[opsomath]

Good morning y'all. I came across this interesting graph:

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/waal.html

Do you have a simple explanation for the large deviation of oxygen relative to other simple molecular gases?

[sjb]

Good morning y'all. I came across this interesting graph:

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/waal.html

Do you have a simple explanation for the large deviation of oxygen relative to other simple molecular gases?

The only thing that jumps out at me comparing those on the graph is the diradical nature of dioxygen, If R is smaller than expected does that make the pressure lower / volume higher - repulsion of the molecules from each other - would that be significant?

[opsomath]

I think of R as having units of "molar specific oomph". That is, it is how much "push" a gas gives at a certain number of moles of gas and temperature.

Therefore, a negative deviation from it indicates "stickiness" of molecules, reducing PV. I agree that this has to have something to do with the open-shell (triplet) nature of O2. Presumably some force term between two molecules that vanishes if the wave function is a singlet...but hell, I've forgotten all that stuff.

[Corribus]

First, the deviation for none of those shown is large. Even oxygen at 20 atm, the deviation is only a few percent. Compare this with the compression factor (Z) of carbon dioxide, which liquefies at fairly low pressures, and has a deviation of several tens of percent (I believe).

Second, this figure doesn't really show the whole story. If you show a larger pressure range (up to, say, 500 or 1000 atm), all the gases will have a positive deviation from ideality, and the magnitude of deviation for nitrogen is larger than that of oxygen. So it's too simple to say that oxygen has a greater overall deviation from ideality than nitrogen - true, at the temperature shown, and at low pressures, the deviation of oxygen is greater. 

Third: but back to the low pressure results shown in the figure you linked to.  We can scale the magnitude of deviation as CH₄ > O₂ > CO > N₂ > H₂.  Methane isn't on there but I thought I'd list it anyway - it's a lot larger than oxygen.  The deviation from H₂ is actually positive.  Let's consider the magnitude of the deviation first.  A negative deviation of the compressibility factor from ideality mean that the molar volume is smaller than what it should be if the gas behave ideally.  That is - the gas resists expansion (as the pressure is dropped, the gas should expand). This means that a negative deviation indicates that the gas molecules are attracting each other.  A positive deviation, conversely, means that the molecules are repelling each other.

So. We conclude that attractive forces scale by magnitude: CH₄ > O₂ > CO > N₂ > H₂. Perhaps we should not be surprised because the boiling points of these gases are methane (~110 K) > O₂ (90.2 K) > CO (82 K) > N₂ (77.4 K) > H₂ (20 K), and boiling points are largely correlated to the attractive forces between molecules.  The question therefore becomes: why is the magnitude of attractive forces between oxygen greater than that of CO, N₂ and H₂?  Let's take a slightly easier comparison - the magnitude of CO attractive forces is greater than that of N₂ because CO is polar and N₂ is not. This should be the dominant effect because the two molecules have the same mass and approximately the same size (both have a triple bond, with bond length 109.8 and 112.8 pm for N₂ and CO, respectively). However the dipole moment for CO is pretty small and the mass is pretty small, so the boiling point difference between CO and N₂ is also fairly small.

When we go to oxygen, we might predict that CO should have greater attractive forces than O₂ because the former is polar and the latter is not. In most cases it's true that dipole-dipole interactions are stronger than dispersion forces, but not so apparently in this case. Oxygen is a more massive molecule (~18%) and also a larger molecule (~7%, based on bond length) by a not inconsiderable margin. Oxygen also has several more lone pairs on the distal sides of the bonds, which probably make its effective Van der waals size much larger than that of CO, the electrons of which are tied up in an extract pi-bond. The result? Oxygen should be far more polarizeable than CO and thus have considerably more attractive dispersion forces than CO, certainly more than enough to surpass the small permanent dipole-dipole interactions of CO. This effect is shown to greater extent in methane, another nonpolar molecule: methane is very large and highly polarizable (compared to the diatomics), and it has even more attractive forces. Hence, higher boiling point and larger negative deviations from ideality of its compression factor at low pressures. They get worse the larger the molecule gets - for ethane, the negative deviation at 20 atm is several tens of percent, maybe even up to 60-70%.

We might ask why hydrogen has no apparent negative deviation at all. Well, hydrogen is quite small and doesn't have any lone pairs at all. Dispersion forces would be expected to be very small in magnitude, hence very little attraction between individual hydrogen molecules. This is reflected in the very low boiling point and the apparent lack of any negative deviation of the compressibility factor. Do note that the compressibility plots are temperature dependent. I surmise those shown in the link you provided were determined around 300 K. If you were to plot out analogous values at a lower temperature - where deviations from ideality become larger - eventually you would see a negative deviation region for hydrogen as well.  Even a noble gas like helium would, provided you dropped the temperature low enough.