Would it be possible to give a human artificial gills, capable of allowing humans to breathe underwater (with no outside source of oxygen except from H2O)?
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Nope.
Water contains less than 1% of the oxygen (as dissolved O2) that our bodies need for life. (Dissolved oxygen is the only form available to life; the oxygen in molecular H2O being chemically inaccessible.)
No Gill structure that could conceivably be fitted to a human being could draw anything like enough breath for human life.
Interesting one. Sharks are bigger than humans and manage with gills. I suspect the answer is no, because sharks and fish are poikilothermic, they adopt the temperature of their surroundings whereas humans and other mammals are homeothermic – they maintain a constant body temperature. There’s a huge difference in energy and therefore oxygen requirements. Humans burn smoking amounts of oxygen and food just to stay warm. You could have gills, but you’d have to be cold blooded.
And you wouldn’t be able to make enough energy to power a human brain, a seriously power hungry organ. So you wouldn’t be human…
Theoretically you could make such a device, but in order to extract enough oxygen to supply a human’s needs from just the water, the device would have to bigger than the human. (Even if you could miniaturize all the components, the volume of water you’d need to pass through it would result in a flow rate that would have lethal consequences for any human wearing the thing)
At which point you might as well put your human INSIDE the device and call it a submarine.
The theoretical answer is yes, but such an apparatus would be enormous, heavy, and use a huge amount of power.
The other answers all refer to extracting the Oxygen gas dissolved in the water.
How about electrolyzing the water to get O2 and H2 gases? I have not made any calculation but the size of the apparatus will be much smaller (provided you have a suitable power source).
The remaining problem would than be how to dilute the pure oxygen (to about 20% volume) to be breathable. It is well known that oxygen can be diluted with Helium, to replace Nitrogen for deep diving. However, the only other gas available from the electrolysis process is Hydrogen. I have no idea if breathing a mixture of 80% hydrogen with 20% Oxygen is safe. Does anyone of the readers know?