Malonitrile extraction with ether: 3×100mL vs 1×300mL

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Suppose a reaction mixture, when diluted with water, afforded 300mL of an aqueous solution of 30 g of the reaction product malonitrile,CH2(CN)2 which is to be isolated by extraction with ether. The solution of malonitrile in ether at room temperature is 20.0 g per 100 mL, and in water is 13.3 g per 100 mL. What weight of malonitrile would be recovered by extraction with (a) three 100 mL portions of ether; (b) one 300-mL portion of ether. Suggestion: For each extraction let x equal the weight extracted into the ether layer. In case (a) the concentration in the ether layer is x/100, and in the water layer is (30-x)/300; the ratio of the quantities is equal to k = 20/13.3.
 

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what's the problem? You've got most of what you need right here.

Suggestion: For each extraction let x equal the weight extracted into the ether layer. In case (a) the concentration in the ether layer is x/100, and in the water layer is (30-x)/300; the ratio of the quantities is equal to k = 20/13.3.
 
Is this right?

Well, is this right?


1) k = 20/13.3 = 1.5
x/30-x = .50
x = .5(30-x)
1.5x = 15
x = 10g in ether layer
30 – x = 20g in water layer

x = .5(20 – x)
x = 10 -.5x
1.5x = 10
x = 6.67
20 – x = 13.33


x/13.33 – x =.50
x = .50(13.33 – x)
x = 6.67 - .5x
x = 4.44
13.33 – 4.44 = 8.89

a) 21.1g = three 100-mL portions of ether

x/30-x =1.5
x=1.5(30-x)
x =45-1.5x
2.5x/2.5 =45/2.5
x = 18.0

b) 18.0 g = one 300-mL extraction of ether
 
yep everything seems correct