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Here is a MC question from my chemistry professor:

What is the correct order of boiling points for molecules: $\ce{CO2}$, $\ce{LiOH}$, $\ce{CH3OH}$, $\ce{CH2O}$?

I am mainly confused about ordering compounds by boiling points by using dipole-dipole attraction/H-bonding (I did not consider using London dispersion forces because there were Os and Hs involved - do not know if I did the right thing).

How do I find out the dipole moment for polyatomic ions, especially complicated ones like the $\ce{CH3OH}$?

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    $\begingroup$ These are like simplest organic molecules... $\endgroup$ – Mithoron Aug 23 '17 at 22:27
  • $\begingroup$ This is more or less duplicate of chemistry.stackexchange.com/questions/15091/… $\endgroup$ – Mithoron Aug 23 '17 at 22:29
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    $\begingroup$ $\ce{CH3OH}$ is methanol. It is a molecular organic compound and not a polyatomic ion. $\endgroup$ – Zhe Aug 24 '17 at 0:09
  • $\begingroup$ From the homework close reason: ‘should demonstrate understanding of the underlying concepts’. This is the case here as your question demonstrates non-understanding of a fundamental underlying concept. $\endgroup$ – Jan Sep 23 '17 at 4:38
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Generally dipole moments of bonds and dipole moment of a whole molecule are different things. Dipole moment of a bond depends on the value of partial charge on both atoms forming the bond and since it has not only the numerical value but also direction, it can be represented as a vector.
The dipole moment of the whole molecule is basically the sum of all bond dipole moment vectors.
P. S. Methanol is not really an ion rather than a molecule.
P. P. S. The correct order for your professor's question is (from lowest to highest) CO2, CH2O, CH3OH, LiOH. Carbon dioxide is a covalent nonpolar molecule, so there are no dipole-dipole interactions (excluding induced dipoles), so it has the lowest BP. Methanal is polar, but has no hydrogen bonding. Methanol is known for H-bonds as most of the primitive alcohols. LiOH is an ionic compound with ionic lattice and has not dipole-dipole interactions but ion attraction.

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It took me about 20 seconds to find the dipole moment of methanol on Wikipedia and about 3 minutes to find the BPs and DMs of all four compounds. It's generally a BAD IDEA to use a gross molecular property over such a variety of structures. (for instance LiOH exist in the gaseous state mostly as (LiOH)2 while it is ionic in the solid state (I'm not sure how it exists in its liquid state, I'd guess as a molten salt)). I'd have zero idea which had stronger H-bonding MeOH or LiOH but I know that ionic solids have high melting points, so I'd assume that LiOH had the highest BP as well. Since we also know that CO2 is a gas at STP, that leaves us with formaldehyde and methanol. MeOH is a classic example of h-bonding, so that leaves us with HC(=O)H and the question of whether C-H...O=C is going to be h-bonding or not. Well, H-C bond is pretty non-polar so it's not likely to be very good at h-bonding. Given that its also much lighter than MeOH, we've got a ranking.

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