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Incorrect. Hydrogen bonding is the major component of water's large heat capacity but does not explain the variation in boiling point (or freezing point) with the addition of anti-freeze.
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I don't believe I stated that the boiling point elevation was due to the hydrogen bonding of water or even an effect from the the hydrogen bonds, but did in fact state that it was due to addition of anti-freeze and therefore the colligative properties raising the boiling point.
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Incorrect. Anti-freeze does not significantly alter hydrogen-bonding.
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Anti-freeze does significantly affect the hydrogen bonding of water as the surface tension of water is reduced upon the addition of anti-freeze. The surface tension is directly related to the hydrogen bonding of water and reduction in surface tension is a physical manifestation of the reduction in hydrogen bonding.
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Incorrect. The size of these molecules size does not appreciable change because of the presence or absence of inter-molecular forces from other molecules.
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True in the sense of appreciable in a macro way. The original statement was made as a bit of a joke. However, at the atomic level there is "appreciable" bond stretch due to hydrogen bonds which does affect molecule size in an "appreciable" way at the atomic scale. But you are correct as far as molecule size in relation to the affects on a radiator and really as far as any of us are really concerned in most of our day to day lives.