Question

In this experiment, 0.070 g of caffeine is dissolved in 4.0 ml of water. The caffeine is then extracted from the aqueous solution three times, each time using 2.0 ml fresh methylene chloride. Calculate the total amount of caffeine that can be extracted into the three portions of methylene chloride (caffeine has a distribution coefficient of 4.6 between methylene chloride and water).

Answer 1

Mass of caffeine = 0.070 g

Volume of water in which caffeine is dissolved = 4.0 ml

2.0ml of methylene chloride is used for each extraction.

Given, distribution coefficient of Caffeine = 4.2  

Let C be the aqueous concentration of caffeine during each individual extraction.

4.6*C is thus the concentration of caffeine in methylene chloride.

4.0*C is the amount of caffeine left in aqueous solution after each extraction.

The total amount of caffeine is:  

4.0*C + 2.0*4.6*C = 13.2*C  

The fraction of caffeine left in aqueous solution after each extraction: $\frac{4.0}{13.2} = \frac{1}{3.3}$.

Thus the fraction of caffeine is left in aqueous solution after 3 extractions is  (1/3.3)^3

And the fraction of caffeine is left in methylene chloride after 3 extractions is 1-(1/3.3)^3

Therefore, the the total amount of caffeine that can be extracted into the three portions of methylene chloride is:  

$0.070*(1-(1/3.3)^3) = 0.068 g$

Answer 2

2.0ml of methylene chloride solution is used each time to extract caffeine from the aqueous solution.  

Consider the concentration of caffeine obtained during each individual extraction from the aqueous solution to be C.  

The total amount of caffeine obtained during each extraction is calculated as

(Total volume of water used to make up the caffeine aqueous solution) x (concentration of caffeine obtained during each individual extraction from the aqueous solution) + (Volume of methylene chloride added during each extraction x distribution coefficient of caffeine x concentration of caffeine obtained during each individual extraction from the aqueous solution)  

Substituting these values we get                                                            

The total amount of caffeine obtained during each extraction                

 = (4.0×C )+ (2.0×4.6 × C)                                                                              

= 13.2 C

The amount of caffeine remaining in the aqueous solution is calculated as  

(Total volume of water used to make up the caffeine aqueous solution) x (concentration of caffeine obtained during each individual extraction from the aqueous solution)

Substituting these values we get                                                            

The amount of caffeine remaining in the aqueous solution = 4 × C                                                                                            

The fraction of caffeine remaining in aqueous solution is calculated as  

= (The total amount of caffeine obtained during each extraction)/ (The amount of caffeine remaining in the aqueous solution)                    

=4.0 C/13.2 C                                                                                                

= 1/3.3.  

Therefore the fraction of caffeine left in aqueous solution after 3 extractions is =(1/3.3)^3  =0.028

Therefore, the total amount of caffeine extracted                            

=0.070 × (1-(1/3.3)^3)                                                                                      

= 0.068 g