I've been trying to reconcile the form of the van der Waals equation of state and the equations from which they are derived. Stop me where I go wrong:

The VDW EOS includes two terms: one for the consideration of the excluded volume (which results in a higher pressure than predicted by the ideal gas equation) and another for the consideration of attractive forces of the gas (which results in a lower pressure than predicted by the ideal gas equation).

My confusion is mainly with the second term: a/v^2

If I recall correctly, this term is derived from the distance dependence of the potential energy from VDW forces. The explanation being, if v is proportional to r^3, v^2 is proportional to r^6, the potential energy due to attractive forces is proportional to v^2, and thus the reduction in pressure due to those attractive forces should be proportional to v^2.

So here it is: shouldn't the term actually represent the distance dependence of VDW forces? That is, shouldn't the final term of the VDW EOS be proportional to 1/r^7 (the derivative of the VDW force wrt. distance)?

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    $\begingroup$ Your question is answered in the classic paper Hill, Terrell L. (1948). “Derivation of the complete van der Waals’ equation from statistical mechanics.” In: Journal of Chemical Education 25.6, p. 347. You need to understand some statistical physics to make sense of this though. Mainly the partition function and its uses. Do you? $\endgroup$ – frapadingue Oct 29 '18 at 8:34
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    $\begingroup$ looks like I was just a few days ahead of lecture, thanks though! $\endgroup$ – Ugochukwu Nwosu Oct 31 '18 at 18:29

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