Van der Waals equation adapted for paramagnetic gases

[mississippichem]

The Van der Waals equation of state for gases:

 

[math]\left(p + \frac{n^2 a}{V^2}\right)\left(V-nb\right) = nRT[/math]

 

where "a-prime" is the attractive force between gas particles.

 

My question is, does "a-prime" already account for any paramagnetic interaction that may arise in gases with un-paried electrons like triplet [ce] O_2[/ce]? Or, does "a-prime" only factor in the Van der Waals (induced dipole-induced dipole) interactions present meaning that one would have to account for paramagnetic interactions separately? I realize one could neglect the paramagnetic interactions entirely for most purposes, obviously they shouldn't add up to much in the gas phase. This is sheer morbid curiosity.

 

*I'm familiar with the standard derivation of the Van der Waals equation, but I've never had an opportunity to use it in real life because [math] PV=nRT [/math] has always been sufficient. I never work with the mega-pressures, micro-volumes, or small experimental margins where any of this really matters.

[Mr Skeptic]

I think it is supposed to account for the pressure increase due to particle collisions/interactions with each other. That said, it can only really be an estimate, as it accounts for all sorts of interactions simultaneously as a single value.

[mississippichem]

I think it is supposed to account for the pressure increase due to particle collisions/interactions with each other. That said, it can only really be an estimate, as it accounts for all sorts of interactions simultaneously as a single value.

 

Oh, so "a" counts for all intermolecular interactions. Thanks

[Mr Skeptic]

Yup, but I can't really tell you whether the "b" value would also partially account for those. The "b" value corresponds to a lower effective volume due to molecules having some "size", but interactions between the molecules could also contribute to their effective size. I suppose a more complicated formula could be made to account even more accurately for the different types of interactions, but if you've never even had to use this one then I doubt a more complicated one would be of much use, just yet more accurate and yet less used.

[mississippichem]

Yup, but I can't really tell you whether the "b" value would also partially account for those. The "b" value corresponds to a lower effective volume due to molecules having some "size", but interactions between the molecules could also contribute to their effective size. I suppose a more complicated formula could be made to account even more accurately for the different types of interactions, but if you've never even had to use this one then I doubt a more complicated one would be of much use, just yet more accurate and yet less used.

 

I don't think "b" accounts for changes in molecular size that stem from dipoles and induced dipoles in question. I think it uses the volume extrapolated from the regular covalent radii. I'm sure the equation accounting or all those various "psuedo-coulombic" interactions would become a nightmare because polarizability is different for every effective nuclear charge and therefore every element in every compound would have some different factor making the formula different for every substance.

 

I imagine this equation could be expanded in many interesting and useless ways .

Edited November 30, 2010 by mississippichem