Question

-you are given a substance that is equally soluble in water and hexane (two immiscible solvents)

b) if you start with 10g of the substance dissolved in 100ml of water and are given 100 ml of hexane to extract with, algebraically show that it is better to do two smaller extractions using 50ml of hexane for each extraction than one it is to do one extraction using 100ml of hexane. show all math.

Answer 1

m = 10 g in V = 100 mL of water... 100 mL of hexane..

show

Kd = Concentration of S in water / concentration of S in hexane

Then,

Kd = (mass of S) / (Vwater) / (mass of S)/(Vhexane)

for n = 1 extraction

let

let "q" be the fraction of solute present AFTER extraction,

then

q = V1/(V1+K*V2)

is true...

for the 2nd excraction:

q = V1/(V1+K*V2) * V1/(V1+ K*V2)

q = [V1/(V1+K*V2) ] ^n

clearly

the trend is .. as more extractions, i.e. less volume, but "power n" increases

therefore

as n increases, q increases