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Air has a density of about $\mathrm{1.3 kg/m^3}$.

From Carbon aerogels by Marcus A. Worsley and Theodore F. Baumann:

Though silica aerogels held the title of "world's lightest material" for a long time at $\sim \mathrm{ 1 mg/cm^3}$, recently, carbon-based aerogels have shattered that record with a density of less than $\mathrm{200 \mu g/cm^3}$.

So the above-named aerogels would have densities of $\sim \mathrm{1 kg/m^3}$ and $\mathrm{0.2 kg/m^3}$ respectively.

How can they be lighter than air if a part of them is a solid (silica or carbon) that is heavier than air?

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  • $\begingroup$ @Conelisinspace now I wanna know what's in aerogel's cells! Does it blow up in vacuum? If so that would be another down side for this answer. So I've just asked Does aerogel "blow up" in a vacuum? $\endgroup$ – uhoh Aug 4 '20 at 14:20
  • $\begingroup$ Isn't this exactly the same question as physics.stackexchange.com/questions/71069/… ? $\endgroup$ – Deschele Schilder Aug 5 '20 at 14:58
  • $\begingroup$ @descheleschilder Yes indeed, it looks very much the same, although my question gives the facts from a linked article. Also I asked about aerogel in general. $\endgroup$ – Cornelis Aug 5 '20 at 15:25
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    $\begingroup$ I've deleted a number of obsolete or off-topic comments and/or responses to them. $\endgroup$ – David Z Aug 6 '20 at 0:49
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While the summary you cited is a convenient and easy to understand phrase, it is a paraphrase of another cited paper:

The paper says:

The density was calculated by the weight of solid content without including the weight of entrapped air divided by the volume of aerogel (the density measured in a vacuum is identical to that in the air)

So indeed the other answers are correct: the air is not factored into the density, presumably so aerogels can be compared objectively (despite those at higher altitudes and lower humidity being measured less dense).

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  • $\begingroup$ Thank you for citing the paper. I really don't understand, "(the density measured in vacuum is identical to that in air)" ! $\endgroup$ – Cornelis Aug 4 '20 at 9:30
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    $\begingroup$ @Conelisinspace That seems to mean that air is trapped inside the aerogel, and doesn't escape even in a vacuum. $\endgroup$ – probably_someone Aug 4 '20 at 14:25
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    $\begingroup$ @probably_someone I disagree. This is meant to say that if you put this aerogel into a vacuum, pumping all the air out of it, you'd get the same density as they calculated. If you measured the weight of the aerogel in air you'd get a different figure, but they didn't do that -- they calculated the density based on how much carbon material was used and how much volume the finished product occupies. $\endgroup$ – Ross Presser Aug 4 '20 at 15:39
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They're not lighter than air (or almost certainly are not). The mass of $1\,\mathrm{m^3}$ of such a material, in air, is $\rho_m f_m + \rho_a (1 - f_m)$, where $\rho_m$ is the density of the structure, $\rho_a$ is the density of air, and $f_m$ is the proportion of the bulk volume of the material which is structure rather than air. I think that $f_m \approx 0.002$ for a typical aerogel. The density they are quoting is then $\rho_m f_m$.

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  • $\begingroup$ Yes, 99,8 % of the volume is air. $\endgroup$ – Cornelis Aug 3 '20 at 16:40
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If one measured the density of a huge led zeppelin with a vacuum inside (like is done with aerogels; the until now lightest aerogel is aerographene, with a density of about 13% of air) this density could be lower than air if the led zeppelin is big enough. Can you imagine the led zeppelin floating when it's filled with air?

