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I am studying Infrared Spectroscopy and the book says that unsaturated ketones have a carbonyl group which has weaker bond because it's more single-bond character than single bond because it has these three resonance structures.

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On the other hand, carbonyl group in saturated ketones have more double-bond character because it only has two resonance structures.

I can't really understand - why do the unsaturated ketones have $\ce{C-O}$ bond weaker than saturated ketones? How it is related to resonance structures?

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The statement can actually be said like this. In Unsaturated aldehydes/ketones the $\ce{C -O }$ bond has significant single bond character associated with double bond characters(i.e. partial double bond character), whereas, saturated aldehydes/ketones the $\ce{C -O}$ bond has almost pure double bond character.
In unsaturated carbonyl compounds, as the no. of stable resonating structures increase,( the structure where the $\pi$ electron cloud of $C =C$ double bond delocalises is also very stable) the contribution of that canonical form where the $C$ and $O$ has double bond between them also decreases . So, that's why, in the resonance hybrid of the molecule( which will give the IR spectra) the bond order of $\ce{C -O}$ bond becomes significantly less, and become close to the midway between double and single bond.
But in saturated carbonyls, the other resonating form is relatively very less stable ( not complete Lewis Octet and very close charge seperation) than the canonical form of pure double bond. So, contribution of that other form becomes significantly less. So, the resonance hybrid becomes almost close to that consisting of pure double bond.So, in the IR spectra, the streching frequency of saturated carbonyls correspond to almost perfect $\ce{C=O}$ double bond.

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