Question

You have 100 mL of a solution of benzoic acid in water; the amount of benzoic acid in the solution is estimated to be about 0.30 g. The distribution coefficient of benzoic acid in diethyl ether and water is approximately 10. Calculate the amount of acid that would be left in the water solution after four 20-mL extractions with ether. Do the same calculation, using one 80-mL extraction with ether, to determine which method is more efficient.

Answer 1

amount left after n extractions formula is

w = W ( KV/KV +v) ^n , where K= distribution coeff, V= solvent vol, v= extractant vol, W = mass of solute, w = amt left after extraction in solvent , lets cal for 1st case n = 4 extractions, v = 20 ml,

Kd = 1/10 = 0.1 = amt in water/amt in ether

hence w = 0.3( 0.1x100/10 + 20)^4 = 0.0037 gm left ,

now single extractnting n =1,

w = 0.3(0.1x100/10+80) = 0.033 gm left

hence more extractions using small volumes is better extraction