how do I solve this problem? Consider a 10 g sample of a sugar (Kp = 5) that is

Question

how do I solve this problem?

Consider a 10 g sample of a sugar (Kp = 5) that is dissolved in 20 mL water. You have 20 mL of ether available to extract the sugar. How much sugar will be extracted with a single extraction, using a 20 mL portion of ether? Instead, how much sugar would be extracted after two, successive extractions with 10 mL portions of ether? Compare these numbers and determine which process is more efficient: using a single 20 mL portion of ether to extract a compound or using two, successive 10 mL portions of ether. Show your work and explain your conclusion.

Explanation / Answer

wt. of sugar = 10g

Kp = 5

vol. of water = 20mL

Case1: single extraction when 20 mL ether is added:-

Let xg 0f sugar is extracted

Kp = [solute]0/ [solute]aq

5 = (x/20) / [(10-x)/20]

x = 5(10-x)

x = 50 - 5x

6x = 50

x = 8.3g or 83% sugar is extracted.

Case2: two extractions when 10 mL ether is added

First extraction:

5 = (X1/10) / [(10-X1)/20]

X1 = 7.14g

Second extraction:

5 = (X2/10) / [(2.86 - X2)/20]

X2 = 2.04g

Total sugar extracted = X1 + X2

                               = 7.14 + 2.04

                               = 9.18g or 91.8% sugar

As amount of sugar extracted in two successive extractions is 91.8% and in single extraction is 83%. Therefore the process of two successive extractions is more efficient as more amount of sugar is extracted.

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