5. One hundred milligram of caffeine is dissolved in 50 mL of water.
a. How many mg of caffeine will remain in the water if you extract with 20 mL of methylene chloride?
Show your calculations (KD = 4).b. How many mg of caffeine will remain in the water if you extract two times with 10 mL of methylene
chloride each? Show your calculations (KD= 4).
Kd = 4.0 = [(x/20)/(100-x)/50]
Solve for x = amount in the methylene chloride layer. 100-x is the amount in the water.
To calculate how many milligrams (mg) of caffeine will remain in the water after extraction with methylene chloride, we need to use the partition coefficient (KD) as provided. The partition coefficient represents the distribution of a compound between two immiscible solvents, which in this case are water and methylene chloride.
a. If you extract with 20 mL of methylene chloride:
Step 1: Calculate the amount of caffeine that will transfer from water to methylene chloride.
Caffeine transferred = 100 mg × (Volume of methylene chloride / Total volume of water + methylene chloride)
Caffeine transferred = 100 mg × (20 mL / (50 mL + 20 mL))
Caffeine transferred = 100 mg × (20 mL / 70 mL) = 28.57 mg
Step 2: Calculate the amount of caffeine remaining in the water after extraction.
Caffeine remaining = Initial caffeine amount (100 mg) - Caffeine transferred (28.57 mg)
Caffeine remaining = 100 mg - 28.57 mg = 71.43 mg
Therefore, 71.43 mg of caffeine will remain in the water after extraction with 20 mL of methylene chloride.
b. If you extract two times with 10 mL of methylene chloride each:
Step 1: Calculate the amount of caffeine transferred in the first extraction.
Caffeine transferred in first extraction = 100 mg × (10 mL / (50 mL + 10 mL))
Caffeine transferred in first extraction = 100 mg × (10 mL / 60 mL) = 16.67 mg
Step 2: Calculate the amount of caffeine remaining in the water after the first extraction.
Caffeine remaining after first extraction = Initial caffeine amount (100 mg) - Caffeine transferred in first extraction (16.67 mg)
Caffeine remaining after first extraction = 100 mg - 16.67 mg = 83.33 mg
Step 3: Repeat the extraction process for the second time.
Step 4: Calculate the total amount of caffeine transferred in both extractions.
Total caffeine transferred = Caffeine transferred in first extraction + Caffeine transferred in second extraction
Total caffeine transferred = 16.67 mg + 16.67 mg = 33.33 mg
Step 5: Calculate the amount of caffeine remaining in the water after both extractions.
Caffeine remaining = Initial caffeine amount (100 mg) - Total caffeine transferred (33.33 mg)
Caffeine remaining = 100 mg - 33.33 mg = 66.67 mg
Therefore, 66.67 mg of caffeine will remain in the water after two extractions with 10 mL of methylene chloride each.