I have a soda bottle (consider no leaks) at room temperature and 55 psi. Oxygen is saturated in the water inside. After removing the cap, what law or formula can I use to estimate the time oxygen dissolved will take to un-dissolve and reach the saturation point at room temperature/pressure?
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2 Answers
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Probably not, here is why.
Gases dissolved in water can exist in a metastable, supersaturated state for long times- only to suddenly come out of solution when the water is slightly perturbed or when a seed site for exsolvation presents itself. This makes the exsolvation rate of gases in water sensitively dependent on things that are themselves difficult to model mathematically.
answered Nov 19, 2020 at 19:39
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$\begingroup$ A ciral example en.wikipedia.org/wiki/Diet_Coke_and_Mentos_eruption $\endgroup$– DJohnMCommented Nov 20, 2020 at 1:03
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The laws of diffusion are what dominate here; if the partial oxygen pressure in the bottle was 55psi, and when open to air that dropped to circa 3 psi, there's a volume of oxygenated water and a surface exposed. There will be a rate of evolution at the surface that depends on temperature and on the concentration of oxygen in the liquid, and proportional to the air/water surface area.
Now, it gets complicated, because the temperature of the surface will go down as gas is evolved, as well as the concentration at the surface. This means that a layer below the surface has higher concentration than the surface, and higher temperature as well, so there will be a net flow upward of the oxygen.
It is possible to make a one-dimensional diffusion equation, with a constant (square millimeters per second) representing the diffusion in the liquid, and couple it with the temperature profile. Or, you can quasi-empirically do it with only diffusion, and ignore thermal effects; one would almost always ignore the stratification of the air above the liquid, because diffusion is much faster in air...
Calculations will only approximate a real condition; minor stirring in the container, or convection that might result from nonuniform temperatures, will result in asymmetric (random, unpredictable) conditions.
There will be no true equilibrium reached; air pressure variations through a day or season are significant, and the liquid will slowly come to an average value similar to equilibrium.
There's a fuller discussion here oxygen diffusion in water.
