Question

Suppose that you have a reaction mixture which consists of 13.2 g of KBr and 11.0 g of an interesting organic compound dissolved in 100 mL of water.

You would like to have the pure organic compound, separate from water and salt, so you decide to carry out an extraction. You add 100 mL of dichloromethane and vigorously shake in a separatory funnel

Suppose that instead of one extraction with 200 mL, or two extractions with 100 mL, you had performed three successive extractions with 67 mL of fresh dichloromethane each time. How much of the interesting compound would you expect to have recovered?

PARTITION COEFFICIENT: 1.75

Answer 1

When the extraction is done with 200ml of dichloromethane,

Let x= amount of organic compound in the organic phase

11-x= amount of organic compound in the aqueous phase

Hence partition coefficient, K = 1.75

K= (mass of organic compound /volume)organic phase/ ( mass of organic compound/volume) aqueous phase

1.75= x/200/(13.2-x)/100

Hence x/(13.2-x)= 3.5, x= 3.5*(13.2-x)

Hence x*(1+3.5)= 3.5*13.2, x= 10.33 gm

b)for the case of two extraction with 100ml

1^st extraction with 100ml,   writing the equation for partition coefficient , K= 1.75 = x/100/(13.2-x)

Hence x = 1.75*(13.2-x)

Hence x= 1.75*13.2/2.75= 8.4 gm in the 1^st extraction

So remaining organic compound in =13.2-8.4= 4.8 gm, this will be sent for 2^nd extraction

Writing the partition coefficient equation for the second extraction of 100 ml of dichrloromethane

   x/100/(4.8-x)/100= 1.75         

hence x= 1.74*(4.8-x)

x = 3 gm

total amount extracted= 8.4+3= 11.4 gm

3. When the extraction is done with 67 ml thrice, 1^st extraction

x/67/(13.2-x)/100 = 1.75

100x/67= 1.75*(13.2-x)

1.5x= 1.75*13.2-1.75x

3.25x= 1.75*13.2

Hence x= 7.1 gm

Remaining organic product will be sent for 2^nd stage = 13.2- 7.1= 6.1

Writing the equation for partition coefficient for the 2^nd extraction with 67 ml

100x/67= 1.75*(6.1-x)

3.25x= 1.75*6.1, x= 1.75*6.1/3.25= 3.3 gm

So remaining organic compound= 6.1-3.3= 2.8 gm

Writing the partition coefficient equation for the 3^rd time

3.25x= 1.75*2.8

Hence x= 1.75*2.8/3.25= 1.51 gm

Extracted total amount= 7.1+3.3+1.51=11.91 gm