Why can't methanol and carbon dioxide hydrogen bond?

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BBVET123

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I took the AAMC Gchem assessment, and one of the questions (#8) asked to pick the two compounds that can hydrogen bond. The answer was glycine and methanol, but I'm confused why the other answer choice (methanol and carbon dioxide) cannot hydrogen bond also?
Thanks for your help!

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Through process of elimination, Gly+MeOH is easily the best choice because of the O-H bonds in both compounds, and the N-H in Gly.

Someone correct me if I'm wrong, but C=O bonds do not have a strong enough dipole to participate in H-bonding. That is, the difference in electronegativity between C and O is negligible compared to O-H and N-H.
 
A carbonyl on another compound could act as a hydrogen bond acceptor (i.e. in DNA base pairing), but CO2 is non-polar overall and the 2nd carbonyl directly opposite the first will cut down CO2's ability to H-bond drastically.
 
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