|MadSci Network: Physics|
There are competing processes involved in this situation. Which one wins will ultimately determine what happens.
The temperature of space varies depending on where you are. Very deep space, i.e., intergalactic space, has a temperature of about 4 K. Near Earth Orbit (NEO) has a temperature ranging from about 173 K to 373 K depending on if you are in shade or sunlight. The temperature may thus be sufficiently low to freeze the water nearly instantaneously.
The pressure will also affect the phase of the water. The triple point of water where liquid, gas and solid can all be present can be raised to room temperature if the pressure is decreased. This can be easily demonstrated by placing triple distilled water in a bell jar chamber and pulling a vacuum with a mechanical pump. At some point, the liquid water will be observed to simultaneously boil and freeze.
The introduction of a container, even a thin balloon implies that any gas generated will be contained. Therefore, the water would no longer be in a vacuum. The equilibrium phase(s) for water at a given temperature will therefore shift as the pressure changes.
The most similar situation I can find involves the Space Shuttle. During flight, the excess water is expelled into space. It freezes. Therefore, it is most likely that any water in a balloon in the situation you describe would freeze solid before boiling.
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