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
