Conceptual question: Volume in Gas Laws

[blueblueblue]

Okay, so I've been trying to wrack my brain around this concept for a while but to no avail.

PV = nRT
(P_real + n²*V^-2a)(V_real - nb) = nRT

From these equations, it's clear that real volume is greater than ideal volume under real conditions. I understand that this is because the molecules have a definite volume, and therefore, Volume_real = Volume_container + Volume_molecules.

But on the microscopic level, aren't you more concerned with the mean free path between molecules? So a smaller volume would mean that the gases have a smaller mean free path and vice versa for bigger volumes. In that light, wouldn't taking into account the molecule's volume actually decrease the overall mean free path between molecules, therefore, decrease the real volume? When you include the volume of the molecules, you're essentially decreasing the amount of free space between each molecule, aren't you?

Does that make sense? I'll try to reword it if it doesn't... Thanks!

 

[nickjer]

That equation of state applies to the Van der Waals force. And I think you are confused about the volume term in that equation. The "V" in that equation is the volume of the container. The parameter "n*b" is more like the volume of the actual molecules. That way, the volume of the available free space is (V-nb).

You can read much more about this on http://en.wikipedia.org/wiki/Van_der_Waals_equation