[mimags]

I have 50ml of seawater in a 100ml bottle. The seawater is supersaturated with N2O. How do I calculate the time it takes for the headspace to be in equilibrium with the water?

[Enthalpy]

I can't imagine an accurate answer exists.

First, "supersaturated" can mean: explosive separation.

Then, for undersaturated solutions, some methods do exist, similar to evaporation, but they are known to be inaccurate. Essentially, you compute the equilibrium pressure, deduce how much gaseous N₂O hits the water surface per time unit under these conditions, claim that they stay stuck and that as many evaporate during the same time for equilibrium. Then, the difference between the actual partial pressure and the saturation pressure gives an evaporation rate.

As the processes converges exponentially, "equilibrium" must be defined with some tolerance to get a finite delay.

Well, this would be if Nature wanted to work as we model it. Bubbles for instance change the liquid's area, while seeds increase the desorption speed - like bubbles appearing at a few places in a Champagne glass, typical for a supersaturated solution.

There may be additional tricks I ignore, like salt decomposing N₂O.