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Liquefaction of gases is physical conversion of a gas into a liquid state (condensation).

I found that liquefaction is used to get liquid air and then split it into liquid compounds O2, N2, CO2, etc (each gas has its own boiling and melting points and density which can be used to split them).

Imagine a world with an atmospheric pressure of, I don't know... 45 kPa made of 90% N2 and 10% O2, so:

$$ \left| \begin{array}{cc|ccc|c} \text{Gas}&\text{%}&\text{gr/mol}&\text{Mols}&\text{Fractal Mol}&\text{Partial Pressure (kPa)}\\ \text{O2}&\text{10%}&31.99&0.31&\text{8.86%}&3.98\\ \text{N2}&\text{90%}&28.01&3.21&\text{91.13%}&41.01\\ \text{Total}&\text{100%}&60.01&3.16&\text{100%}&45 \end{array} \right| $$

  • O2 10%: 3.98 kPa partial pressure. Hypoxia, in this answer I explain it.
  • N2 90%: 41.10 kPa partial pressure. Nothing bad, in this answer I explain it (and about hypoxia).

Atmophere in this $X$ planet is about 45 kPa, our atmosphere is 101.325 kPa but at 45 kPa we don't die (or at least I think we won't die and water will boil at 41.32 °C (How to calculate it)), the only problem here is the O2 value.

To survive in this planet we could do these 2 ideas:

  • Build domes: We can live in sealed domes where we have machines that make liquefied air and extract the liquid oxygen at 3.98 kPa from the atmosphere and inject it into our dome at 1 atm (21 kPa O2 PP and the rest of N2). This way we don't have to make our own oxygen from water or plants.
    My question is if it's possible to make that machine to "condense" the oxygen from the atmosphere and infuse to our dome constantly (never stopping, otherwise we would die). Obviously this machine would have an emergency power supply.
  • Have a pocket liquefaction personal machine: My other idea is make personal and portable liquefaction machines for each person to concentrate the O2 PP from the air each time they take a breath. My question is if it's possible to make such small and portable machine for each person. Maybe it could be like a backpack with inner batteries.
    Obviously this second idea can be replaced with a simple tank, in the base colonists could recharge their breathing tanks.

Please I don't want "Yes, it could be possible.", I want some explanation behind answers.

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  • $\begingroup$ You already have all the required hard science in the question. Yes, you can liquefy the air on planet X using for example a Linde machine; once the air is liquefied you can use fractional distillation to get the desired mixture of oxygen and nitrogen and pump it into the dome. I've never heard of pocket air liquefiers; I suppose that's mostly because handling liquid air is somewhat hazardous and because of the necessity to find a means to dissipate the heat of condensation. $\endgroup$ – AlexP Jun 24 '17 at 22:27
  • $\begingroup$ Oxygen concentrators are real products I see advertised. I don’t see them replacing a tank for wearing, since it will be heavier than an all-day supply. But use those at home to refill tanks and maintain indoor air. $\endgroup$ – JDługosz Jun 25 '17 at 0:14
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You can certainly do what You envisage, but cheaper and more efficient way of concentrating Oxygen is using membranes.

The relevant data is here and here.

Oxygen concentrators are also used to provide an economical source of oxygen in industrial processes, where they are also known as oxygen gas generators or oxygen generation plants. Oxygen concentrators utilize a molecular sieve to adsorb gases and operate on the principle of rapid pressure swing adsorption of atmospheric nitrogen onto zeolite minerals and then venting the nitrogen. This type of adsorption system is therefore functionally a nitrogen scrubber leaving the other atmospheric gases to pass through. This leaves oxygen as the primary gas remaining. This is the method normally used in many fields ranging from medicine to production of Nitrox (enriched air bottles) for scuba diving.

Note: I don't know if this kind of answer is appropriate for "hard-science". If not I can expand (essentially copying data from the linked pages).

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    $\begingroup$ Right now I can't read them (later I'll read the links). You should "copy" relevant information of the link into your answer to improve it (users don't have to read external links in order get the useful data). Thanks. $\endgroup$ – Ender Look Jun 24 '17 at 23:16
  • $\begingroup$ Oxygen concentrators are not a "cheaper and more efficient way" they are exactly what the OP is describing. $\endgroup$ – John Jun 25 '17 at 4:31
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    $\begingroup$ @John: OP was asking about "Using liquefaction of gases", I was pointing out this is not efficient, using membranes is (and it is in widespread use). $\endgroup$ – ZioByte Jun 25 '17 at 9:55
  • $\begingroup$ @ZioByte then you included the wrong description of how oxygen concentrators work, that is the description of a PSA type generator. $\endgroup$ – John Jun 25 '17 at 14:25
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Liquefaction of gasses is generally done these days using a Stirling engine, but powering the device externally rather than using it to convert thermal energy into mechanical energy. (If you really want to be clever, use one Stirling engine to drive a second one.....

enter image description here

A Stirling engine

The use of a Stirling engine as a cryocooler is well established technology. Using one or more large cryocoolers in the dome is probably the more efficient way of using resources, but in theory it would be possible to have a small cryocooler with each person.

enter image description here

Stirling cryocooler

The downside to this is efficient Stirling engines are fairly complex devices and need to be built to close tolerances, but it is possible to build Striling engines even with fairly low technology (it was invented in the 1800's, after all), accepting lower levels of efficiency.

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Yes, in fact what you are describing already exists. It is called an oxygen concentrator and relies on high surface area materials and rapid pressure change to liquefy nitrogen, extract the gaseous oxygen, then re-pressurize and vent the nitrogen. The come in a variety of sizes and forms including giant industrial and tiny portable versions. Mechanically they are fairly simple and reliable which is what you want in a life support system.

The functional aspect is called "pressure swing absorption" which is used to purify a variety of gasses and is described here.

popular beds (the high surface area thing the nitrogen condenses on) include carbon, zeolite, and even some resins. A breakdown of a slow high purity carbon machine can be found here. Fast cycle devices are common for home use, where extreme purity is not important, they only increase the oxygen concentration and still pass quite a bit of nitrogen, however these can run continuously and produce much larger volumes.

A video breakdown of how the most common industrial form of the device works can be found here just keep in mind when they say nitrogen is absorbed they are referring to the now liquid nitrogen being absorbed the same way water is absorbed into a anything porous.

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