Is the VSEPR theory correct in determining the bond angle of sulfur dioxide?

Question

Recently when we were doing the VSEPR Theory in class and discussing the bond angles in various compounds. That's when I thought of sulfur dioxide whose structure can be like this:

According to the Internet, the bond angle between the two oxygen atoms = 120°. But mathematics shows a little off. I was taught that the VSEPR Theory states that

Lone Pair-Lone Pair Repulsion > Bond Pair-LonePair Repulsion > Bond Pair-Bond Pair Repulsion

According to this, the angle between the two oxygens should be less than 120º and I can prove it.

Imagine that instead of the lone pair there was a double bond of oxygen with sulfur. This would imply that the bond angle between the oxygens would be exactly 120° on the same plane because each one of them would repel each other with the same repulsion force. But now instead of a bond pair, we have a lone pair which means (according to the VSEPR Theory) that it would repel the two oxygens much more than the imaginary bond pair was repelling. Therefore the angle between the lone pair and the bond pairs with oxygen would be more than 120°. This would result in a smaller than 120º angle between the two oxygen atoms. Then how does the net say that the bond angle is close to 120°? If what the web says is right, it implies that the repulsion of a lone pair and 2 bonds is exactly equal to the repulsion between 2 double bonds. Is it correct?

Answer 1

First off, your structure violates the octet rule on sulphur and is thus not a good representation of the molecule. A better one is this one:

Figure 1: electronic structure of $\ce{SO2}$.

All methods of approximation of bond angles you have learnt or will learn about are no more than educated guesses. VSEPR gives very good approximations for e.g. $\ce{NH3}$ and $\ce{H2O}$ but fails horribly at $\ce{PH3}$ and $\ce{H2S}$. For the latter two, an estimation based on the most likely orbitals used for bonds (all p) does a much better job. To accurately determine a bond angle, one needs to perform a structure elucidation experiment such as X-ray diffraction.

This has indeed been performed with $\ce{SO2}$ (likely multiple times using different methods; I am too lazy to check the references) and the results give a bond angle $\angle(\ce{O-S-O})\approx119^\circ$. This is indeed very close to $120^\circ$ so you can say that the VSEPR method gives a good approximation of the $\ce{SO2}$ bond angle.

Figure 2: Structural data of $\ce{SO2}$. Taken from Wikimedia, where a full list of authors is available.

Answer 2

From nowhere you can cited that the repulsion of a lone pair and a double bond are exactly the same. Instead, the lone pair is little closer to sulfur than the other two, as oxygen is far more electronegative compared to sulfur. As a result, the repulsion of the lone pair is little stronger than the other two; and the molecular angle is a little smaller than 120 degrees.