If 15 grams of an organic solid is dissolved in 80 mL of water, how many grams remain in the water after extraction with 50 mL of a solvent which has a partition (distribution) coefficient with water of 8? Show calculations.

2.5 g

Explanation:

The partial coefficient (K) is the ratio of the solubility (S) of a solute in two different solvents. For the given problem:

K = Ssolvent/Swater

The solubility is the mass divided by the volume. If the fraction of the solute in water is called q, the fraction of it in the solvent is 1-q. Let's call m the initial mass of the solute, so, after the extraction:

mass at the solvent = (1-q) m

mass at water = qm

Ssolvent = (1-q) m/50

Swater = qm/80

8 = [ (1-q) m/50]/qm/80

8 = 80 * (1-q) / 50q

400q = 80 - 80q

480q = 80

q = 0.167

The mass that remains at the water is:

0.167*15 = 2.5 g