Question

The hybridization scheme for the central atom includes a $d$ orbital contribution in (a) ${\mathrm{I}}_3^{-};$ (b) ${\mathrm{PCl}}_3$ (c) ${\mathrm{NO}}_3^{-};$ (d) ${\mathrm{H}}_2$ Se.

Short answer

Only ${\mathrm{I}}_3^{-}$ involves a d orbital in its hybridization scheme.

Step-by-step solution

Identify the Central Atom and Electron Pairs for ${\mathrm{I}}_3^{-}$

The central atom for ${\mathrm{I}}_3^{-}$ is iodine (I), with two other iodine atoms and one lone pair of electrons. This gives it a total of 3 electron pairs.

Identify the Central Atom and Electron Pairs for ${\mathrm{PCl}}_3$

The central atom for ${\mathrm{PCl}}_3$ is phosphorus (P), with three other chlorine atoms and one lone pair of electrons. This gives it a total of 4 electron pairs.

Identify the Central Atom and Electron Pairs for ${\mathrm{NO}}_3^{-}$

The central atom for ${\mathrm{NO}}_3^{-}$ is nitrogen (N), with three other oxygen atoms. This gives it a total of 3 electron pairs.

Identify the Central Atom and Electron Pairs for ${\mathrm{H}}_{2}Se$

The central atom for ${\mathrm{H}}_{2}Se$ is selenium (Se), with two hydrogen atoms and two pairs of lone electrons. This gives it a total of 4 electron pairs.

Identify Which Molecules Involve a d Orbital

Looking at the total number of electron pairs, the only molecule with more than four electron pairs is ${\mathrm{I}}_3^{-}$. Therefore, ${\mathrm{I}}_3^{-}$ involves a d orbital in its hybridization scheme.

Key concepts

d Orbital

The d orbital is a type of atomic orbital that plays a crucial role in the chemistry of elements primarily located in the central block of the periodic table, known as the transition metals. However, d orbitals can also be involved in the hybridization schemes of molecules containing elements from outside the transition metals, especially when these elements form bonds using more than four electron pairs.
In hybridization, atomic orbitals combine to form new hybrid orbitals that are suitable for pairing electrons to form chemical bonds. The inclusion of a d orbital in hybridization is typically associated with elements that can exceed the octet rule, such as iodine in the ion ${\mathrm{I}}_3^{-}$.

• For ${\mathrm{I}}_3^{-}$, the presence of five electron pairs around iodine suggests the utilization of d orbitals, contributing to the hybridization and allowing for an expanded valence shell. This is characterized by the involvement of d orbitals in the hybridization process, resulting in structures like dsp${}^3$ or d${}^2$sp${}^3$, where the d orbitals are active participants.

Understanding the role of d orbitals aids in the comprehension of complex molecular geometries and the electronic characteristics of such molecules.

Electron Pairs

Electron pairs are sets of two electrons that occupy the same orbital but have opposite spins. They are fundamental in determining the shape and geometry of molecules through the VSEPR (Valence Shell Electron Pair Repulsion) theory. In this theory, electron pairs arrange themselves to maximize their distance from each other, minimizing repulsion and resulting in specific molecular geometries.
In hybridization, electron pairs include both bonding pairs, which are involved in chemical bonds, and lone pairs, which are not directly involved in bonding but still affect the molecule's shape. Consider the following examples:

• In ${\mathrm{I}}_3^{-}$, iodine has three electron regions with one being a lone pair, leading to a linear structure.
• In ${\mathrm{PCl}}_3$, phosphorus has four electron regions including one lone pair, resulting in a trigonal pyramidal shape.
• ${\mathrm{H}}_2\mathrm{Se}$, selenium possesses four electron regions with two lone pairs, forming a bent or V-shaped geometry.

Understanding these electron pair arrangements is crucial for predicting molecular shapes and hybridization types.

Central Atom

The central atom in a molecule is typically the atom that forms the most bonds and usually possesses the highest number of electron pairs. It serves as the anchor point from which the molecular geometry is determined.
In the molecules discussed, the central atoms have distinctive roles based on their number of bonding and lone electron pairs:

• For ${\mathrm{I}}_3^{-}$, iodine acts as the central atom. It bonds with two other iodine atoms and holds a lone pair, making the inclusion of d orbitals necessary for stability and structure.
• In ${\mathrm{PCl}}_3$, phosphorus is the central atom, bonded to three chlorine atoms and having one lone electron pair, contributing to its hybridization and geometry.
• With ${\mathrm{H}}_2\mathrm{Se}$, selenium is the central atom with two bonded hydrogens and two lone pairs, heavily influencing its bent shape and hybridization.

The nature of the central atom, its electronegativity, and its electron pair configuration lead to its specific hybridization type and the resulting molecular geometry.