Floating Masses in Gas Giants This may be a very stupid question, as I know little about astrophysics, but if solids like Aerogel can float in gasses like sodium hexafluoride, could there be pressures high enough on gas giants to compress a gas to the point where solid particles such as dust collide and create floating landmasses?
Buoyancy, following Archimedes' law, depends on the volume the body and the density of displaced material. The force is 
$$ F_{buoy} = \rho_{gas} \cdot V_{body}\cdot g$$
which has to act against the bodies' own weight $F_{weight} = -m_{body} \cdot g$.
Here $\rho$ is density, $V$ is Volume, $g$ the local gravity.

If you're referring to this video, then the aerogel that was created in the 1980's is essentially a high-tech balloon.

There are a few points that need discussion here.

1. Balloons the size of continents don't occur naturally anywhere.
I think we can take this as given.

2. The filling gas
acts to decrease $F_{weight}$ and its pressure must be enough to hold up the body volume. Else the body will collapse and the buoyancy decreases to zero.  

A floating continent would need some appropriate filling gas in large quantities, that has lower density than the gas giant atmosphere.
Impossible is a strong word, but this seems very impossible to me. Also for the continent then be able to uphold its structure under its own weight would be very difficult.

3. Particles either float or experience drag.
If they float, they're coupled to the gas flows. Once they would grow larger, they start experiencing gas drag. When this happens, they loose their momentum and are dragged down into the depths of the planet.
They then will contribute to the structure of the deep planet, but are lost to any continent-building process.

So even if your floating continents seem impossible, I think is not a stupid question at all. I might just throw this on our students and test their understanding of buoyancy!