Question

Calculate the percentage of a compound that can be removed from liquid phase 1 by using one to four extractions with liquid phase 2. Assume that k=2 and the volume of phase 2 equals 50% of that of phase 1.

a) 12.5%
b) 25%
c) 37.5%
d) 50%

Answer 1

The question involves calculating the removal percentage of a compound from one liquid phase to another using a given partition coefficient and volume ratio. After four extractions, over 80% of the compound is removed, which is more than the given options, indicating that none of the provided choices (a to d) are correct.

Step-by-step explanation:

To address the question of calculating the percentage of a compound removed from liquid phase 1 using extractions with liquid phase 2, you first must understand the concept of the partition coefficient (Kp or K) and the volumes of the two phases involved. Assuming K=2 and that the volume of phase 2 is 50% of that of phase 1, we can use successive extractions to calculate the percentage removal.

For each extraction, the amount of compound in phase 2 (V2) relative to phase 1 (V1) is determined by the partition coefficient: Amount in V2 = K * Amount in V1 / (K+1). After one extraction, 2/3 of the compound will be in phase 2, and 1/3 will remain in phase 1. Therefore, 2/3 of the total compound has been extracted, which corresponds to 66.67%. However, because V2 is only 50% of V1, the absolute amount removed is 66.67% * 50%, resulting in 33.33% extraction per step.

The process is iterative, so after each extraction, new calculations must be made based on the remaining amount in phase 1. Let's go through the calculations:

1. 1st extraction: 33.33% of the compound is removed.
2. 2nd extraction: 33.33% of the remaining 66.67%, equating to an additional 22.22% (rounded), thus totalling 55.55% when combined with the first extraction.
3. 3rd extraction: 33.33% of the remaining 44.44%, which is an additional 14.81% (rounded), totalling around 70.36% extraction combined.
4. 4th extraction: A further 33.33% of the remaining 29.63%, which is 9.87% (rounded), leading to a total of approximately 80.23% of the original compound removed after four extractions.

Hence, option (d) 50% is not the correct percentage removed after one to four extractions. Instead, we find that after four extractions, over 80% of the compound can be separated from phase 1 using liquid phase 2.