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Surely Hydrogen is four times lighter than Helium so it should float much better in balloons? No, this is not so!
Helium is used for balloons and airships, and it floats in air because it's much lighter than air. Why not use Hydrogen? Because it's very inflammable. Yes, but if we leave aside that air safety issue for a moment, surely Hydrogen is only half the weight, so it should float twice as well in air?
An easy mistake to make. Hydrogen (atomic weight 1, but exists as pairs of atoms (diatomic), molecular weight 2), should weigh 2g per 24 litres at room temperature, whereas Helium (exists as lone atoms (monatomic), atomic weight 4), should weigh 4g per 24 litres at room temperature. But the mistake is to think that this would automatically make it float twice as buoyantly. The fact that's important is not the weight of the gas in the balloon, but the weight of the air which it displaces.
One way to see how this works is to imagine a 25 litre empty oil drum underwater. This will float and will have an apparent negative weight underwater which is equivalent to about 25Kg. You can imagine trying to sink it, and you know it would take about 25Kg of weight to force it down. Now when I said it was an "empty" oil drum, everyone assumed it was of course full of air, and we can ignore the weight of the air. That is how it works. For argument's sake, if it was truly empty or we filled it with a different gas, a light gas such as hydrogen, helium, or even methane, or a heavier gas such as xenon, it would make almost no difference, and the oil drum would still have a buoyancy of about 25Kg. That buoyancy is mainly the effect of the container not being full of water. The 25 litres of water which would be in the full drum would weigh 25Kg. That's not there, so underwater it seems to weigh minus 25Kg. That's how much flotation there is.
Similarly, with a lighter than air balloon, what's important is the weight of air which is not in the balloon. Whether that space is taken up by a light gas such as helium or a lighter gas such as hydrogen, it's the displaced air weight which causes the flotation, equivalent to the weight of the air that would be in a balloon full of air.
But surely the weight of the gas must have SOME effect? Yes, it's true, but the difference is minimal. Both Hydrogen and Helium weigh almost nothing for the purposes of buoyancy in air. In contrast, air is mainly nitrogen, as pairs of atoms, which has a weight of about 28g per 24 litres at room temperature.
To put some figures on it, a 24 litre helium balloon would seem to weigh 4g minus 28g = minus 24g in air. In comparison a 24 litre hydrogen balloon would seem to weigh 2g minus 28g = minus 26g in air. -24g or -26g, take your pick? The difference is about 8%. The insurance risk on the flammable hydrogen gas probably compensates for this!
In the early days of science fiction, it was suggested that balloons could be filled with vacuum. Although this is ultimately a further 8% more buoyant even than Hydrogen, the additional structural reinforcement required for the balloons would swamp such an advantage, probably enough to stop the craft getting off the ground at all.
Incidentally, all gases tend to fill 24 litres (at room temperature) for every gramme-molecular weight's worth.
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