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Is there any difference between a molecule having $\vec\mu=0$ and being Non-Polar?

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$\vec\mu$ is just the electric dipole moment. However, a molecule can be polar with $\vec\mu=0$, as polarity has to do with charge separation, so a particle with any form of multipole moment is polar.

In chemistry, polarity refers to a separation of electric charge leading to a molecule or its chemical groups having an electric dipole or multipole moment.

Molecules like methane, carbon dioxide, and perchlorate have $\vec\mu=0$, but have some level of charge separation, making them polar (these have quadrupole moments, not sure about higher order moments).

Actually, all molecules are polar by this definition, just that many aren't polar enough for this to matter. Generally, when we call a molecule "polar", we are talking about only $\vec\mu$.

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And what about molecules which does not have a net $\vec\mu$ but have electrovalent bonds. eg. If we have two molecules 1st)$BF_3$ and 2nd)$p-dinitrobenzene$ or $\ trans 1-cloropropene$ . 1st have net $\vec\mu$ but 2nd set does not.Are both of them polar? –  ABC Apr 3 '13 at 13:25
@exploringnet: $\rm BF_3$ doesn't have a net $\vec\mu$. All three of your examples seem to have a quadrupole moment. –  Manishearth Apr 3 '13 at 13:27
why doesn't $BF_3$ have net $\vec\mu$? Can u give me some link to a reliable source for information on these things? –  ABC Apr 3 '13 at 13:44
@exploringnet: Why would it? It is symmetric -- each $\rm B-F$ bond has a $\vec\mu$, but the three of them cancel out. Not sure if I can find a source other than Wikipedia for this, check the refs on Wikipedia. –  Manishearth Apr 3 '13 at 13:47

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