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Hydrogen and oxygen gases can be combined to form water and a lot of heat. As with many exothermic reactions, the heat from this process can provide activation energy to the reaction of more H2 with more O2 in a runaway process commonly referred to as an explosion. I would like an atmosphere rich in both hydrogen and oxygen gases, but I don’t want it to explode. Well, I don’t want it to explode too much. Weather systems creating pockets of high pressure that spontaneously ignite, or lightning strikes resulting in exploding pockets of atmosphere sound awesome. What I need to avoid are planet-consuming runaway explosions that spectacularly scour the surface of the world of all life. A second consideration is that I would like this atmosphere to be breathable by humans.

How much hydrogen and oxygen can coexist in the atmosphere before apocalyptic runaway combustion becomes a possibility?

My current explanation for this world is that a biological or geological process constantly emits large amounts of hydrogen into the atmosphere but that constant small fires and explosions prevent it from accumulating to more dangerous levels. I’m trying to determine what level that is, where explosions are happening but there isn't a risk of extinction level events.

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The explosive range for Hydrogen is 4% to 75%

This is really a question about stoichiometry. If your planet's air (without the Hydrogen) is roughly the same as the earth, then Hydrogen will start to burn (given an appropriate ignition source) at 4% Hydrogen by volume. If you get above 75%, then it's actually the oxygen you won't have enough of and you won't be able to burn again.

What we're talking about here is called the lower and upper explosive limits for a given gas, in this case Hydrogen.

The most explosive concentration is at about 35% hydrogen, this is when there is exactly twice the amount of hydrogen as there is oxygen, so neither of their concentrations are limiting. The reason it's not 42% (twice the 21% oxygen in air) is because the hydrogen displaces both the oxygen and the nitrogen.

It is worth noting that as you get closer to the 35% concentration that the explosion will progress from what just looks like a fire (whooshing flames) to a much more potent, almost instantaneous explosion (like a pop or a bang).

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    $\begingroup$ "The reason it's not 42% (twice the 21% oxygen in air) is because the hydrogen displaces both the oxygen and the nitrogen" - could you explain?. $\endgroup$
    – theRiley
    Commented Nov 1, 2018 at 1:30
  • $\begingroup$ Stoichiometry governs the amount of energy you can get from burning a given mixture, but the question of whether it will burn on its own (without an external heat source) is MUCH more complicated. For a gas mixture to explode, it needs to generate heat (significantly) faster than the heat is taken away, which involves questions of heat transport and fluid dynamics that, for practical purposes, can only be decided empirically. Prior to the first atomic bomb test, it wasn’t know for certain whether the temperature of the explosion would be enough to ignite the nitrogen in the atmosphere... $\endgroup$
    – bobtato
    Commented Nov 1, 2018 at 1:59
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    $\begingroup$ @bobtato A nuclear explosion is certainly hot enough to oxidise nitrogen. The (very slight) concern was whether the reaction would be self-sustaining and spread through the whole atmosphere rather than being confined to the immediate vicinity of the nuclear explosion. $\endgroup$
    – Mike Scott
    Commented Nov 1, 2018 at 7:22
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    $\begingroup$ @theRiley To keep the math simple, suppose the current atmosphere is 20% oxygen and 80% nitrogen. If you "add 10% hydrogen" to that, you DON'T end up with "10% hydrogen, 20% oxygen and 80% nitrogen" because the percentages have to add up to 100%, not 110%. You actually get 9% hydrogen, 18% oxygen, and 73% nitrogen. $\endgroup$
    – alephzero
    Commented Nov 1, 2018 at 12:11
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    $\begingroup$ Thanks @alephzero that's exactly what I was saying. The actual math is as follows: Assume the air composition is 21% oxygen, and 79% nitrogen (and other inert gasses). When Hydrogen is added to the system up to X% then the atmospheric composition becomes: X% Hydrogen, (21-0.21*X)% Oxygen, and (79-0.79*X)% Nitrogen. The point at which X%=2*(21-0.21*X)% is at X%=35% (approximately) $\endgroup$
    – Mathaddict
    Commented Nov 1, 2018 at 18:26
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Gaseous molecular hydrogen doesn't stick around; it escapes into space. The places where it doesn't do so are places with substantially more gravity than Earth (eg. gas giants).

The hydrogen that doesn't escape will react, but (for the most part) non-explosively, because hydrogen and oxygen will, left to their own devices, settle like oil and water, with the hydrogen in the upper atmosphere, either escaping, or undergoing UV excitation which breaks the hydrogen into atomic hydrogen, which will react with just about anything to form hydrides or salts.

If you had a uniform distribution of, say, 20% hydrogen by volume across the planet, then yes, a single spark would trigger a cataclysmic exothermic reaction. It would be loud. But there's no way such a distribution could remain mixed for any substantial period of time, and you'd need to continuously produce enormous quantities of hydrogen (assuming your planet is earthlike).

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    $\begingroup$ +1, but also : on geological time scale hydrogen would oxidize non explosively. Would be hard to produce it fast enough to accumulate 20% $\endgroup$
    – Mołot
    Commented Oct 31, 2018 at 22:07
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    $\begingroup$ Would be hard to produce it fast enough to accumulate any substantial value - the Earth is not short on sources of ignition. $\endgroup$
    – jdunlop
    Commented Oct 31, 2018 at 22:55
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    $\begingroup$ + "it would be loud". $\endgroup$
    – Willk
    Commented Oct 31, 2018 at 23:41
  • $\begingroup$ +1 and don't forget that you'd expand the volume of the atmosphere by just pumping more gas into it, unless you increase gravity as well to keep it all together in the same volume, thus making the escape of hydrogen even easier. $\endgroup$
    – jwenting
    Commented Nov 1, 2018 at 5:32

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