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Answer:
Dr. K.S. kindly answered this question:
The acidic condition is usually employed when fatty acid is extracted by an organic solvent. Since the pKa of –COOH group of fatty acids is around 4.7 to 5.0, it cannot be extracted very much at neutral condition (pH 7) because of its negative charge. Therefore, it is usually extracted under acidic conditions.

Figure: Stearic acid (one of fatty acids)
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Acknowledgement
We would like to thank Dr. K.S. for his kind answer.
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