Van der Waals EOS: Why Pc/Tc, and not Pc/Vc or Vc/Tc?

[maistral]

TL;DR

The title.

As far as I know the van der Waals constants can be expressed as functions of Pc and Tc. Why is it so? Why is it not a function of Vc/Tc, or Pc/Vc?

Say for example, b = Vc/3. Why is this expressed in terms of Pc and Tc instead? Why is a also in terms of Pc and Tc, and not Vc? Is this just a matter of preference?

 

[Chestermiller]

Summary:: The title.

As far as I know the van der Waals constants can be expressed as functions of Pc and Tc. Why is it so? Why is it not a function of Vc/Tc, or Pc/Vc?

Say for example, b = Vc/3. Why is this expressed in terms of Pc and Tc instead? Why is a also in terms of Pc and Tc, and not Vc? Is this just a matter of preference?

Please show how you would reduce the van der Waals equation to dimensionless form.