Identify the hybridization of the central atom in each of the following molecules and ions that contain multiple bonds: (a) CINO (N is the central atom) (b) \(\mathrm{CS}_{2}\) (c) \(\mathrm{Cl}_{2} \mathrm{CO}\) (C is the central atom) (d) \(\mathrm{Cl}_{2} \mathrm{SO}\) (S is the central atom) (e) \(\mathrm{SO}_{2} \mathrm{F}_{2}(\mathrm{S}\) is the central atom) (f) \(\mathrm{XeO}_{2} \mathrm{F}_{2}\) (Xe is the central atom) (g) \(\mathrm{ClOF}_{2}+(\mathrm{Cl}\) is the central atom)

Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule, which can significantly affect its physical and chemical properties. Understanding the geometry helps in predicting molecular behavior and reactivity. For instance, the central nitrogen atom in the compound CINO has a tetrahedral arrangement due to sp3 hybridization, which involves four electron domains, including bonding pairs and lone pairs.

To predict the shape, we use the VSEPR (Valence Shell Electron Pair Repulsion) theory. It posits that electron pairs around a central atom arrange themselves in a way to minimize repulsion. This theory works hand in hand with hybridization to give us a clear picture of the molecule's shape.

The electron domain theory is a component of VSEPR theory, and it focuses on predicting the molecular shapes based on the number of electron domains or regions of electron density around an atom. These domains can be bonding pairs of electrons in single, double, or triple bonds, or non-bonding lone pairs. For example, the carbon in CS2, despite forming two double bonds, has only two electron domains, leading to a linear molecular shape through sp hybridization.

The idea is that these domains will arrange themselves as far apart as possible to minimize electron pair repulsion, which then determines the geometry of the molecule.

When we talk about sp3 hybridization, we refer to the mixing of one s orbital with three p orbitals on an atom to form four equivalent sp3 hybrid orbitals. This type of hybridization occurs when the atom is surrounded by four electron domains. These sp3 hybrid orbitals are arranged in a tetrahedral geometry and have an angle of 109.5 degrees between them.

• Sulfur (S) in SO2F2 exhibits sp3 hybridization, indicating a tetrahedral arrangement of its electron domains.
• Xenon (Xe) in XeO2F2 also shows sp3 hybridization, accommodating two lone pairs and two bonding pairs.

This hybridization is key to understanding the three-dimensional arrangement of atoms within a molecule and thereby its reactivity and interactions.

sp2 hybridization involves the combination of one s and two p orbitals on the central atom forming three sp2 hybrid orbitals. These hybrids lie in a single plane and form a trigonal planar arrangement with 120 degrees between them. This hybridization is seen in molecules where the central atom has three electron domains.

For example, the central carbon in Cl2CO has a planar structure due to sp2 hybridization because it has three regions of electron density - two single bonds with chlorine and one double bond with oxygen. Similarly, chlorine in ClOF2+ is sp2 hybridized, resulting in a trigonal planar arrangement.

sp hybridization occurs when one s and one p orbital mix together to form two identical sp hybrid orbitals. This leaves two unhybridized p orbitals. In sp hybridization, the two hybrid orbitals are oriented 180 degrees apart, leading to a linear geometry for the molecule. A molecule like CS2 where the central carbon atom forms two double bonds with sulfur atoms, exhibits sp hybridization, creating a straight-line shape for the molecule.

Valence bond theory explains how atomic orbitals overlap to form covalent bonds in molecules. It posits that bonding results from the pairing of electrons between atoms through the overlapped orbitals.

Each type of hybridization, be it sp3, sp2, or sp, tells us which atomic orbitals are involved in bonding. Valence bond theory, when supplemented with the concept of hybridization, makes it possible to describe the electron distribution around an atom and predict molecular shapes more accurately. For example, the sulfur atom in Cl2SO forms a bond with two chlorine atoms and one oxygen atom using sp2 hybrid orbitals, accurately predicted by valence bond theory along with electron domain theory.