Читать книгу Geochemistry - William M. White - Страница 35

Factors we need to consider in constructing an equation of state for a real gas are the finite volume of molecules and the attractive and repulsive forces between molecules arising from electric charges. The van der Waals equation is probably the simplest equation of state that takes account of these factors. The van der Waals equation is:

(2.14)

Here again we have converted volume from an extensive to an intensive property by dividing by N.

Let's examine the way in which the Van der Waals equation attempts to take account of finite molecular volume and forces between molecules. Considering first the forces between molecules, imagine two volume elements v₁ and v₂. The attractive forces will be proportional to the number of molecules or the concentrations, c₁ and c₂, in each. Therefore, attractive forces are proportional to . Since c is the number of molecules per unit volume, , we see that attractive forces are proportional to . The a term is a constant that depends on the nature and strength of the forces between molecules, and will therefore be different for each type of gas.

In the first term on the right, has been replaced by . b is the volume actually occupied by molecules, and the term is the volume available for movement of the molecules. Since different gases have molecules of differing size, we can expect that the value of b will also depend on the nature of the gas. Table 2.1 lists the values of a and b for a few common gases.