# Why is it difficult to mix helium and nitrogen gases?

I recently learned an interesting fact: That it's difficult to mix helium and nitrogen gases in a compressed gas cylinder. Gas suppliers that need to mix the two gases have to rotate the cylinders for hours or even days after the two gases are injected to get the two gases to mix.

And once they are mixed they do not separate again.

I was told that the reason this occurs is the large difference in density. And then I suppose the pressure from diffusion is much smaller than the pressure exerted by gravity and density difference. But hours to days of mechanically agitating sounds excessive, and makes me wonder if there is something more going on than just the tension between the forces of gravity and diffusion.

I have two questions regarding this behavior:

(1) Are density differences the only reason it's difficult to mix the two gases?

(2) Is there simple way to calculate an estimate of how long it would take for nitrogen and helium to mix in a closed container (without mechanical agitation) just under the forces of diffusion? - Assuming He on top.

With (2) perhaps the same calculation can be done for two gases with similar densities like oxygen and nitrogen for comparison.

• It sounds like a myth to me, especially since a commercial supplier will not mix gases in the cylinder to begin with. They will have two gas lines meeting in a mixing chamber and then pipe the resulting mixture into the cylinders. Did you look at the diffusion coefficients for these gases in each other? Jun 10, 2015 at 21:53
• Given how cheap a He/N2 mix is, it really is hard to believe. Also, I've never seen a problem with mixing of N2 and He in various vacuum systems that I've run. The diffusivity of He is quite high. Jun 10, 2015 at 22:18
• @CuriousOne where would I find diffusion coefficients for specific gases in one another? I don't believe the CRC HB of Chem & Physics has that. Jun 10, 2015 at 22:26
• @JonCuster perhaps its not an issue in vacuum systems where the density of the gases would be low. The information I'm getting is in regards to high pressure systems on the order of 2000 psig. Jun 10, 2015 at 22:29
• There is a big difference between filling a cylinder first with one gas and then adding another gas, and mixing the two gases by having them flow (turbulently) into a small mixing chamber. I believe in the latter case you will be able to achieve homogeneous mixing very quickly. This does require substantial turbulence - you need to decrease the distance over which one gas has to diffuse into the other. The natural energy difference due to gravity may otherwise trump entropy... at least for some time. Jun 11, 2015 at 2:40

It's true. Special equipment and a long time is required to mix helium and nitrogen. According to one study, a mixture of 2.7% He, 93.3% N$$_2$$ at 800 p.s.i.g. required a special cradle to repeatedly upend the cylinder, and 20.5 hours to reach equilibrated gas, which then remained mixed: http://doi.org/10.1021/je60005a002. The helium repeatedly slid from one end of the cylinder to the other. The authors overcame this difficulty by devising a mixing mechanism internal to the cylinders.

The molecular weight of helium is 4.02, and density is .1786 kg/m^3 at standard temperature and pressure. For nitrogen, molecular weight is 28.02, and density is 1.2506 kg/m^3. Here's a table of molecular weight and density for various gases: http://www.engineeringtoolbox.com/gas-density-d_158.html.

Helium doesn't mix easily with nitrogen because of the great difference in their densities. But once mixed, the gas molecules are close together and they move around quite a bit with kinetic energy so they stay mixed and don't separate out into layers.

• What's interesting is the equipment used to mix (valves, tubing etc.) probably results in turbulent rather than laminar flow, so you would think the turbulence and eddies would provide a good mixing. That's what makes me think there might be something more than just the difference in densities. Van der Waal forces are short range, right? Jun 11, 2015 at 0:19
• It's like the floating Yen demo. For a long time people believed that the force that floats the coin is all surface tension. I did some calculations and it turns out a good part of the force is buoyant (fluid displacement) force. Jun 11, 2015 at 0:21
• @docscience: The larger the atomic radius and the greater the number of electron shells, the more likely it is that temporary van der Waals dipoles will be strong enough to polarize adjacent atoms and attract them to one another. Helium has only a single electron shell, so it doesn't seem to be a strong van der Waals vehicle. Its low boiling point (-269 degrees C) indicates very weak attraction among helium atoms. But the He atoms may not be good candidates for van der Waals attraction to other molecules, either. I don't know which effect would predominate. Jun 11, 2015 at 1:50
• @docscience: If you scroll down to about midway in this link, it compares boiling points of the noble gases, and talks about temporary dipole formation in He atoms: chemwiki.ucdavis.edu/Physical_Chemistry/…. (The dispersion forces it talks about are attraction forces.) Jun 11, 2015 at 1:57
• The "hours and hours" case was when they flipped the cylinder over every 30 min. Manually inverting it every 5 seconds or so would mix it pretty well in under a minute. Aug 18, 2016 at 23:32

Diffusion is a slow process over the length of a gas cylinder. The diffusivity of helium in air is about $0.7$ cm$^2$/s (source). At 100 atmospheres it would be about a hundred times slower, about $0.006\ {\rm m}^2$/day.

Not really a direct answer to the original questions. I offer two observations that everybody experienced. 1) He can escape a rubber balloon in one day (i.e. He go through tiny holes in rubber) 2) gases are less solid than rubber. Therefore He can penetrate any gas given sufficient time.

• But that is only one millimeter or so. Diffusion over a 1 meter cylinder would take a million times longer than diffusion over 1 mm.
– user137289
Jul 26, 2018 at 17:03
• @Pieter Perhaps even orders of magnitude longer. The relationship may not be so linear. Seems like a fairly moot point anyways, since we need to account for how gravity would affect this system, which is a main problem.
– JMac
Jul 26, 2018 at 17:05
• Thanks for clarification. I read now carefully the other responses too. The most important factor is the particularly high pressure of the system, greatly reducing the mean free path of molecules and atoms (say by factor 100). Aug 1, 2018 at 16:25