Question

A solute with a partition coefficient of 7.4 is extracted from 25 mL of water into...

A solute with a partition coefficient of 7.4 is extracted from 25 mL of water into toluene.

a) What volume of toluene is required to recover 99% of the solute in a single extraction?

b) What total volume of toluene is required to recover 99% of the solute in four extractions?

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Answer #1

a) Assuming that the solute has only chemical form in each phase
KD = D =7.4
To extract 99% of the solute (qaq) 1= 0.01
Vorg = [Vaq - (qaq)1 * Vaq ] / (qaq)1 * D = [25 - 0.01*25] / 0.01*7.4 = 334.45945 mL
Therefore 334.5 mL of toluene is required to recover 99% of the solute in single extraction

b) ( Qaq)n = ( Vaq / DVorg + Vaq )n
   n=4 ;   ( Qaq)4 = 0.01
0.01 = ( 25 / 7.4* Vorg + 25)4
   (0.01)1/4 = 25 / 7.4Vorg + 25
7.4Vorg + 25 = 25 / 0.3162277
7.4Vorg +25 = 79.0569415
Vorg = 54.0569415 / 7.4 = 7.304992 mL
   Therefore 7.305 mL of toluene is required to recover 99% of the solute in four extractions

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