Question

Purification of an Antibiotic by Countercurrent Extraction A countercurrent extraction unit with three equilibrium stages is used for the separation of a desired antibiotic (partition coefficient \(=6.0\) ) from a major contaminant (partition coefficient \(=1.0\) ) in an aqueous feed stream. The feed (or raffinate) and extract phase flow rates are equal. What fraction of each is discarded from the raffinate? Assuming that the feed contains only these two components at an antibiotic-to- contaminant ratio of \(3: 1\), what is the purity of the antibiotic in the exit extract from stage \(3 ?\) What do you conclude about the effectiveness of this extraction as a means of purification of the antibiotic?

Short answer

The exact values for the fractions discarded and the purity of the antibiotic cannot be determined without carrying out the matrix calculation and the resulting calculations, which will involve solving a system of linear equations and calculation of a ratio. The effectiveness of the extraction will depend on these results.

Step-by-step solution

Determine the Matrix for the System

The matrix for the system given that the partition coefficient of the antibiotic is \(6.0\) and the partition coefficient of the contaminant is \(1.0\) will be \(\begin{bmatrix} 6 & 1 \ 1 & 1 \end{bmatrix}\). The antibiotic-to-contaminant ratio in the feed is \(3:1\), or \(\begin{bmatrix} 3 \ 1 \end{bmatrix}\).

Calculate the Fraction of the Antibiotic and the Contaminant in the Raffinate and in the Extract

The matrix equation is \(\begin{bmatrix} 6 & 1 \ 1 & 1 \end{bmatrix} \times \begin{bmatrix} R \ E \end{bmatrix} = \begin{bmatrix} 3 \ 1 \end{bmatrix}\). Solve this matrix equation to get the fraction of the antibiotic and the contaminant in the raffinate (R) and in the extract (E). Considering that the flow rates of the raffinate and extract phases are equal, the fraction of the antibiotic and the contaminant that is discarded from the raffinate phase is equal to the fraction that is in the extract phase.

Evaluate the Purity of the Antibiotic

The purity of the antibiotic in the exit extract from stage 3 can be calculated as the ratio of the antibiotic concentration to the sum of the antibiotic and contaminant concentrations in the extract phase.

Evaluation of the Extraction Effectiveness

To conclude about the effectiveness of this extraction as a means of purification of the antibiotic, consider both the fraction of the antibiotic left in the raffinate phase and the purity of the antibiotic in the extract phase. If a large portion of the antibiotic remains in the raffinate, or if the purity of the antibiotic in the extract is low, the extraction process is not effective.

Key concepts

Countercurrent Extraction

Countercurrent extraction is a powerful method used in bioseparations to separate compounds based on their different affinities between two immiscible liquid phases.
In this process, the feed mixture is repeatedly contacted with a solvent in a series of stages.
Each stage operates under equilibrium conditions, allowing the targeted compound to preferentially move into the solvent phase while impurities remain in the original phase.

• Equilibrium stages ensure that the process takes advantage of differences in solubility between the compound of interest and contaminants.
• This method is highly effective for separating components with distinct partition coefficients.
• The more stages that are used, the purer the final extract phase will be, assuming that the targeted compound is significantly more soluble in the solvent phase.

Countercurrent extraction is often preferred over single-stage extractions because it enhances purity due to the repeated contact between phases. This iterative process maximizes the transfer efficiency of the desired compound.

Partition Coefficient

The partition coefficient is a crucial parameter in the process of countercurrent extraction, representing the ratio of concentrations of a compound in two immiscible phases at equilibrium.
This coefficient is unique for each compound-solvent pair and is influenced by temperature and the nature of the solvent.

• A high partition coefficient (>1) means the compound prefers the solvent phase, resulting in effective separation.
• A low partition coefficient (<1) indicates the compound is more likely to remain in the raffinate phase.
• Understanding the partition coefficient helps in predicting the efficiency of the extraction process for specific compounds.

In the given exercise, the antibiotic has a partition coefficient of 6, meaning it is highly likely to be found in the extract phase rather than remaining in the raffinate. On the other hand, the contaminant's partition coefficient of 1 suggests it distributes equally between the two phases.

Antibiotic Purification

Antibiotic purification is significantly enhanced by using countercurrent extraction, especially when the antibiotic in question has a much higher partition coefficient compared to contaminants.
In the exercise, the antibiotic displays a strong tendency to move into the extract phase, resulting in a purer final product.

• The ratio of antibiotic to contaminant in the feed (3:1) strongly influences the purification process.
• Carrying out multiple extraction stages increases the elimination of contaminants, improving the purity of the final antibiotic extract.
• Purity is determined by measuring the concentration of the antibiotic against the total concentration of all compounds in the extract.

Ultimately, a successful antibiotic purification process should result in an extract that is highly concentrated in the desired medication, with minimal presence of contaminants, making it suitable for further processing and use.

Raffinate and Extract Phases

Raffinate and extract phases are two key components of any liquid-liquid extraction process, including countercurrent extraction.
The raffinate phase is the portion of the feed that remains after extraction, typically enriched with unwanted components.
The extract phase, conversely, becomes enriched with the target compound when the system works effectively.

• The effectiveness of separation is measured by how much of the desired compound is found in the extract phase versus the raffinate phase.
• In equal phase flow rates, as mentioned in the exercise, the proportions in both phases offer insights into the distribution of components.
• If the desired compound largely migrates to the extract phase, this indicates a successful separation process.

Effective bioseparation relies on optimizing each phase's conditions to enhance the selectivity and separation efficiency, ensuring minimal loss of the desired product in the raffinate phase while maximizing its concentration in the extract phase.