Question

Compound A is three times more soluble in diethyl ether than in water, so its partition coefficient is K = 3, for partitioning of Compound A between diethyl ether and water. for a sample of compound a dissolved in 50mL of water, answer the questions:

1) Determine the fraction of A that remains in the water, F_A, after one extraction with 200mL of diethyl ether.

2) Determine F_A after two extractions, using 100mL of diethyl ether in each of the extractions.

3) Determine F_A after four extractions, using 50mL of diethyl ether in each of the extractions.

Please explain. Thanks!

Answer 1

1) lets say x amount of sample was extracted in diethylether, so remianing in water would be 1-x

K = 3 = (x/200)/(1-x/50)

3/50 - 3x/50 = x/200

0.06 = 0.065x

x = 0.92

so 0.92 is the mole fraction extracted in diethylether

amount of A in water = 1-x = 0.08

mole fraction of fraction A remaining in water = 0.08

2) repeating similar procedure as above.

lets x be the amount of A extracted after first extraction,

3 = (x/100)/(1-x/50)

3/50 - 3x/50 = x/100

0.06 = 0.07x

x = 0.86

so 0.86 is the mole fraction extracted in diethylether

amount of A in water = 1-x = 0.14

Lets say y is the amount extracted second time,

3 = (y/100)/(0.14-y/50)

0.42/50 - 3y/50 = y/100

y = 0.12

amount remaining in water = 0.14-0.12 = 0.02

Total amount in water F(A) = 0.02

3) Lets say x is amount extracted by first extraction,

3 = (x/50)/(1-x/50)

3/50 - 3x/50 = x/50

x = 0.75

Amount remaining in water = 1-x = 0.25

second extraction, say y amount extracted,

3 = (y/50)(0.25-y/50)

0.75/50 - 3y/50 = y/50

y = 0.187

amount remaining in water = 1-y = 0.063

Third extraction, say z amount is extracted,

3 = (z/50)(0.063-y/50)

0.189/50 - 3z/50 = z/50

z = 0.041

amount remaining in water = 1-z = 0.022

Fourth extraction say a is extracted in diethyether,

3 = (a/50)/(0.022-a/50)

0.066/50 - 3a/50 = a/50

a = 0.0165

amount remaining in water = 0.022-0.0165 = 0.0055

F(A) in water = 0.0055 after four extractions.

0.0055

amount remaining in water = 1-y = 0.063

Third extraction, say z amount is extracted,