size decreases across rows of the periodic table

is that generally true ? And if so why ? Does it hold for row one: hydrogen & helium? Also what matters in this case is the size of the molecule, not the atom

As others have alluded to, it's not the gas that matters as much as the dryness of it. If there's moisture in the air that's in your tyres, it will alter the pressure as temperatures increase, even well below boiling point.

I don't understand the science of it much, beyond knowing that the warmer air is, the more water vapour it will hold. I have seen it happen when I've finished a drink that comes in a lucozade sport type bag, closed it back up and left it in the car on a warm day. When I got back the bag had inflated itself!

As for sizes across the periodic table, look at the numbers. Less protons & neutrons = smaller. And helium diffuses through rubber at a daft rate, so I doubt we'll ever see it in bike tyres unless we start running mylar inner tubes.

The power of marketing increases exponentially when you add a little bit of science (1st year degree level in this case)!
I remember spending a 'fun' afternoon in the lab bouncing a ball bearing in a tube of different gasses to see how they behaved. N2 is the closest to a ideal gas and therefore it's expansion under heating is linear. Oxygen is less so, and CO2 and water are far from ideal under the gas laws. So for F1 tyres N2 filling makes sense.
Practically, you just need some fancy zeolite filters after a compressor to get your pure N2 feed (no bulk N2 so no safety worries), so for Kwik fit it is a few £1000 per garage for a new sales gimmick…

aircraft use nitrogen

Not true – I have proof

If there's moisture in the air that's in your tyres, it will alter the pressure as temperatures increase, even well below boiling point.

all gasses increase their pressure at constant volume (or volume at constant pressure) as the temperature rises. And it goes without saying that any water in the gas in the tyre has already boiled unless it's sloshing round

the more water vapour it will hold

the vapour pressure of water increases with temperature, independantly of any other gasses present.

Less protons & neutrons = smaller.

aparently not:

And it goes without saying that any water in the gas in the tyre has already boiled unless it's sloshing round

I'm out of my depth here, but this bit doesn't make sense to me.
Surely most air has got water in it, in the form of vapour, well below boiling temperature/above boiling pressure ?
Increasing the pressure reduces air's capacity to hold water as vapour. That's why air braked vehicles have air dryers and workshop compressors have water traps.

I'm wrong and so is everyone else who thinks it'll make a difference:

http://www.carbibles.com/tyre_bible_pg3.html

From that site…

Let's say your standard tyres are 185/65R14 – a good middle-ground, factory-fit tyre. That means the tread width is 18.5cm side to side.

The tread width will be less than 185mm.
Imperial tyres are measured across the tread, metric tyres are measured over the maximum width at the sidewalls. A 7.50" tyre is equivalent width to a 235mm tyre.

Surely most air has got water in it, in the form of vapour, well below boiling temperature/above boiling pressure ?

water vapour and steam (not condensation) are the same thing – water molecules in the gaseous state. All simple molecules (non polymers) have a vapour pressure at any temperature above absolute zero, where a certain proportion are in the gaseous state in equilibrium with any other phases present. Above the boiling point, that proportion is 100%.

As far as I can make out the vapour pressure doesn't depend on the partial pressure of the other gasses present (if any), so it's not the capacity of the air or whatever to hold water, as it could still be there in a vacuum.

Corrosion , who would have thought of that….the AA?

http://www.theaa.com/motoring_advice/safety/filling-tyres-with-nitrogen.html

Why not use bowel gas?

I think I'm getting water vapour and condensation mixed up then.
Condensation is water vapour that has met a cold surface or an area of high pressure, so that the molecules form drops of water. Is that right ?
Most workshops have a water separator in the airline somewhere to remove this condensation, so very little of it will end up inside the tyre.