An organic compound has a distribution coefficient of 1.5
inmethylene chloride and water. if 50 mg of this compound
aredissolved in 15 ml of water, in which case will more of
thecompound be extracted into the methylene chloride: oneextraction
with 15 ml of methylene chloride or three extractionsusing 5 ml of
methylene chloride each time? show allwork.

Three times with 5 ml will yield more

Explanation:

Let x represent the amount yield

Kd = (x/15) / ((50-x) / 15) where Kd = 1.5

1.5 = (x/15) / ((50-x) / 15)

x / (50 - x) = 1.5

x = 75 - 1.5x

x + 1.5x  = 75

2.5x = 75

x = 75 / 2.5 = 30 mg

when extraction  three times

1st extraction

(x1/5) / ((50 - x1) / 15) = 1.5

3x1 / 50 - x1 = 1.5

3x1 = 75 - 1.5x1

3x1 + 1.5x1 = 75

4.5x1 = 75

x1 = 75 / 4.5 = 16.67 gm

second extraction

(x2/ 5) / (33.33 - x2 ) / 15) = 1.5

3x2 / ( 33.33 - x2) = 1.5

3x2 = 1.5(33.33 - x2)

3x2 = 49.995 - 1.5x2

3x2 + 1.5x2 = 49.995

4.5x2 = 49.995

x2 = 49.995 / 4.5

x2 = 11.11 mg

Third extraction

(x3/5) / ((22.22 - x3) / 15) = 1.5

3x3 = 1.5 ( 22.22 - x3)

3x3 + 1.5x3 = 33.33

4.5x3 = 33.33

x3 = 33.33 / 4.5 = 7.41 mg

total extraction = x1 + x2 + x3 =16.67 + 11.11 + 7.41 = 35.19 mg

the three times extraction using 5ml yields 5.19 mg more