Calculate the partition coefficient of caffeine in water/methylene
chloride from the following data: 10.3 g/100 mL for methylene
chloride and 2.04 g/100 mL for water.
Using the same data a student follows our procedure and extracts the caffeine using 3 extractions of 7 mL of methylene chloride. How much caffeine is in the combined 21 mL of methylene chloride? How much remained in the water?
You don't say but I assume these numbers you give are the solubility of caffeine in the two solvents.
Ko/a = 10.3/2.04 = 5.049
fn = [(1+K(Vo/Va)^-n
fn is the fraction of the solute REMAINING in the aq phase after n extractions.
NOTE: I don't see any number for the volume used for the aq phase. I see the 7 mL for organic phase but nothing for the aq phase. I've show you how to do if assuming you just didn't type that information in.
To calculate the partition coefficient of caffeine between water and methylene chloride, we need to divide the concentration of caffeine in the organic phase (methylene chloride) by the concentration of caffeine in the aqueous phase (water).
Given data:
Concentration of caffeine in methylene chloride (organic phase): 10.3 g/100 mL
Concentration of caffeine in water (aqueous phase): 2.04 g/100 mL
Partition coefficient (P) = Concentration of caffeine in methylene chloride / Concentration of caffeine in water
P = (10.3 g/100 mL) / (2.04 g/100 mL)
P = 5.05
The partition coefficient of caffeine in water/methylene chloride is approximately 5.05.
Now, let's calculate how much caffeine is in the combined 21 mL of methylene chloride after 3 extractions of 7 mL each:
Caffeine extracted in one extraction = (Mass of caffeine extracted / Total volume of methylene chloride used) * Volume of methylene chloride in one extraction
Caffeine extracted in one extraction = (10.3 g/100 mL) * (7 mL)
Caffeine extracted in one extraction = 0.721 g
Total caffeine extracted in 3 extractions = Caffeine extracted in one extraction * Number of extractions
Total caffeine extracted in 3 extractions = 0.721 g * 3
Total caffeine extracted in 3 extractions = 2.163 g
Therefore, there is approximately 2.163 g of caffeine in the combined 21 mL of methylene chloride.
To determine how much caffeine remained in the water, we subtract the amount extracted from the initial amount present in the water.
Amount of caffeine in water = Initial amount of caffeine in water - Total amount of caffeine extracted
Amount of caffeine in water = (2.04 g/100 mL) - 2.163 g
Since the remaining amount of caffeine cannot be negative, we assume that all the caffeine was extracted from the water phase in this case.
Therefore, the amount of caffeine remaining in the water is 0 g.
To calculate the partition coefficient of caffeine in water/methylene chloride, we need to divide the solubility of caffeine in methylene chloride by the solubility of caffeine in water.
Solubility of caffeine in methylene chloride = 10.3 g/100 mL
Solubility of caffeine in water = 2.04 g/100 mL
Partition coefficient = Solubility of caffeine in methylene chloride / Solubility of caffeine in water
Partition coefficient = 10.3 g/100 mL / 2.04 g/100 mL
Partition coefficient = 5.05
Now, let's calculate the amount of caffeine in the combined 21 mL of methylene chloride. The student performed 3 extractions of 7 mL each, so the total volume of methylene chloride used is 3 x 7 mL = 21 mL.
Amount of caffeine in 21 mL of methylene chloride = Partition coefficient x Amount of caffeine in water
Amount of caffeine in 21 mL of methylene chloride = 5.05 x 2.04 g/100 mL x 21 mL
Amount of caffeine in 21 mL of methylene chloride = 2.15 g
Therefore, there is 2.15 g of caffeine in the combined 21 mL of methylene chloride.
To find out how much caffeine remained in the water, we need to subtract the amount of caffeine in the methylene chloride from the initial amount of caffeine in the water.
Amount of caffeine in water = 2.04 g/100 mL x 100 mL = 2.04 g
Amount of caffeine remained in the water = Initial amount of caffeine in water - Amount of caffeine extracted into methylene chloride
Amount of caffeine remained in the water = 2.04 g - 2.15 g = -0.11 g
The negative value indicates that there is no caffeine remaining in the water after extraction.