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    $\begingroup$ +1 if this is a serious answer and "led zeppelin" should have been simply "zeppelin", and also +1 if this answer is about Led_Zeppelin :-) $\endgroup$ – uhoh Aug 4 '20 at 14:10
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    $\begingroup$ Another example of a nearly empty thing here: Did Echo 2 remain spherical without requiring gas pressure? If so, how is this known to be true? $\endgroup$ – uhoh Aug 4 '20 at 14:13
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    $\begingroup$ @uhoh - led zeppelin with a vacuum inside? Would that be "Houses of the Holey"? $\endgroup$ – ItWasLikeThatWhenIGotHere Aug 4 '20 at 15:31
  • $\begingroup$ @ItWasLikeThatWhenIGotHere nice! :-) $\endgroup$ – uhoh Aug 4 '20 at 15:41
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    $\begingroup$ @ItWasLikeThatWhenIGotHere Haha! Well, it only goes to show you CAN use a Led Zeppelin to float to heaven instead of taking a stairway! $\endgroup$ – Deschele Schilder Aug 5 '20 at 15:43
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It sounds like they are measuring the weight in vacuum.

OK, try this. You weigh an open glass beaker. It not only contains air, it has about 15 pounds of air above it to the top of the atmosphere. Does the weight of the beaker include the weight of the air above it or in it? No. The air pressure is the same on all sides, and it doesn't count.

If you weigh a balloon that's full of air, you only count the air that's under pressure.

So an aerogel can be mostly empty space, and the weight of the aerogel itself is very low. But it isn't lighter than air unless the empty spaces are filled with vacuum.

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    $\begingroup$ No, an aerogel can't be mostly empty space, the pores are all filled with air. $\endgroup$ – Cornelis Aug 3 '20 at 16:37
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    $\begingroup$ Yes, and then its no aerogel anymore ! $\endgroup$ – Cornelis Aug 3 '20 at 17:14
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    $\begingroup$ I had to read this answer twice before I got it, but I think it's right. I don't think the measurements were done in vacuum, though I haven't read the literature. Rather, I think you're saying that placing a cubic meter of aerogel on a kitchen scale would make the scale say "200 grams," because the kilogram of air trapped within the aerogel is neutrally buoyant in the atmosphere. $\endgroup$ – rob Aug 3 '20 at 19:53
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    $\begingroup$ An analogy: consider a kitchen sponge which floats on water when dry, but which sinks when waterlogged. The sponge itself is less dense than the water, but the sponge plus water is not. $\endgroup$ – rob Aug 3 '20 at 20:04
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    $\begingroup$ You could, theoretically, create a material which consists of a bunch of bubbles filled with helium or hydrogen, which would then be overall lighter than air, but it's near impossible to prevent such gases from quickly leaking out (without adding more weight than you lose from the gas just to keep it sealed). Or else we might all be using helium-filled bubble wrap to reduce shipping costs? $\endgroup$ – Darrel Hoffman Aug 4 '20 at 13:53
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It's lighter than the air it displaces.

However, it doesn't actually displace the air. The aerogel is almost entirely empty space, and air is free to occupy the voids in the aerogel. Thus the aerogel, in air, is less than twice the density of air alone.

If you tried to wrap the aerogel in plastic and suck all the air out, the considerable force of 100 kPa would surely collapse the aerogel. If the aerogel was strong enough to prevent that, then yes, you could build foam airships that way.

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  • $\begingroup$ Maybe some skeleton could help the aerogel to hold. However, there is no need for the aerogel if it can happen. $\endgroup$ – peterh Aug 5 '20 at 20:25
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Nice question. For this problem is good to grasp Wigner–Seitz radius - it's radius of a sphere whose volume is equal to the mean volume per atom in a solid. Wigner radius relates to mass density in such way :

$$ r_{w}= \sqrt[\Large{3}~~~]{{\frac {3M}{4\pi Z\rho N_{A}}} } $$

where $M$ is molar mass, $Z$ is amount of free electrons per atom, $\rho$ is mass density, and $N_{A}$ is the Avogadro number. So when you will pack atoms/molecules in a scarce way,- Wigner radius will become big and so mass density of material will decrease. Using this methodology you can even make nano-structures composed from iron or other metals which density will be smaller than that of air. There's no any magic here.

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  • $\begingroup$ This answer has very nice Latex code. $\endgroup$ – peterh Aug 5 '20 at 20:06
  • $\begingroup$ @peterh-ReinstateMonica Thanks $\endgroup$ – Agnius Vasiliauskas Aug 5 '20 at 20:12

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