Problem 13 - A Complete Resource Book in Chemistry for JEE Main

Question

In an octahedral structure, the pair of d orbitals involved in \(\mathrm{d}^{2} \mathrm{sp}^{3}\) hybridization is (a) \(\mathrm{d}_{x^{2}-y^{2}} d_{x^{2}}\) (b) \(\mathrm{d}_{x z}, \mathrm{~d}_{x^{2}-y^{2}}\) (c) \(\mathrm{d}_{z^{2}}, \mathrm{~d}_{\mathrm{xz}}\) (d) \(\mathrm{d}_{\mathrm{xy}}, \mathrm{d}_{y z}\)

Step-by-Step Solution

Answer

The correct choice is none; the expected pair is \\(d_{z^2}, d_{x^2-y^2}\\). Opcija (c) contains an error in pairing.

Step 1: Understanding Hybridization

In an octahedral structure, the hybridization involves a mixture of one s, three p, and two d orbitals. This results in six equivalent hybrid orbitals, denoted as \(d^2sp^3\). These orbitals accommodate six pairs of electrons that form bonds with ligands.

Step 2: Identifying d Orbitals in Hybridization

The two d orbitals that participate in the \(d^2sp^3\) hybridization are typically the \(d_{z^2}\) and \(d_{x^2-y^2}\) orbitals. These orbitals are chosen because they can point directly towards the ligands along the Cartesian axes, which is necessary for forming strong covalent bonds in an octahedral geometry.

Step 3: Analyzing Given Options

Looking at the options provided: (a) \( \mathrm{d}_{x^{2}-y^{2}} d_{x^{2}} \) involves a nonexistent orbital \(d_{x^2}\).(b) \( \mathrm{d}_{x z}, \mathrm{~d}_{x^{2}-y^{2}} \) involves a relevant orbital but not in the correct pair.(c) \( \mathrm{d}_{z^{2}}, \mathrm{~d}_{ ext{xz}} \) includes \( \mathrm{d}_{z^{2}} \) but not the other expected orbital.(d) \( \mathrm{d}_{ ext{xy}}, \mathrm{d}_{yz} \) involves orbitals typically associated with \(sp^3d^2\) hybridization.Therefore, the correct answer is likely \( \mathrm{d}_{z^{2}}, \mathrm{~d}_{x^{2}-y^{2}} \), but this is not one of the options. This suggests that there is an error in the choices.

Step 4: Conclusion from Analysis

Upon reviewing the concepts and the provided answers, none of them matches the correct pair for \(d^2sp^3\) hybridization in an octahedral geometry. Assuming a mistake in the options, the closest correct choice using logic is combination involving the \(d_{z^2}\) orbital, although it is inaccurately paired here. This exercise may need clarification or re-evaluation of the provided options.

Key Concepts

d2sp3 hybridization

When we talk about \(d^2sp^3\) hybridization, we're referring to a specific kind of hybridization in chemistry that involves the mixing of one s orbital, three p orbitals, and two d orbitals. This results in the creation of six hybrid orbitals, which are all equivalent. These hybrid orbitals form in such a way that they can accommodate six electron pairs.
This type of hybridization is typically associated with octahedral shapes, allowing the central atom within a molecule to form six covalent bonds.

• One s orbital
• Three p orbitals
• Two d orbitals

All collaborate to create the \(d^2sp^3\) hybridization.

octahedral geometry

Octahedral geometry refers to the shape associated with molecules or complexes where the central atom is surrounded by six ligands at the corners of an octahedron. This is a three-dimensional arrangement that can be achieved through \(d^2sp^3\) hybridization.
This geometric structure enables molecules to form strong covalent bonds due to the optimal placement of ligands. The electron pairs are positioned equidistantly around the central atom, minimizing repulsion and providing a stable configuration.
Characteristics of octahedral geometry include:

• Central atom surrounded by six ligands
• Symmetrical distribution of electron pairs
• Coordination number of six

d orbitals

The d orbitals in chemistry are crucial for understanding more complex bond formations, especially in transition metals. These orbitals are known for their complex shapes, which play a significant role in hybridization processes.
In the context of \(d^2sp^3\) hybridization, the relevant d orbitals are \(d_{z^2}\) and \(d_{x^2-y^2}\). These are particularly significant as they have the right orientation to interact with ligands effectively.

• \(d_{z^2}\): Points along the z-axis, aligns well with ligands in octahedral shapes.
• \(d_{x^2-y^2}\): Lubricates bonding in the x and y axes, facilitating interactions in octahedral geometry.

covalent bonding in chemistry

Covalent bonding represents one of the strongest forms of chemical bonding and involves the sharing of electron pairs between atoms. This type of bond is fundamental in creating stable chemical compounds.
In octahedral complexes, covalent bonding is crucial because it allows for the symmetrical arrangement of atoms. This symmetrical arrangement minimizes repulsion among electron pairs, resulting in stable, energy-efficient molecules.
Key aspects of covalent bonds in this context:

• Electron pairs are shared rather than fully transferred.
• Creates molecular stability and integrity.
• Strongest when formed between atoms with similar electronegativity.

Together, these concepts reveal the fundamental nature of strong and stable molecular structures, emphasizing the importance of understanding hybridization and geometry in chemical bonding.