Solve the following calculation: In this experiment, 0.170g of caffeine is disso

Question

Solve the following calculation: In this experiment, 0.170g of caffeine is dissolved in 10.0 mLof water.  the caffeine is extracted fromt he aqueous solutionthree times with 5.0 mL portions of 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 andwater. Solve the following calculation: In this experiment, 0.170g of caffeine is dissolved in 10.0 mLof water.  the caffeine is extracted fromt he aqueous solutionthree times with 5.0 mL portions of 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 andwater.

Explanation / Answer

My understanding of your question is that 5.0ml of methylene chloride is used for each extraction.
Let C be the aqueous concentration of caffeine during each individual extraction. 4.6*C is thus the concentration in methylene chloride. The total amount of caffeine is:
10.0*C + 5.0*4.6*C = 33*C
The amount of caffeine left in aqueous solution is: 10.0*C, and the fraction of caffeine left in aqueous solution is: 10/33 = 0.3. It is obvious that the fraction of 0.3^3 is left in aqueous solution after 3 extractions. Therefore, the final answer is:
0.170*(1-(0.3)^3) = 0.16541 (g)

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