The Van der Waals Constants

The constants and are different for different substances. We can get the estimates of and of a substance by knowing the critical values of that substance.

Before we proceed further, let us look at the mathematical function

For the maximum value of x: and

For the minimum value of x: and

For the point of inflection, and

From the Figure 9.2 we can see that the critical point is a point of inflection.

The critical isotherm must show a point of inflection at the critical point

	(10.1)
	(10.2)

At the critical point, the Van der Waals equation is

(10.3)

One can solve the above three equations to obtain

(10.4)

Alternatively, one can calculate the Van der Waals constants and in terms of critical constants.

(10.5)

The constants and can be determined for any substance from the critical point data (Table 10-1) At the critical point, one can see that

(10.6)