1. Generally polar and non-polar are rather subjective terms, as like most things this is on a spectrum and thus depends on where the line (in electronegativity) is drawn.

2. The dipole of a molecule just gives the average distribution of electrons across a molecule. It does not give you information about the individual bonds.

3. That being said for simple (diatomic) molecules the rule does apply (polar bonds = polar molecule and vice versa).

4. Ozone is bent, hence it has a dipole. Just like e.g. water, which also has a dipole. Carbon dioxide on the other hand does not have a permanent dipole, but can have an induced dipole (through radiation absorption or collision with other molecules, where it also gets bent)

Yes - because geometry matters. Carbon dioxide is non-polar because the individual bond dipole moments are equal in magnitude and opposite in direction, leading them cancelling each other out. So if we consider the bond polarity and the relative orientation then we can deduce the overall polarity.

Carbontetrachloride? Four polar bonds, but they are evenly spaced about a tetrahedron, so no net dipole moment. Chloroform, dichloromethane, and chloromethane, where the symmetry is broken? All polar to greater or lesser extent.

I recommend that in analyzing a molecule, you start with the Lewis structure in an approximately accurate orientation of the atoms. Doing so for ozone reveals two things. One that the molecule is bent and has no charge neutral octet Lewis structure. That's a big hint that (a) electron distribution in the molecule isn't just due to polarity and (b) the lack of symmetry means that it's unlikely that the uneven charge distribution will be canceled out.

There's also a fair number of polar molecules where all the atoms are roughly the same electronegativity but due to the nature of charge distribution in the ground state (which often can be approximated with Lewis structures) lead to a dipole. The best example might be azulene, which is a hydrocarbon with a large dipole moment due to the molecular orbital arrangement of the p-orbitals of the carbon atoms. https://en.wikipedia.org/wiki/Azulene

In addition to what the other guy said, I teach AP chemistry and right now what is being taught at the advanced high school level is that if there is a molecular bond between elements that are not the same, then it is polar due to the inherent difference in electronegativity. For instance H2 or a carbon carbon bond would be non polar examples.

Also, what was not stressed in the other comment is the shape of the molecule. Carbon dioxide is linear

O=C=O so while the oxygen-carbon bonds are each polar due to O high electronegativity, the shape of the molecule will cancel out because of opposing pull of electrons. Same goes with something that is tetrahedral with polar bonds. The symmetrical shape cancels out the dipoles. So a shape that is not symmetrical such as the bent shape of water or ammonia, will have polar bonds AND be a polar molecule.

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Got it. Thank you!

Thank you so much for the detailed response!

>if there is a molecular bond between elements that are not the same, then it is polar

But aren't there some bonds between different elements that are nonpolar? Like CH4 the bond between carbon and hydrogen is nonpolar.

In general, like in a lab setting, we would regard CH4 as a non-polar molecule overall. However, what has been agreed upon by the powers that be is that technically each individual C-H bond is in fact polar because of the difference in electronegativity of carbon and hydrogen. And technically this is a correct statement, no matter how small of a difference it might be.

It must also be recognized that there is a sliding scale of polarity that ranges from slightly polar like the example given, to very polar such as in water. To be fair this is getting very technical and for all intents and purposes, no one really talks about pure hydrocarbons as being polar molecules.

Got it. Thank you for your time!