(Polar molecules, Non-polar molecules, etc.)
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Polar bonds occur when the charge distribution between two atoms is unequal. For example, if two atoms do not share electrons equally, it is possible their bonds are polar. A polar molecule is one where the charge distribution is also asymmetric, so there are partial charges on the molecule.
Ionic bonds form when the difference in electronegativity is large between the molecules. However, sometimes the electronegativity difference in molecules is not large enough to form ionic bonds. The electrons are not shared equally, creating partially negative and partially positive regions. These polar molecules have slightly opposite charges on opposite ends, creating a dipole moment.
Yes, this is possible. For example, carbon tetrafluoride would have four very polarized bonds, but due to the symmetry about the molecule, there would be very little polarity. This also explains why perfluorocarbons, which are like hydrocarbons but containing only C-F bonds, are very nonpolar despite having very polarized bonds.