Question

The K_D of coffee water at 25 °C is 7.8 in a methylene chloride/water system. If there is 2.0g of caffeine in 200ml of water, calculate the grams and the % of caffeine that can be extracted with a single 100 mL portion of methylene chloride.

Please show all work with relevant formulas. Thank you!

Answer 1

Distribution coefficient

KD = solubilty of solute in organic phase / solubilty of solute in aqueous phase

Let mass of caffeine extracted = x g

Mass of caffeine in water = 2 - x

solubilty of solute in organic phase = x g / 100 mL

solubilty of solute in aqueous phase = (2-x) g / 200 mL

7.8 = (x/100)/[(2-x)/(200)]

7.8 = 200x/[100(2-x)]

2x = 7.8*(2-x)

2x = 15.6 - 7.8x

9.8x = 15.6

x = 1.59

mass of caffeine extracted = 1.59 g

% mass of caffeine extracted = 1.59*100/2 = 79.5%