From these two equation, by rearranging and dividing,

(2.163)

Substituting the value of b in Eq. (2.65)

(2.164)

Substituting the values of b and R in Eq. (2.152a)

(2.165)

(2.166)

Therefore, the value of R becomes

(2.167)

The values of a, b, and R have thus been expressed in terms of critical properties, substituting these in van der Waals equation of state

(2.168)

or,

(2.169)

Using the reduced parameter

(2.170)

In the reduced equation of state (2.170) the individual coefficients a, b and R for a particular gas have disappeared. So this equation is an expression of the law of corresponding states because it reduces the properties of all gases to one formula.