Caffeine has a partition coefficient Kd=4.6 between dichloromethane (DCM) and water at 25 °C, defined as [caffeine]DCM/[caffeine]water. A 100 mL aqueous tea solution contains 0.200 g of caffeine. A student plans to extract the caffeine with three separate 20 mL portions of fresh DCM, combining the organic layers at the end.
(a) Derive an algebraic expression for the mass of caffeine remaining in the aqueous phase after a single extraction with an organic solvent volume Vorg, given an initial mass m0, aqueous volume Vaq, and the partition coefficient Kd. Clearly state any assumptions.
(b) Use your expression to calculate the mass of caffeine removed from the aqueous layer after one 20 mL extraction.
(c) Perform the required calculations to predict the total mass of caffeine present in the combined organic layers after three successive 20 mL extractions. Express the result as a percent recovery relative to the original 0.200 g.
(d) Provide one practical reason, grounded in solubility considerations, why performing multiple small-volume extractions is preferred over a single extraction using the same total volume of organic solvent.