How high can it float?
This question is easily answered: 53 km http://www.isas.jaxa.jp/e/special/2003/yamagami/index.shtml
But, that is not what I am really after.
Imagine a balloon made of unobtanium and filled with impossibrium gas with a volume big enough that, when combined with the payload, the bulk density is about 5E-11 kg/m^3. (This matches the atmospheric density in the vicinity of the International Space Station at about 400 km http://www.braeunig.us/space/atmos.htm)
How high would that imaginary balloon float, and why would it stop going up? Remember, this is an imaginary balloon and therefore it bursting is not the answer I am looking for.
My best guess is that the balloon stops going up when it reaches the turbo pause at 80 to 100 km. https://en.wikipedia.org/wiki/Turbopause This is the altitude where the atmosphere is so rarefied that it no longer supports convection - molecular diffusion becomes the dominant gas transport mode.
So what about it? can anyone think of a reason the imaginary balloon would not make it to 80 km, or that it would keep going past 100 km?