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Shuttle's SSME uses cryogenic Hydrogen(LHX) and Oxygen(LOX) as their propellent to give hot water vapour. If I somehow manage to get the exhaust plume and condense it to liquid, Can I drink it directly(or is that toxic) ?

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I wouldn't recommend it, and there's several reasons why.

First, even if we assumed you'd get chemically pure water out of the exhaust plume, in essence distilled water, it would lack any dissolved minerals and cause you to lose electrolytes. If that was all that was wrong with it, then small quantities wouldn't hurt you, but you'd have to substitute lost intake of trace minerals before your electrolyte levels become dangerous to your health. Distilled water would essentially cause you to require more liquids in your body, since it would reduce levels of your body fluid solvents and all your cells would swell up through a process called osmosis, trying to match levels of solvents with their surroundings and in turn requiring more water. While on itself not life threatening, you'd actually be undergoing faster dehydration, funny enough, and combined with dropped levels of electrolytes can lead to complications like high blood pressure, arrhythmia, and so on.

Second, such condensed and cooled exhaust plume water would be highly ionized. Depending on the levels of ionisation and amounts of such water that you'd drink, it could go from a mildly alkaline irritant to corroding through and dissolving your internals. It might also form hydrogen peroxide with atmospheric oxygen, although it isn't really stable so that wouldn't last too long. Either case, it wouldn't be a bad idea to first test its pH levels.

Third, those propellants went through a lot of metallic machinery at extremely high pressure to get to the rocket's exhaust. They also changed their temperature from one extreme (LOX and LH2 are both cryogenic liquids) to the other as they burn and result in mostly molecular water at the exhaust. It might contain heavy metals, perhaps in trace amounts, or perhaps enough to be toxic or even kill you. Other impurities, such as lubricants aren't excluded either.

And there are likely other reasons why you shouldn't drink it that I can't think of now, but let's say that these three reasons I mention should suffice to discourage anyone in trying it out, at least without thoroughly testing the liquid first before drinking it.

I should probably note that even though this sounds deadly toxic and less than friendly to the environment, it actually isn't that bad and these exhaust plumes would naturally deionize long before they would fall back to earth during a normal rocket launch using LOX/LH2 propellants as they condense and combine with atmospheric vapor. They however wouldn't purify too, so yes, even such green rockets can pollute. By far not as much as most other alternatives though.

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The biggest risk I foresee is nitric acid. A hot open flame in the atmosphere will cause N2 and O2 to react, creating a number of different molecules such as NO and NO2. These dissolve reasonably well in water and will form acids.

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