Question

An organic compound has a distribution coefficient of 1.5

Answer 1

Answer:

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