0.60 g of a solute is dissolved in 100 cm3 of water. It is shaken once with 50 cm3 of ether. The distribution coefficient (ether/water) is 4. What mass of solute passes into the ether?
- Let x g pass into the ether. Then (0.60 − x) g stays in the water.
- K = (x ÷ 50) ÷ ((0.60 − x) ÷ 100) = 4, which gives 2x ÷ (0.60 − x) = 4.
- 2x = 2.40 − 4x, so 6x = 2.40 and x = 0.40 g.
- Check: ether 0.40 ÷ 50 = 0.008 g cm−3; water 0.20 ÷ 100 = 0.002 g cm−3; ratio = 4.
Answer: 0.40 g passes into the ether and 0.20 g stays in the water.