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There ain't no such thing as a free lunch was often a plot point in the works of Robert Heinlein, particularly in regards to air. We know that Air in International Space Station comes at price, in Heinlein's work even the largest stations required regularly payments for oxygen, with penalties usually around loss of access to air.

On Earth oxygen is made available by the biosphere (plants). Nowhere else in our solar system is free (unbound) oxygen readily available. There are some processes that generate Oxygen such as Chemical oxygen generators.

Is there any place in the solar system where oxygen would be a waste product of industry, effectively making oxygen free (without additional cost) to the inhabitants?

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  • $\begingroup$ If you can find a handy use for hydrogen, you could split some water molecules apart, which would give you oxygen. $\endgroup$
    – Ellesedil
    Mar 24, 2015 at 17:40
  • $\begingroup$ Rocket fuel. LH2 chemical rockets normally run fuel-rich, so cracking water via solar power for LH2 and LOX will leave you with some surplus of O₂. If you're using nuclear thermal rockets, you need the hydrogen and none of the oxygen. $\endgroup$
    – Russell Borogove
    Mar 24, 2015 at 18:12
  • $\begingroup$ @Russell Borogove: Why would you use hydrogen in a nuclear thermal rocket in preference to oxygen, or indeed, to liquid H2O? Much less tankage for the same mass, plus you don't need cryogenic storage. $\endgroup$
    – jamesqf
    Mar 24, 2015 at 18:46
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    $\begingroup$ My understanding is that you want a low atomic mass in the exhaust, to yield maximum exhaust velocity and specific impulse. See this thread for good alternatives: spacebanter.com/showthread.php?t=7650 and the nuclear salt-water rocket for a really crazy alternative: en.wikipedia.org/wiki/Nuclear_salt-water_rocket $\endgroup$
    – Russell Borogove
    Mar 24, 2015 at 19:21
  • $\begingroup$ Looks like nuclear-ammonia engines were expected to have an ISP in the 470-550 sec range, while nuclear-LH₂ gets you above 800. That more than pays for additional tankage mass. $\endgroup$
    – Russell Borogove
    Mar 24, 2015 at 19:33

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Agriculture.

According to a MIT MarsOne paper, on the feasibility of the MarsOne program, they found that "our habitation simulations revealed that crop growth, if large enough to provide 100% of the settlement’s food, will produce unsafe oxygen levels in the habitat".

AKA: The industry of creating food for the people living on Mars, would produce excessive amounts of oxygen. So it'd be free to breath oxygen, just not free to eat.

Granted, growing plants on Mars definitely isn't free, as they require water and fertilizer, neither of which are free on Mars. (Mars has no shortage of CO2 at least, which is a very important part of photosynthesis)

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A colony on one of Jupiter's moons, say Europa or Callisto, could have a rocket fuel extraction industry that yielded cheap oxygen as a byproduct. You'd mine ice, melt it, and electrolyze it into H₂ and O₂. The high-thrust rockets you'd want for manned travel back and forth to Jupiter would be LH₂/LOX chemical rockets or nuclear thermal rockets using LH₂ as reaction mass. LH₂/LOX rockets run best fuel-rich, so in either case you'd have surplus oxygen.

I don't know if that would make oxygen free, though. You'd need a vast amount of power to run that industry (and solar doesn't work well 5 AUs out, so I think you want a big fission power plant), and the oxygen still has to be handled and directed where it needs to go -- but it seems like providing breathing air to colonists would be a reasonable, taxable function of the colony state (pace Heinlein).

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