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I am in 12th standard and was revising the concept of determining which polyatomic molecule can be polar and which can be non polar. So when this example was given we were told that vertical dipole moment will not be cancelled out. But isn't it possible that it can be cancelled out? is there any other molecule which has a shape like $\ce{SO_2}$ i.e. the central atom is $sp^2$ hybridised and has one lone pair, and is non polar? Also where is the net dipole moment in $\ce{SO_2}$, upwards or downwards and why?

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    $\begingroup$ You are confusing two different (though related) concepts. Being polar is not the same as having dipole moment. CO2 has none, but still is pretty polar. $\endgroup$ – Ivan Neretin Dec 20 '19 at 5:24
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Sulfur dioxide has a dipole moment because of its shape

Bonds between dissimilar atoms in molecules inevitably have dipole moments (though they are sometimes small). The only way the whole molecule can be free of a net dipole is if the individual bond dipoles are exactly cancelled out. This means the one criterion for determining whether a molecule has a net dipole is geometric ie it depends on the shape of the molecule.

If the symmetry of the molecule means the individual bond dipoles cancel exactly, then there will be no net dipole. Compare carbon dioxide with sulfur dioxide. Carbon dioxide is a linear molecule so the two (relatively strong) C-O bond dipoles exactly cancel; the formula for sulfur dioxide looks superficially similar but the molecule is bent. Because the molecule is bent the bond dipoles cannot cancel and the molecule has a net dipole moment (with with a dipole resulting from net positive charge on the sulfur and negative on the oxygen).

It is possible, in principle, that a bunch of dipoles in a complex molecule could cancel out, but this is incredibly unlikely. Geometry essentially always predicts whether a molecule has a dipole, though calculating how big it is can sometimes be a challenge. None of this applies in simple cases like sulfur or carbon dioxide where the net molecular dipole is intuitively obvious once you know the shape of the molecule.

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