branches of physics.

Permanent dipole moments do not exist for the diatomic molecules of the elemental gases such as hydrogen, nitrogen, oxygen, fluorine, or chlorine because they share their valence electrons equally. Dipole moments also do not exist for the inert noble gases such as helium, neon, or argon, which are mono-atomic. However, the induced dispersion dipoles can exist.

To account for the discrepancies caused by these previously described forces and other such forces, scientists have developed complicated equations of state for nonideal gases; for example, the Ideal Gas Law is an equation of state. Two of those equations of state for nonideal gases with additional terms can be studied in Appendix 4A. Also, because the behavior of nonideal gases varies according to the molecular mass, the differences in the electronegativity of the molecules’ atoms, the molecules’ volume, and sometimes other contributing factors, those equations of state must use different values for the different parameters of the different gases. Also, different equations of state work better for different gases.

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