Question

You want to extract a solute from 100 mL of water using only 300 mL of ether. The partition coefficient between ether and water is 3.0. Calculate q, the fraction of solute that would remain in the water under each of the following extraction conditions: (a) A single extraction with 300 mL of ether.(b) Three extractions with 100 mL of ether.(c) Six extractions with 50 mL of ether.

Answer 1

Let amount of solute in water is 1 unit  

                                 X / 300mL ether

Kc  =  3.0  =    ????????????????--------------- where x is amount extracted with ether

                        (1 ? X) / 100 mL water

so 3-3x / 100 = x/300

9-9x = x

9 = 10x

x = 0.9

so q = 90%

b)

Xn = amount extracted

V = volume of water

V = volume of ether in each extraction

n= number of extraction

so xn = 1(100 / 100+ 100X3)^3

q = 0.0156

c)

q = (100 / 100 + 50 X 3)^6 = 0.00409