Interpretation:
The reason for ethanoic acid to be soluble in water but palmitic acid to be insoluble in water needs to be explained.
Concept introduction:
An organic compound can be soluble in water if it shows effective hydrogen bond formation with water molecules. The stronger is the interaction with water, more soluble is the compound.

Explanation of Solution
The structure of ethanoic acid (acetic acid) is represented as follows:
The hydrogen bond formation is represented as follows:
Also, it can undergo dimerization by forming hydrogen bond with it self.
The structure of palmitic acid is as follows:
It can form hydrogen bond with water molecule but, due to long carbon chain the hydrogen bonding is not dominant intermolecular force.
If the carbon chain of an alcohol increases, its solubility in water decreases. Due to large number of carbon atoms in the carbon chain there is greater magnitude of dispersion forces between the chains. Therefore, more important intermolecular force is dispersion force in case of long carbon atom chain. This results in decrease in the solubility of higher alcohols in water.
Thus, ethanoic acid is water soluble but long chain carboxylic acids like palmitic acid is water insoluble.
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