[chris (OP)]

If a cup of water were taken outside the International Space Station and observed, would it boil off, freeze solid, or do both (but not at the same time)?

I'd be interested in everyone's opinion...

[Halc]

Well, if you put water in a jar and pump the air out, it does boil until it freezes, and yes, at the same time.
Space is a little different since there's no jar to keep the pressure up.  It would probably just flash boil and fly from the cup without ever getting a chance to freeze.  It takes pressure to freeze, and there is none outside the ISS.

[chris (OP)]

Pretty cold in the shade though isn't it? And pretty hot in the sun too...

[Janus]

According to this article, waste water dumps usually freeze into ice crystals and then sublimates.
https://www.space.com/7274-mystery-explained-glow-night-sky-astronaut-urine.html

[chris (OP)]

not to absolute zero that it would need to freeze.

Absolute zero?

[Halc]

not to absolute zero that it would need to freeze.

Absolute zero?

Janus links an article that shows that what I say is not entirely true.  The water apparently forms some tiny frozen ice balls.  Looking at a phase diagram of water, such as https://upload.wikimedia.org/wikipedia/commons/0/08/Phase_diagram_of_water.svg
at negligible pressure, water is solid below about -60^oC, and the boiling of the water outside the ISS easily cools it to that temperature, and the physical effect of the boiling will maintain real pressure for a time, so the fact that the graph is in log scale for pressure (and thus continues infinitely down) doesn't matter.  Pressure on the water doesn't drop to zero just because you threw it out into the vacuum of space.

I had been looking at less detailed phase diagrams, many of which depict the line occurring near absolute zero, not at  over 200^oK.

[Tomassci]

If a cup of water were taken outside the International Space Station and observed, would it boil off, freeze solid, or do both (but not at the same time)?

I'd be interested in everyone's opinion...

Well, I suggest it will first freeze, due to absence of any molecules, and then sublimate. Exactly how comets "glow"

[Stephbaker]

If a cup of water were taken outside the International Space Station and observed, would it boil off, freeze solid, or do both (but not at the same time)?

I'd be interested in everyone's opinion...

I think it would end up freezing.

[syhprum]

I see problems trying to perform this experiment, firstly you cannot carry  cup of water around in the quasi zero gravity of the ISS it would simply float out of the cup and form a floating ball of water.
Let us assume you took a bottle of water into the exit air lock and attempted to pour it into a cup it would then form the afore mentioned floating ball now what would happen next ? I assume that it would form a skin of ice and if the pressure was lowered sufficient slowly that it would maintain sufficient pressure to stop it sublimating and outside where the black body temperature is about 250°K form a solid ball of ice but if the pressure was lowered rapidly it would simply sublimate to ice crystals