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In critical applications tires are inflated using pure nitrogen (link).

Nitrogen molecules have a more difficult time escaping through the microscopic spaces that exist between a tire's rubber molecules. [...] Nitrogen reduces the loss of tire pressure due to permeation through rubber over time by about 1/3. (source)

According to WebElements, nitrogen bond length (109.76 pm) is smaller than oxygen bond length (120.74 pm), so why nitrogen permeation through rubber is said to be lower than oxygen?

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    $\begingroup$ I don't believe oxygen leaks any faster. The problem with oxygen is that it oxidizes things, which nitrogen does not. $\endgroup$
    – Ivan Neretin
    Jul 4, 2016 at 7:51
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    $\begingroup$ I agree with @Ivan Neretin. You show that $O_2$ and $N_2$ are similar in size and both very small. Hydrogen and helium would leak out faster though. Given time, oxidation possibly round the glue on the rim may be important. Carbon dioxide may be a better gas to use. $\endgroup$
    – porphyrin
    Jul 4, 2016 at 10:03
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    $\begingroup$ As mentioned by @Ivan Nertin, oxygen is more reactive... leading to rusting of steel wheels, particularly if a water-based tire sealer/inflater is used. In the form of ozone, it does damage rubber, but usually to the outside of the tire. Mostly, it's hype to sell nitrogen. $\endgroup$
    – DrMoishe Pippik
    Jul 5, 2016 at 3:48
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    $\begingroup$ See e.g. nvlpubs.nist.gov/nistpubs/ScientificPapers/… or people.ds.cam.ac.uk/jae1001/cus/teaching/materials/…. $\endgroup$
    – aventurin
    Jul 5, 2016 at 22:17
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    $\begingroup$ We don't know that the rate of leakage of anything through the material of tyres is significant at all. The original experimental rates were determined on thin sheets of balloon rubber. Tyres are not thin sheets and the actual rate of gas permeation in them could easily be insignificant. $\endgroup$
    – matt_black
    Nov 12, 2018 at 22:06

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The rate of oxygen, $\ce{O2}$, permeation through tire rubbers is about 3.4 times faster than nitrogen. The reference for this is "Permeability Properties of Plastics and Elastomers" by L. W. McKeen.

The reason is that $\ce{O2}$ is a smaller molecule than $\ce{N2}$. The size of a molecule is not determined by only the bond lengths between atoms but the size of the electron cloud around the atoms. The kinetic diameter of $\ce{O2}$ is 0.346 nanometers and $\ce{N2}$ is 0.364 nanometers. So, $\ce{N2}$ is larger than $\ce{O2}$ even though the $\ce{N-N}$ bond length is shorter than the $\ce{O-O}$ bond length.

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  • $\begingroup$ Can't we apply Graham's law? That would indicate N2 diffuses faster $\endgroup$
    – Black Jack 21
    Feb 10, 2017 at 3:23
  • $\begingroup$ If it is a solid empirical finding, then we have to accept it. But those statistics on the size of the molecules do not convincingly explain the large scale of the empirical difference in rates. Is something other than pure diffusion happening here? $\endgroup$
    – matt_black
    Nov 12, 2018 at 16:16
  • $\begingroup$ Actually, it is worth reading the original source for the permeation numbers. It speculates that the issue is solubility not diffusion. Moreover the experiments were conducted in the early 1900s on thin rubber balloons (or balloon materials) and might not apply to thick modern tyres. Most likely the permeation in modern tyres is so low (because of their thickness) it would be hard to measure. I suspect it is insignificant and some people just didn't read the original source to check for relevance. $\endgroup$
    – matt_black
    Nov 12, 2018 at 16:31
  • $\begingroup$ Moreover, the small difference in size is seriously insufficient to explain the large difference in permeation. This is clearly something more complex than diffusion making the statement that "the reason is that O2 is a smaller molecule" just wrong. $\endgroup$
    – matt_black
    Nov 12, 2018 at 22:04
  • $\begingroup$ I would hazard a guess that surface adsorption to the rubber surface is also quite different between nitrogen and oxygen. I would think that has a greater role to play than the atomic size. $\endgroup$
    – Stian Yttervik
    Jan 16, 2019 at 20:13
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While the comments are basically correct, this is a teaching opportunity. You can't just look at bond lengths for determining the size of the molecule as the atoms also have radii which have to be considered. The longest part of the molecule (or widest surface) then can be simply be "bond length + 2x(atomic radius)".

I was able to get some covalent radii data from this website, and if we use it to calculate we find:

Width of dioxygen = 1.21 + 0.73 x 2 = 1.21 + 1.46 = 2.67 Angstroms

Width of dinitrogen = 1.10 + 0.75 x 2 = 1.10 + 1.50 = 2.60 Angstroms

So the original difference of 11 angstroms is down to 7 angstroms. Not much of an improvement, and Oxygen is still larger than Nitrogen. However, if you incorrectly used the atomic radius...

Width of dioxygen = 1.21 + 0.48 x 2 = 1.21 + 0.96 = 2.17 Angstroms

Width of dinitrogen = 1.10 + 0.56 x 2 = 1.10 + 1.12 = 2.22 Angstroms

Suddenly Nitrogen is bigger.

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  • $\begingroup$ Good point. It'd be nice to see some work on the prediction of diffusivity, based on molecule size, polarity, polarisabilty etc. That's been done for sure. $\endgroup$
    – Karl
    Jul 5, 2016 at 14:26
  • $\begingroup$ Yes to checking the molecular sizes properly. But this does precisely nothing to illuminate the issue because small differences like that would be barely detectable if the process were basically diffusion. $\endgroup$
    – matt_black
    Nov 12, 2018 at 22:01

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