why do pk values of ionizable groups differ between free amino acids and amino acid residues in polypeptides

Because of electrostatic interactions.

Explanation:

The pk values associated with ionizable groups are the result of the electrostatic interaction that occurs with the interaction of the ionizable side chain groups with groups of side chains that have charges, or that have neutral charges. This interaction directly influences the pk values of ionizable groups, leaving them different between free amino acids and amino acid residues in polypeptides.

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