The bond angle of \(\mathrm{SO}_{2}\) is very close to \(120^{\circ},\) even though there is a lone pair on \(\mathrm{S} .\) Explain.

Molecular geometry is a way of describing the shapes of molecules. It refers to the three-dimensional arrangement of the atoms within a molecule.
Understanding molecular geometry is critical because it determines several properties of a substance, including reactivity, polarity, phase of matter, color, magnetism, and biological activity.

Various factors influence molecular geometry, such as the number of bonds, whether there are single, double, or triple bonds, and the presence of lone pairs of electrons. Different geometries include linear, bent, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral shapes.

Each molecular geometry has its particular angles between bonds, known as 'bond angles,' which minimize repulsion and thus stabilize the molecule.

The Lewis structure is a graphical representation of the valence electrons in molecules. It's used to depict the bonding between atoms as well as the lone pairs of electrons that may exist.
Creating a Lewis structure involves the following steps:

• Counting the total number of valence electrons available for bonding.
• Connecting atoms with single bonds.
• Distributing remaining electrons to complete the octet (or duet for Hydrogen) for each atom.
• If necessary, forming multiple bonds (double or triple bonds) to satisfy the octet rule.

Lewis structures do not provide three-dimensional structures, but they are a vital precursor for predicting molecular geometry using the VSEPR theory.

The VSEPR (Valence Shell Electron Pair Repulsion) theory is based on the principle that electron pairs around a central atom will repel each other, as electrons are negatively charged and like charges repel.
This repulsion causes the molecule to adjust its shape so that the valence electron pairs are as far apart as possible, minimizing their repulsive interactions. The shape of the molecule is thus determined by the positions that allow for the least electron pair repulsion.

There are two types of electron pairs to consider: bonding pairs involved in sigma bonds and lone or non-bonding pairs. Non-bonding pairs exert a greater repulsive force than bonding pairs, so their presence can lead to adjustments in the expected bond angles in a molecule's geometry.

The trigonal planar molecular shape is a geometry with one atom at the center and three atoms at the corners of an equilateral triangle. This geometry is associated with the molecule having three electron groups (either lone pairs or bonds) around the central atom.
Due to electron pair repulsion, the bonds are arranged 120 degrees apart, providing an even distribution of electrons in the plane.

For example, in the sulfur dioxide (SO2) molecule, even with a lone pair on the sulfur atom, the molecular shape remains essentially trigonal planar. This helps to maintain a bond angle close to 120 degrees, providing a good balance between the repulsive forces of the double bonds and the lone pair electrons.