Question

# The pain reliever phenacetin is soluble in cold water to the extent of 1.0g/ 1310 ml...

The pain reliever phenacetin is soluble in cold water to the extent of 1.0g/ 1310 ml and soluble in diethyl ether to the extent of 1.0g/ 90 ml. The distribution coefficient for it in the two solvents is 0.0167. If 50 mg of phenacetin were dissolved in 100 ml of water, how much will be extracted using one 100 mL portion of ether and how much will be extracted ussing two 50 mL portions of ether? Please show calculations.

What do the calculations indicate about how to optimize extraction of a compound using a limited amount of solvent?

D = solute in organic/solute in aqueous

let x amount of phenacetin remains in aqueous phase

With 100 ml ether

0.0167 = ((50-x)/100)/(x/100)

0.0167x = 50 - x

x = 49.179 mg remains in aqueous phase

Amount extracted = 50 - 49.179 = 0.821 mg

with 50 ml ether Ist extraction

0.0167 = ((50-x)/50)/(x/100)

0.00835x = 50 - x

x = 49.586 mg remained in aqueous phase

amount extracted = 0.414 mg

with 50 ml ether IInd extraction

0.0167 = ((49.586-x)/50)/(x/100)

0.00835x = 49.586 - x

x = 49.175 mg remained in aqueous phase

amount extracted = 0.411 mg

Total amount extracted by two step extraction process = 0.825 mg

As we can see the amount of phenacetin extracted by a two step process is more effecient and is the desired method in extraction.