94. In a single stage continuous extraction system, solvent is added to cell-free culture filtrate
containing the product. If the partition coefficient of the product is 5, then to extract 90% of the
product, assuming ideal single stage, the flow rate of solvent should be times the flow rate of the
culture filtrate.
1. 1.5 times
2. 1.8 times
3. 2.1 times
4. 2.4 times

 

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Question:

In a single-stage continuous extraction system, solvent is added to a cell-free culture filtrate containing the product. If the partition coefficient of the product is 5, then to extract 90% of the product, assuming ideal single stage, the flow rate of solvent should be how many times the flow rate of the culture filtrate?

Options:

1. 1.5 times

2. 1.8 times

3. 2.1 times

4. 2.4 times

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Correct Answer:

2.1 times

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Explanation:

In a single-stage liquid-liquid extraction, the fraction of solute remaining in the raffinate can be calculated using the formula:

CrCf=11+K(SF)\frac{C_r}{C_f} = \frac{1}{1 + K \left( \frac{S}{F} \right)}CfCr=1+K(FS)1

Where:

• Cr/CfC_r/C_fCr/Cf: Fraction remaining (i.e., unextracted)

• $K$: Partition coefficient (here, 5)

• $S/F$: Ratio of solvent flow rate to feed (filtrate) flow rate

• For 90% extraction, only 10% remains, so Cr/Cf=0.1C_r/C_f = 0.1Cr/Cf=0.1

Solving:

0.1=11+5⋅(S/F)0.1 = \frac{1}{1 + 5 \cdot (S/F)}0.1=1+5⋅(S/F)1 $$1+5(S/F)=10$$ $$5(S/F)=9$$ S/F=95=1.8S/F = \frac{9}{5} = 1.8S/F=59=1.8

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Conclusion:

To extract 90% of the product in a single-stage extraction with a partition coefficient of 5, the solvent flow rate should be 1.8 times the flow rate of the culture filtrate.