Q.55 An aqueous solution containing 6.8 mg/L of an antibiotic is extracted with amyl acetate.
If the partition coefficient of the antibiotic is 170 and the ratio of water to solvent is 85,
then the extraction factor is ________

Antibiotic Extraction Factor Calculation: Partition Coefficient 170, Water:Solvent Ratio 85 Solved

Extraction Factor Overview

The extraction factor for this antibiotic in amyl acetate solvent extraction is 2.

Extraction Theory

The partition coefficient K measures solute distribution:

K = [solute]_organic / [solute]_aqueous

Given K = 170.

Water-to-solvent volume ratio:

V_aqueous : V_solvent = 85 : 1

Thus:

r = V_solvent / V_aqueous = 1/85

The extraction factor E (distribution ratio term) is:

E = K × (V_solvent / V_aqueous)

Step-by-Step Calculation

1. r = 1/85 ≈ 0.01176
2. K × r = 170 × (1/85) = 2
3. Fraction extracted:

   (K r) / (1 + K r) = 2 / (1 + 2) = 2/3 ≈ 66.7%

This fraction is independent of initial antibiotic concentration (e.g., 6.8 mg/L).

The extraction factor is therefore:

E = 2

Why This Formula Works

• 6.8 mg/L drops out since ratios cancel concentration terms
• High K = 170 favors antibiotic in the organic phase
• E = 2 means twice as much antibiotic moves to solvent as remains in water
• Incorrect possible values:
  • 85 ignores K
  • 170 ignores volume ratio
  • 0.012 misinterprets volume ratio