Discussions in comments below How can aerogel be lighter than air? really make an answer to this important. The conclusions there are that aerogel could in some cases be "lighter than air" if one takes only the mass of the aerogel material and ignores the mass of any trapped gas within each cell, and divides by the volume of the whole thing (aerogel including all trapped volume in its cells).
- If you put aerogel in a vacuum does it "blow up" because pressure of trapped gas inside is not balanced by external pressure?
- If not, is that because the structure is strong enough to contain the trapped gas, or because there's not much trapped gas to begin with?
For #2 the latter is more interesting because it suggests that aerogel could conceivably be produced that could float away even at STP.