Question

The extraction of 8.0 g of a particular organic compound dissolved in 100 ml of water into diethyl ether proceeds with a distribution coefficient of 5. How much of the compound is extracted after three separate extractions using 50 ml of diethyl ether each time?

***Please show work as I am not 100% sure how to solve for X****

Thank you!

Answer 1

When extraction is done two or more times, then we can use the formula

Q_aq = [V_aq / {(K * V_org) + V_aq}]ⁿ

where

Q_aq = fraction of compound in aqueous phase

V_aq = volume of aqueous phase = volume of water = 100 mL

K = distribution coefficient = 5

V_org = volume of organic phase = volume of diethyl ether = 50 mL

n = number of extractions = 3

Substituting the extractions,

Q_aq = [100 mL / {(5 * 50 mL) + 100 mL}]³

Q_aq = [100 mL / {250 mL + 100 mL}]³

Q_aq = [100 mL / 350 mL]³

Q_aq = (0.2857)³

Q_aq = 0.0233

mass of compound in aqueous phase after 3 extractions = (fraction of compound in aqueous phase) * (mass of compound)

mass of compound in aqueous phase after 3 extractions = (0.0233) * (8.0 g)

mass of compound in aqueous phase after 3 extractions = 0.1866 g

mass of compound extracted = (total mass of compound) - (mass of compound in aqueous phase after 3 extractions)

mass of compound extracted = (8.0 g) - (0.1866 g)

mass of compound extracted = 7.8 g