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Title says it all. If hydrogen and helium are lighter than air, why won't liquid hydrogen and liquid helium defy gravity?

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up vote 14 down vote accepted

Gaseous hydrogen and helium are lighter than air. Hydrogen, helium and air are close approximations to ideal gases, and for an ideal gas the volume of one mole of gas is about 22.4 litres. That means the density of an ideal gas is proportional to its molecular weight, so hydrogen ($M_w = 2$) and helium ($M_w = 4$) are lighter than air (average $M_w = 28.8$).

However you're asking about liquid hydrogen and helium, and liquids are much denser than gases because the molecules are much more tightly packed. For example the density of liquid hydrogen is around $68 \,\mathrm{kg/m}^3$ compared to air at about $1.3 \,\mathrm{kg/m^3}$. That's why liquid hydrogen doesn't float in air.

Incidentally, the density of liquid nitrogen (a close approximation to liquid air) is about $800 \,\mathrm{kg/m^3}$ so liquid hydrogen would float on liquid air.

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Because liquid hydrogen and liquid helium are much heaver than air.

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please explain why. – think123 Jan 22 '13 at 7:22
Well, this is an experimental fact - it is easy to look up their densities and the density of air. Or do you want some theoretical explanation why liquids typically have higher densities than gases? – akhmeteli Jan 22 '13 at 7:28

First of all, no mass 'defies' gravity. Second, the normal state of these two is air so they cannot be 'lighter than air' which would in effect be lighter than themselves. If you were meaning to ask why the liquid forms of these elements won't float, the answer is simply because liquids don't float. This is one of the properties that defines a gas. The molecules must overcome the IMF's and have a high enough KE but liquids do not. The density of the liquid would have to be lower than that of the gas and no liquid has a lower density than a gas. Although hydrogen has a low gaseous density, it's liquid density is still considerably greater than any gas.

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Actually, hydrogen and helium are lighter than air. Air is made up of other gases as well, and H and He will sit at the top of a room filled with air. – Kitchi Feb 24 '13 at 13:25

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