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....
                suppose you have 100mg of a sample dissolved in 0.6ml of water. the partition coefficient or kp for this compound in water and diethyl ether is 4.0
                
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                a. calculate how much total compound you would obtain with 3 x 0.2ml extractions with ether
                
                b. calculate how much you would obtain with 1 x 0.6ml extraction
                
                c. which method is more efficient?
                
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Explanation / Answer

ans a)

for extraction #1

0.2ml diethyl etehr is mixed

partition coefficient = mass of solute in diethyl ether per unit volume/mass of solute in water per unit volume

let mass extracted by ether = x

so mass in water left = 100-x

4 = (x/0.2) / (100-x)/0.6

4 = x/(100-x) * 0.6/0.2

100*4/3 - 4x/3 = x

4*100/3 = 7x/3

x = 57.14 mg

so solute left in water = 100-57.14 = 42.86 mg

similarly for extraction #2

4 = (x/0.2)/(42.86-x)/0.6

x = 24.49 mg

so left in water = 42.86-24.49 = 18.37 mg

for extraction #3

4 = (x/0.2) / (18.37-x)/0.6

x = 10.49 mg

so solute left in water = 18.37-10.49 = 7.88 mg

so amount of compound obtained from 3*0.2ml extractions = 10-7.88= 9212 mg

ans 2)

for 1 0.6ml extraction

4 =( x/0.6 ) / (100-x)/0.6

4 = x/(100-x)

x = 80 mg

so compound extracted = 80mg

ans 3)

as more compound is sxtracted from method 1 it is more effective than method 2

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