Why does the carbon-oxygen double bond in carbonyl compounds exhibit polarity, and what roles do the carbonyl carbon and oxygen play in terms of Lewis acid-base interactions?

The carbon-oxygen double bond in carbonyl compounds exhibits polarity due to the difference in electronegativity between carbon and oxygen. Oxygen is more electronegative, attracting electron density towards itself, resulting in a partial negative charge on oxygen and a partial positive charge on carbon. In Lewis acid-base interactions, the carbonyl carbon serves as a Lewis acid, capable of accepting an electron pair. The oxygen, with a lone pair of electrons, acts as a Lewis base, donating its electron pair to the carbonyl carbon. This interaction plays a crucial role in various chemical reactions, such as nucleophilic addition and acid-base reactions involving carbonyl compounds.