Polarity and Hydrogen bonding

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What is the relationship between polarity and hydrogen bonding? I have come across several problems saying that an alcohol is more polar than a ketone because of hydrogen bonding but I don't see the relationship between these two. Intuitively, I thought ketone would be more polar because it has a larger dipole but the explaination says that alcohol is more polar due to hydrogen bonding. In order to determine polarity I have been thinking about it in terms of electronegativity difference and dipole moment. But when we compare compounds like an ester vs a carboxylic acid structure, I haven't been able to tell which is more polar. The explaination only say that due to hydrogen bonding it's more polar but this seems like it came out of nowhere. Does anyone know what the relationship is?
 

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