If I were to steep the same amount of tea in two vessels of hot water: one 12oz cup and one 24oz carafe, would the 24oz carafe have more caffeine or the same amount? Assume steeping is the same amount of time.
The amount of difference is a complicated question as there are many variables involved. There is an osmotic pressure differential and there is also an equilibrium that will be reached between the tea compounds in the leaves and the water, so technically speaking tea steeped in more water will have more caffeine and other compounds, but there are many factors that will affect how much more.
To do an experiment correctly you'd need to have two bags with the same concentration of tea per volume unit and the same surface area exposed to the water and two cups of the same size and material with the same amount of water at the same temperature. Putting a tea bag into a larger vessel will introduce other factors (such as fluid dynamics and temperature).
Here are some of the variables that would have to be taken into account:
- volume of water
- temperature of water
- surface area of tea:water
- turbulence of water
- type of tea
- pH and other chemical properties of water
- infusion time
- surface area of water:volume of water
- permeability of tea bag (if any)
- type of tea
- loose leaves vs in a bag; stirred loose leaves vs. clumped loose leaves
Sure, the caffeine in tea is bound to something in the tea leaves. It has a binding constant. Put the same amount of tea leaves in double the volume of water, and you'll roughly halve the rate at which free caffeine binds to whatever it sticks to in tea leaves. So you'll end up with more caffeine in solution. Play this game too hard, and you'll end up with very weak tea. Maybe even so weak that your digestive system won't absorb much of that "extra" caffeine you've released by brewing with too much water for a tasty cuppa.