You have 100 mL of a solution of benzoic acid in water; the amount of benzoic acid in the solution is estimated to be 0.30 g. The distribution coefficient of benzoic acid in diethyl ether and water is approxi- mately 10. Calculate the amount of ben- zoic 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.

The extraction with four 20-mL extractions with ether is more efficient.

Explanation:

We are given the following parameters which are going to help in solving this particular Question.

=> The volume of the solution of benzoic acid in water = 100mL, the estimated amount of benzoic acid in the solution = 0.30 g and the distribution coefficient (approximately ) = 10 = 1/ 10 = 0.1

Therefore, the amount of acid that would be left in the water solution after four 20-mL extractions with ether = 0.3( 0.1 × 100 ÷ 10 + 20)^4 = 0.0037 g.

Also, the amount of acid that would be left in the water solution after one 80-mL extractions with ether = 0.3( 0.1 × 100/ 10 + 80)^1 = 0.033 g.

Since 0.033 g > 0.0037 g, the extraction with four 20-mL extractions with ether is more efficient.