Describe the molecular geometry and hybridization of the \(\mathrm{N}, \mathrm{P},\) or \(\mathrm{S}\) atoms in each of the following compounds. (a) \(\mathrm{H}_{3} \mathrm{PO}_{4},\) phosphoric acid, used in cola soft drinks (b) \(\mathrm{NH}_{4} \mathrm{NO}_{3},\) ammonium nitrate, a fertilizer and explosive (c) \(\mathrm{S}_{2} \mathrm{Cl}_{2}\), disulfur dichloride, used in vulcanizing rubber (d) \(\mathrm{K}_{4}\left[\mathrm{O}_{3} \mathrm{POPO}_{3}\right]\), potassium pyrophosphate, an ingredient in some toothpastes

In chemistry, the term sp3 hybridization refers to a specific way an atom's orbitals combine to provide a particular geometry for bonding with other atoms. It occurs when one s orbital and three p orbitals from the same shell mix to form four hybrid orbitals of equal energy. This is commonly seen in atoms that form four bonds with no lone pairs of electrons.

For instance, in a molecule like phosphoric acid (H3PO4), the central phosphorus atom bonds with four oxygen atoms. Since there are four areas of electron density (comprising bonds and lone pairs), the phosphorus atom undergoes sp3 hybridization. All resulting hybrid orbitals orient themselves as far apart as possible, resulting in a tetrahedral arrangement to minimize electron repulsion. This principle applies equally to nitrogen in ammonium nitrate (NH4NO3) and sulfur in disulfur dichloride (S2Cl2), which both showcase sp3 hybridization due to their tetrahedral electron-pair geometries.

When discussing tetrahedral electron-pair geometry, we're looking at one of the fundamental shapes predicted by VSEPR theory, which stands for Valence Shell Electron Pair Repulsion. This model suggests that electron pairs in the valence shell of an atom will arrange themselves as far apart as possible to minimize repulsion.

A tetrahedral configuration arises when there are four electron domains surrounding the central atom. This could include bonding pairs, as in the phosphorus atom of phosphoric acid, or a combination of bonding pairs and lone pairs, as seen in the sulfur atoms of S2Cl2. Tetrahedral geometry has bond angles of around 109.5 degrees, and this spatial arrangement is instrumental in determining the molecule's three-dimensional shape and chemical properties.

Moving on to sp2 hybridization, it describes the mixing of one s orbital and two p orbitals from an atom's valence shell to create three equivalent hybrid orbitals. This type of hybridization leads to a trigonal planar electron-pair geometry. It happens in atoms that are connected to three other atoms with one lone pair or double bond contributing to the electron domains.

For example, in the nitrate ion (NO3-), the nitrogen atom has sp2 hybridization; it is bonded to three oxygen atoms with one of these bonds being a double bond and has one lone pair. These four domains of electron density push the bonds into a planar, or flat, configuration with 120-degree bond angles between them. This allows each hybrid orbital to be as distant as possible from the others on the same plane, satisfying the VSEPR principle.

The trigonal planar electron-pair geometry is another key structure in molecular geometry, typically resulting from sp2 hybridization. In this configuration, there are three domains of electron density arranged around the central atom, creating a planar shape with bond angles of 120 degrees.

This geometry is exemplified in the nitrate ion associated with ammonium nitrate. Here, the nitrogen atom, central to the NO3- ion, shares this planar geometry as it is surrounded by three oxygen atoms and has a lone pair, emphasizing the VSEPR concept of electron pair repulsion. In contrast to the tetrahedral geometries arising from sp3 hybridization, the trigonal planar layout offers a flatter molecular structure that is pivotal in predicting and understanding reactivity and interaction with other molecules.