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Do lone pairs have an effect on overall polarity of a molecule? For example the answers say SF4 is polar, even though all the atoms around the central atom are the same and exhibit the same dipole moments that should cancel out. Is it because the lone pairs effects the shape of the structure and pushes the bonding pairs closer together, therefore changing the net direction of the dipole moments?
That is correct. When looking at dipole moments you need to consider the shape with regard to the effect lone pairs have on it. The lone pairs push atoms closer together and thus not all dipole moments will cancel out depending on the structure.
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