5. Solvent extraction using ethanol is used to purify a target metabolite from an aqueous broth. The
partitioning coefficient is 3. The ratio of solvent to broth that is required to extract 80% of the metabolite in
a single step is:
1. 0.8:1
2. 2.4:1
3. 2.67:1
4. 1.33:1

How to Calculate Solvent-to-Broth Ratio in Single-Step Extraction Using Partition Coefficient

Solvent extraction is a widely used technique to recover metabolites from aqueous solutions, such as fermentation broths. The effectiveness of this process depends on the partition coefficient and the volume ratio of solvent to broth. Here’s how to calculate it for a desired recovery percentage.

Question:

Solvent extraction using ethanol is employed to purify a target metabolite from an aqueous broth. The partitioning coefficient (K) is 3, and you want to extract 80% of the metabolite in a single step. What should be the solvent to broth ratio?

Options:

1. 0.8:1

2. 2.4:1

3. 2.67:1

4. 1.33:1

Step-by-Step Explanation

Step 1: Understand the Partition Coefficient

The partition coefficient (K) is defined as:

K=CorganicCaqueousK = \frac{C_{\text{organic}}}{C_{\text{aqueous}}}K=Caqueous​Corganic​​

Where:

• CorganicC_{\text{organic}}Corganic​: concentration of solute in organic (ethanol) phase

• CaqueousC_{\text{aqueous}}Caqueous​: concentration in aqueous (broth) phase

• In this case, $K=3$

Step 2: Use the Single-Step Extraction Equation

The fraction of solute remaining in the aqueous phase after extraction is:

f=11+K⋅VsVaf = \frac{1}{1 + K \cdot \frac{V_s}{V_a}}f=1+K⋅Va​Vs​​1​

Where:

• $f$: fraction remaining in aqueous phase

• VsV_sVs​: volume of solvent

• VaV_aVa​: volume of aqueous phase (broth)

• VsVa\frac{V_s}{V_a}Va​Vs​​: solvent-to-broth ratio (what we are solving for)

If 80% is extracted, then 20% remains, so:

$$f=0.20$$

Substitute values into the formula:

0.20=11+3⋅R0.20 = \frac{1}{1 + 3 \cdot R}0.20=1+3⋅R1​

Where R=VsVaR = \frac{V_s}{V_a}R=Va​Vs​​

Step 3: Solve for R

0.20=11+3R⇒1+3R=10.20=5⇒3R=4⇒R=43=1.330.20 = \frac{1}{1 + 3R} \Rightarrow 1 + 3R = \frac{1}{0.20} = 5 \Rightarrow 3R = 4 \Rightarrow R = \frac{4}{3} = 1.330.20=1+3R1​⇒1+3R=0.201​=5⇒3R=4⇒R=34​=1.33

✅ Correct Answer: (4) 1.33:1

Why It Matters

Knowing the correct solvent-to-broth ratio ensures:

• Maximum recovery of target compound

• Reduced solvent use (cost-saving)

• Optimal process design for scale-up

This is especially important in industries like pharmaceuticals, food, and biofuels where extraction steps must be efficient and cost-effective.

Summary

To extract 80% of a metabolite using ethanol with a partition coefficient of 3, you need a:

• Solvent-to-broth ratio of 1.33:1

Answer: (4) 1.33:1