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You want to look at the strength of the intermolecular forces that the molecule can form. This is because boiling requires the intermolecular attractions between molecules to be broken. Thus, stronger intermolecular forces require more energy and therefore higher temperatures to be broken. Hydrogen bonding is the strongest intermolecular force, followed by dipole-dipole, then by London forces. Thus molecules that can participate in hydrogen bonding will have the highest boiling points. When comparing molecules that experience the same attractive forces, we then look at size and shape. Molecules that are larger have more electrons and are thus more polarizable, making the London forces between their molecules stronger. They will thus have higher boiling points than smaller, less electron dense molecules. For shape, rod-shaped or linear molecules have higher boiling points than spherical ones because a larger proportion of the molecules are in closer contact with each other in rod-shaped molecules compared to spherical ones.
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