Pretty much just what the thread title says. Imagine starting right now, all processed/exhaled air by animals including humans just vanishes as it is exhaled. How long do we have until there is not enough oxygen for us or co2 for the plants?
I was reading an article just the other day in a similar vein that answered this question (it was related to the sun just disappearing). Apparently, approximately a thousand years. I’ll see if I can dig the article back up.
Alright, it was a Youtube video, here: What If The Sun Disappeared? - YouTube.
“What if the sun disappeared?”
A lot of it is a retread of stuff commonly discussed in GQ, but an awesome view nonetheless.
Thanks for the link and the info!
No problem! He’s got some other videos with promising titles as well, if you feel like going down the YouTube rabbit hole 
TL;DW
How did they estimate the total respiratory rate of all animal life?
Here’s mine. I’ll work with the human race, since the number is calculable; I’m at a loss to estimate repiratory rates for all animal life on earth.
Assume average human (including all adults and children) weighs 60 kg.
Respiratory tidal volume then is 445 ml.
Respiration rate is 12 times per minute, so each human being expels/destroys 5.345 liters of air per minute.
Human population is 6.688 billion people.
So the human race exhales 35,750,400 cubic meters of air per minute. at 1.2 kg/m[sup]3[/sup], that’s 29,792,000 kg/min.
This site says we need an oxygen concentration of at least 15 percent to avoid affecting our mental function. This assumes standard sea-level pressure of 101.325 kPa. Alternatively, we could maintain relative concentration, and just let ambient pressure drop until the O[sub]2[/sub] partial pressure is equivalent to the former case. Since normal seal level O[sub]2[/sub] concentration is 20.9%, we need to lower sea level pressure to 15/20.9*101.325 = 72.72 kPa.
So we have to get rid of (101.325-72.72)/101.325 = 28.2% of the atmosphere.
How much does the atmosphere weigh?
surface area of the earth = 4 * pi * r[sup]2[/sup] = 4 * 3.1416 * 6,400,000[sup]2[/sup] = 514x10[sup]12[/sup] m[sup]2[/sup]
total mass of the atmosphere = 101.325 kPa * 514x10[sup]12[/sup] m[sup]2[/sup] / 9.81 m/s[sup]2[/sup] = 5.3x10[sup]18[/sup] kg
How long does it take to exhale 28.2% of that?
5.3x10[sup]18[/sup] kg * 28.2% /(29,792,000 kg/min) = 50x10[sup]12[/sup] minutes, or 95.6 million years.
If the video’s answer was 1000 years, then he’s suggesting the total mass (and therefore respiratory rate) of all animal life on earth is about 100,000 times as great as that of the human race. Anyone know whether that’s a plausible figure?
[sub]Also, somebody check my math…[/sub]
TL;DW followed by a TL;DR
The thousand year figure may have been taking into account that, by 1000 years with no sun, the atmosphere would have condensed into liquid. Admittedly, that’s not exactly what the OP was looking for, but it was a good place to start.
There is a short science fiction story called “Exhalation” by Ted Chiang that is a little on point, and also a very good story. I’ll leave it at that so as not to spoil things.
When you say that the air disappeared, is it being replaced by something that our lungs/body can’t use or does the atmosphere start drawing a vacuum? If we start living in a vacuum, I could see that causing issues before the lack of oxygen does. I wouldn’t be surprised if we couldn’t physically inhale after a while (at least weaker people/animals).
I was thinking that the gas just “vanished” so yeah I guess a vacuum. But if you want to assume we just breathe out pure hydrogen or nitrogen or something, that’s cool with me.
Also, thanks to the poster who did such a fine calculation and showed their work! That was an awesome post.
Either way, (reduced total pressure or decreased O[sub]2[/sub] concentration), the primary problem for animals is decreased O[sub]2[/sub] partial pressure. when ppO[sub]2[/sub] goes down, we run into physiological difficulties well before zero total pressure.
Inhalation effort does not change with changes in atmospher pressure. the pressure inside your lungs is the same as the pressure on the outside of your body.
Here are some test subjects in a high-altitude simulation chamber. The caption says the chamber is simulating 25,000 feet; at that altitude, ambient pressure is about 5.5 psi, which means O[sub]2[/sub] partial pressure is about 37% of normal. The subjects are breathing normally, no exceptional effort. The guy second from the right lasts about two minutes in these conditions before he is completely unable to function and on the verge of passing out (the attendant has to put his oxygen mask back on for him here.) The rest of the people start showing various symptoms of hypoxia soon after that.
From here
humans total 105 million tonnes of dry biomass, out of (say) 500 billion tonnes for the whole biosphere. (Don’t forget that plants and bacteria respire too).
So the ratio is about 1/5000. Maybe 20,000 years.
Of course this describes a completely unrealistic scenario - the amount of oxygen in the atmosphere is so large compared to the total biomass that we would never run out of oxygen, even if we burnt the entire biosphere to ash.
-
The thread is mistitled. The OP actually wants to know how long 'til our doom, that is, how long before the end. “Doomed” means having an end, in the future, not being at it. If the fantasy scenario spells our doom, then we are doomed immediately.
-
I see no accounting for the effects on and of photosynthesizers?
By this definition, everything is doomed from the moment it begins (entropy). Don’t put too fine a point on it 
It’s probably the only genuinely beautiful depiction of entropy you will see in fiction. Can’t recommend it highly enough. I’m very fond of StarshipSofa’s reading of it, as well: Aural Delights No 66 BSFA Nominee 2008 Ted Chiang | StarShipSofa