When performing extractions it is often better to do multiple extractions rather

Question

When performing extractions it is often better to do multiple extractions rather than one large volume extraction. (See pg. 70-71 of Mayo) Suppose you have 100mg of a sample dissolved in 0.6mL of water. The partition coefficient for this compound in water and diethyl ether is 4.0.

a. Calculate how much total compound you would obtain with 3 x 0.2 mL extractions with ether. Show your work. (See pp.70-72 of Mayo)

b. Calculate how much you would obtain with 1 x 0.6mL extraction. Show your work.

c. Which method is more efficient?

Explanation / Answer

Partition coefficient = 4

a) For three extractions:

Kd = [Sorg]/[Saq]

4 = [x/0.2]/[100-x/0.6]

4 [100-x/0.6] = [x/0.2]

(400-4x)/0.6 = x/0.2

666.67 - 6.667x = x/0.2

133.33 - 1.333x = x

133.33 = 2.333x

x = 57.14 g

Fraction left in water = (100-57.14)/100 = 0.4286

Fraction left in water after three extractions = (0.4286)3 = 0.07873

Fraction retained by organic layer = 1 - 0.07873 = 0.9213

Mass in organic layer = 0.9213 * 100 = 92.13 mg

b) For single extraction:

Kd = [Sorg]/[Saq]

4 = [x/0.6]/[100-x/0.6]

400 - 4x / 0.6 = x / 0.6

400 - 4x = x

400 = 5x

x = 80 mg

c) Method 1 is more effective due to more solid is extracted in the organic layer.

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