Hi Scott, great question! The answer can be found by looking into what makes one thing more buoyant than another--Archimedes' principle describes this well (see below). Here, let's go through each of the variables:

Fb - is the buoyant force, which basically tells us how heavy of an object (here, an airplane) we can lift using this force p - is the density of the liquid that we are displacing, here it's the density of water V - is the volume of the liquid that we are displacing, which is again water: see this image.

So you might be wondering, then "wait, so the density of the gas I use to fill the wheels doesn't matter?" Turns out, that's correct! As long as your fluid is not adding significant mass, then it really doesn't matter what gas you are using to fill up your tires or floats. Based on Archimedes's principle, if you want to have less buoyancy force (letting your airplane sit lower in water), then you should decrease the volume displaced--for example, by making your wheels smaller. And vice versa: if you want to have a higher floating airplane, you should make your wheels larger.

Look at this image.

So really, it doesn't matter if you use noble gases or air (although air is free, so I might stick with this). What you should focus on ishow big or small you make your floats / tires. If you can't change the size of your tires, add more weight to your amphibious plane and it will sink lower into the water. Good luck!

I don't see why not one could use for example Xenon , Xe. This behaves more or less like an ideal gas but it has a high molar mass of 132 g/mol. Air on the other hand has a mean molar mass of about 28 g /mol.

Interesting question! Buoyancy, or the ability for an object to float in a fluid, is entirely dependent on the fluid properties and the volume of the object. There is actually an equation to determine the buoyant force, which looks like:
Buoyant Force = - (Fluid Density) * (Gravitational Acceleration) * (Volume of Fluid Displaced by the Object)

The heavier that object can be while still floating, the greater the buoyant force! You can try this out yourself with a few things from around your house. I grabbed a big glass bowl to fill with water, a plastic container that can displace volume while still being light, and something small that can fit into the plastic container like a small candle (just make sure whatever you choose can get wet!). If you place the plastic container upright on the surface of the water, it should float. If you look through the side of the glass bowl, you'll see that the container is resting slightly below the water line, and it has displaced the same volume of water as the volume of the container that is currently submerged. That correlates directly with the volume of fluid displaced by the object that we use in our buoyant force equation. It's not a lot, but it's noticeable! This means that we have a small buoyant force because the plastic container is not very heavy. Next, if you place the candle into the container that is floating in the bowl, you'll see that the bowl still floats. The weight of the bowl has increased with the addition of the candle, and the buoyant force is large enough to keep it floating. This is because, if you look through the side of the bowl, you'll see that the plastic container is now sitting lower in the water and that more of it is submerged. This means that, with the increased weight, the container is also displacing a larger volume of water-- which also works to increase the buoyant force!

Lastly, if you take the plastic container out of the water and instead place the candle in the water by itself, you'll see that it either sinks or is almost completely submerged but still floats. This shows us that the size of the object, and most importantly the volume of water that it can displace, is a very important variable in this problem. The candle was able to float when in the plastic container because it could displace a greater amount of water, but when it is just on its own it sinks even though the weight of the candle within the container was almost the same as the weight of the candle alone.

We can see from this little experiment that the buoyant force is heavily tied to both the shape and the weight of the object, andthe buoyant force will change in response to changes that we make to that object. All of this is to say that, for your question of an amphibious plane, there are a lot of factors to consider here!

Changing the gas that fills the tires will certainly change the weight of the plane, but it likely won't change the size of the tires nor the shape of the plane. If we look back to our buoyant force equation, we see that the fluid density of the water won't change with this new gas in the tires and the gravitational acceleration certainly won't change unless we move this to a different planet, but we do expect that the volume of displaced water may change.

What we need to consider is whether or not this slight change in weight due to a different gas in the tires is enough to change the volume of displaced water by a noticeable amount as the plane is floating. If the gas is heavier than the air that usually fills the tires then the plane will be heavier, it will displace a slightly larger volume of water because more of the plane will be submerged, and the buoyant force will increase as a result. If the gas is, instead, lighter than the normal tire air then the plane will be lighter, it will displace a slightly smaller volume of water and the buoyant force will decrease accordingly.

If you want to make minor adjustments, I'd say that it's worth looking into! If you want to make big changes to how the plane floats on the water and how much of it is submerged as it floats, changing the shape of the plane or changing the weight elsewhere in the plane may be a better option.

Thank you for this great question and keep investigating!

One could fill the tires of an airplane with anything they wanted, including an inert gas. To make the tires and/or airplane less buoyant than one using air, the gas would simply need to be denser than air (at the same pressure). The gas being inert is irrelevant though. And even if the tires are filled with normal air, that gas mixture is already mostly inert - nitrogen gas comprises ~80% of the atmosphere and is practically inert. Further, larger airplanes have tires filled with only nitrogen to help with temperature management, oxidation of the rubber, and slowing gas leakage so the tires remain inflated.

'Inert' gases carry out a few reactions, so they're called 'noble gases' now. Wouldn't helium and neon increase the buoyancy of the tires?

Read here for more information.

I'm not sure why an inert gas in tires would make them less buoyant, or why you would even want them to be less buoyant.

The problem with inert gasses is that they are comparatively rare on Earth. If you want an inert gas for its inertness, nitrogen gas is so unreactive that it almost might as well be inert.

Dear Scott, while this is possible, it might not be the most cost effective way to tackle this issue. Almost nothing is as cheap as the air in the atmosphere, and even special tires wouldn't be completely air-tight, they'd have to be refilled with the inert gas.

Nitrogen is a semi inert gas, but that's mostly what the atmosphere is made of anyway (78% nitrogen, 21% oxygen + some other stuff like CO₂, H₂O, H₂ in much smaller amounts). I think pure nitrogen would be less dense than the atmosphere, because each N₂ molecule is a little bit lighter than each O₂ molecule.

Assuming that you meant one of the noble gases (which are all inert), which would be denser than air, the cheapest one is argon gas, which I buy for about $70 per cylinder in my lab.