Even though the anhydride function bears a certain polarity, its presence in a molecule does not make much difference concerning its boiling point as compared to the corresponding alkane, i.e. it doesn't make the intermolecular forces stronger.
Since we know that carboxylic acids form dimers, one should consider them with a "double" molecular weight. With that in mind, acids and anhydrides end up displaying similar boiling points.
Carboxylic acid derivatives can be described by three resonance forms, their relative contribution depending on the nature of L group.
The C=O and C-L bond lengths can be understood by a higher or lower contribution of the first and third resonance forms.
Let's take methanol and acetaldehyde as the reference measurement of true single C-O and double C=O bond lengths.
What conclusion can you draw?There should be a negligible contribution of the third resonance form because the bond lenghts are very close to those of the reference compounds.
