Solution :-
Butyric acid molecular formula = C4H8O2
Palmitic acid molecular formula = C16H32O2
Molecular structure of butyric acid and palmitic acid are shown in the following image.
The solubility of the compounds determined by the polarity of the compound though both are acids and contains the carboxylic acid group in them, the alkyl chain present in the palmitic acid is a very long chain of carbon which increases the nonpolar nature of the palmitic acid. Also when the molar mass increases then solubility of the compound decreases. So because of the more nonpolar nature and higher molar mass, the palmitic acid is less soluble in water as compared to the butyric acid which is more soluble because of the lower molar mass and higher polarity of the molecule. Since water is polar solvent, therefore, it causes the butyric acid to be more soluble than palmitic acid.
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