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?
• This post may interest you. I have linked a couple of journal articles in the comments to one of the answers that was given which you may find useful. cooking.stackexchange.com/questions/41413/… – LordStryker Feb 11 '14 at 15:30
• Dunking the bag up and down within the tea probably helps get the caffeine out as quickly as possible, too. Fick's law... Thanks for the caffeine solubility info! I've wondered about your question for a long time and appreciate your insights. – Helen Apr 20 '17 at 16:41

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 – huge difference. It might be that from caffeine's point of view, the "free space" is more or less the same in both cups.

• The same source mentions an estimate of LD(50) for humans to be in the order of 150--200 mg caffeine/kg body weight, so it were not desirable to attend the formation of a caffeine-saturated solution, either. – Buttonwood Feb 11 '14 at 16:10

How do you prepare you your cup of tea?

Dunking the leaves of tea (solid phase) exposes them the liquid phase (water). The concentration in the liquid phase of caffeine (and other chemicals/ingredients carried by your leaves of tea) will increase. Because hot water is more efficient than cold one for this extraction, temperature plays a role, too. Stirring the liquid phase for a homogenous dissipation of extracted matter across the whole solvent volume at your disposition may be to be considered as a parameter, too. Yet, the more volume of solvent of extraction at your disposition, the more total solvent capacity to get more caffeine out of your leaves of tea.

Yet another thought may arise, too; if you do not spend all the volume at once. As textbooks for physical chemistry, regarding multiple extractions, teach, repeated extraction with a small fraction of solvent of extraction would be then more efficient than deploying the whole solvent of extraction in a single extraction. (However, by time the composition of the ingredients being extracted by hot water, varies, too.)

• Really helpful answer - I've added some assumptions. I think the question behind my question is, is there an upper bound on the rate of dissolving - which has a lot to do with your comments about volume of solvent capacity. – hawkeye Feb 10 '14 at 2:18