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When opening a window in a typical room with higher CO2 and lower O2 concentrations compared to the outside, how fast does it equilibrate again?

Assuming no wind, just diffusion, the answer still depends on the geometry of the problem. Not every point will have the same concentration, points further away from the opening will take longer to equilibrate. A similarity metric between the gas concentrations may also be required.

But what I ultimately want to know is this: In a real room, is reaching equilibrium a matter of seconds, minutes or hours, and is there a way to calculate or approximate this value, or are numerical approaches required?

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    $\begingroup$ As a rough estimate, you could calculate the time it would take to exchange the air in the room based on the air flux at the window. This isn't a very exact estimate, but it should give you a time scale in the right order of magnitude. Pure diffusion ignores the important turbulent processes at the window, I think. Typical values are in minutes, approx 5 when it's cold outside, increasing with increasing the outside temperature. $\endgroup$ – TBissinger Mar 15 at 8:41
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As a starting point , try looking at Grahams law of Diffusion https://en.wikipedia.org/wiki/Graham%27s_law

and there is Fick's law here https://www.engineeringtoolbox.com/air-diffusion-coefficient-gas-mixture-temperature-d_2010.html

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