[SomeGuy]

My understanding is that in a vacuum, you can still 'burn' as long as an oxidizer is present, but what happens to that chemical? Specifically, if I burn hydrogen and oxygen in a vacuum, what happens to those chemicals? I doubt they change into something they weren't, double doubt they just disappear, but I can't wrap around what actually happens. There's very obviously something happening

[Aldebaran]

Outer space is considered a near perfect vacuum yet rockets burn fuel (which could be your example of hydrogen and oxygen). The product of the reaction would be the same.
On a different scale if you had a vacuum container in the lab down here on Earth and you placed some hydrogen and oxygen in the container it would no longer be a vacuum!

[SomeGuy]

Outer space is considered a near perfect vacuum yet rockets burn fuel (which could be your example of hydrogen and oxygen). The product of the reaction would be the same.
On a different scale if you had a vacuum container in the lab down here on Earth and you placed some hydrogen and oxygen in the container it would no longer be a vacuum!

By that extent of logic, within a vacuum chamber (which is more where my thought experiment takes place) one could burn and then reburn the same amount of oxygen/hydrogen indefinitely, which I'm pretty sure violates the first law of thermodynamics...

Important sidenote, the only reason I want to consider the reason in a vacuum is to prevent contamination (like carbon stealing the excited oxygen into carbon dioxide, a nonflammable). Other than that it loses it's need.

[Aldebaran]

Your logic is flawed.
Consider the vacuum chamber with nothing but a vacuum in it. Now add your hydrogen and oxygen. First thing to note is it is no longer a vacuum because it contains hydrogen and oxygen. Nevertheless let’s pass on from that (crucial) detail and assume we ignite the gas mixture. The reaction takes place and if the stoichiometry is right they will produce water vapour which we might expect will condense mostly to liquid water at room temperature . If the proportions of the gases are not exactly per the equation (ie one is in excess) then one or other will be present in addition to the water. There is no possibility that they can somehow spontaneously regenerate and be reused.

[SomeGuy]

I'm aware that's not how that works, nor do I think it would regenerate, but this does partially answer my question. I guess to limit the question, what would happen if only one of those were burned, say oxygen? That way it can't bind with anything that isn't flammable; can that oxygen be used again in combustion? Or is it somehow unable to after it's been used, and why?

[jeffmoonchop]

Oxygen alone wont burn

[billnotgatez]

 Hydrogen alone will not burn either

[Enthalpy]

Rocket engines can operate in vacuum, on Earth too if in a vacuum chamber with proper pump... That's useful to test some engines that expand the gases to a very low pressure. Cutting the nozzle to the 1bar diameter would not tell if the lower part of the nozzle, often uncooled, survives the temperature.

Even for small rockets, such chambers and their pump are an interesting challenge. I heard of a case at Estec where an electrical connector, like 1dm², was just forgotten, leaving a hole. The experimentators noticed an abnormal suction sound but the pump achieved vacuum nevertheless and the experiment proceeded.

"Burning" needs a fuel and an oxidizer (though we might call a few recombinations "burning") that react to form new molecules. The oxidizer is often air, but not always. Hydrogen alone doesn't burn, oxygen neither. Hydrogen burns with the oxygen from air or with an extra supplied oxidizer.

[SomeGuy]

Jeffmoonchop, billnotgatez, and and especially enthalpy, thank you. This specifically answers my question. Hope y'all, and everyone else, have good days