For a given teabag and dunking duration - will I get more caffeine in a bigger cup or the same amount? When choosing a cup of tea, I can choose a big cup or a small cup. I'm wondering if I get more caffeine with the bigger cup or the same amount of caffeine. (in moles)

My question is: For a given teabag and dunking duration - will I get more caffeine in a bigger cup or the same amount?

Assumptions


Teabag is placed in cup first - and hot water poured directly onto the bag
Same amount of stirring across both cups (assume three spoon swirls)
The main varying parameter is the volume of solvent changing


Question behind the question - trying to express it another way


Is there a kind of 'fixed rate of dissolution' that limits the amount of caffeine that comes out over a period of time - ie for two cups where one is 250ml and one is 300ml - and each have a tea dissolving time of 30s - wouldn't they have the same number of moles of caffeine at the end because of an upper bound on the rate of caffeine dissolving?
From what I remember from Fick's laws, I would say that the factor that limits the rate of dissolution is the concentration of the already-dissolved compound. At first, you don't have any caffeine dissolved so the rate of dissolution is fastest. As time goes by, more and more caffeine becomes solvated and that hinders the dissolution of remaining caffeine from the tea leaves. At any point of time until saturation, the 300 ml cup will have faster dissolution rate because it has more "free space" to solvate the caffeine.

Edit: However, after thinking this for a while, I have to add that in practice the difference might be too small to be detected. The solubility (~ saturation point) of caffeine in water is 20 g/l at 20°C while the concentration of caffeine in tea is 0.1 - 0.4 g/l &ndash; huge difference. It might be that from caffeine's point of view, the "free space" is more or less the same in both cups.