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

Question

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

Step-by-Step Solution

Answer

Option (d) \(\mathrm{d}_{\mathrm{xy}}, \mathrm{d}_{\mathrm{yz}}\) is correct.

Step 1: Understanding Hybridization in Octahedral Complexes

In an octahedral complex, the central metal atom needs six hybrid orbitals to accommodate six ligand pairs. The typical hybridization involving 6 orbitals in an octahedral complex is \( d^2sp^3 \). This implies the involvement of two d orbitals, one s orbital, and three p orbitals.

Step 2: Identifying Hybridized Orbitals

In \( d^2sp^3 \) hybridization, the orbitals involved are usually the two lowest energy d orbitals available. In many transition metals, these are the \( d_{xy} \), \( d_{yz} \), or \( d_{zx} \) orbitals. These orbitals lie between the axes, thus minimizing repulsion with ligand electron pairs.

Step 3: Clarifying Which Orbitals are Valence Orbitals

The \(d_{x^2-y^2}\) and \(d_{z^2}\) orbitals are oriented along the axes rather than between them. Hence, they are less likely to be part of the \(d^2\) contribution in \(d^2sp^3\) hybridization as they typically participate only in high-energy configurations where electrons from the first row transition metals are considered.

Step 4: Matching Problem Options with Correct Orbitals

Compare the given options with the correct orbitals involved in \(d^2sp^3\) hybridization:- (a) \(d_{x^2-y^2}, d_{z^2}\)- (b) \(d_{x x}, d_{x^2-y^2}\)- (c) \(d_{z} = d_{xz}\)- (d) \(d_{xy}, d_{yz}\)The correct answer is option (d), \(d_{xy}\) and \(d_{yz}\), because these orbitals are oriented between the coordinate axes.

Key Concepts

Octahedral Complexes

Octahedral complexes are structures where a central metal ion is surrounded by six ligands, which can be atoms, ions, or molecules. These six ligands arrange themselves symmetrically around the metal ion, forming an octahedron shape. This arrangement is crucial because it determines how the metal ion can interact with the ligands, affecting its chemical and physical properties.

• The central metal ion at the core of the complex is crucial to the overall geometry.
• Each corner of the octahedron, which forms the vertices, is occupied by a ligand.
• The coordination number in octahedral complexes is six, reflecting the six ligands attached.

Understanding the octahedral configuration is essential for predicting the geometric, electronic, and magnetic properties of a complex. This structure is common among transition metal complexes, influencing both their color due to d-d transitions and their magnetic properties. Additionally, the octahedral shape allows for different types of isomerism, such as geometric and optical isomerism, which are important in the field of coordination chemistry.

d²sp³ Hybridization

Hybridization is a concept in chemistry where atomic orbitals mix to form new hybrid orbitals, which can accommodate bonding with ligands. In an octahedral complex, the most common hybridization is \(d^2sp^3\), taking place to facilitate bonding with six ligands.

• Six hybrid orbitals are formed, utilizing two \(d\), one \(s\), and three \(p\) orbitals.
• This arrangement allows for a stable configuration that can accommodate the electron pairs from the ligands.
• Hybridization leads to bond angles of 90° between the ligands, typical of an octahedral structure.

In \(d^2sp^3\) hybridization, we commonly see the involvement of the lower energy d orbitals, like \(d_{xy}\), \(d_{yz}\), or \(d_{zx}\), which are interstitial and help minimize repulsion with incoming ligands. As a result, this hybridization is critical in determining the geometry, stability, and overall properties of octahedral complexes.

d Orbitals

d orbitals play a vital role in hybridization, especially in the context of octahedral complexes. They are a set of five orbitals within a given principal energy level. These orbitals have unique shapes and orientations which determine how they interact with surrounding ligands.

• The five d orbitals are \(d_{xy}\), \(d_{yz}\), \(d_{zx}\), \(d_{x^2-y^2}\), and \(d_{z^2}\).
• Among these, \(d_{xy}\), \(d_{yz}\), and \(d_{zx}\) are typically involved in \(d^2sp^3\) hybridization within octahedral complexes due to their orientation between the axes.
• \(d_{x^2-y^2}\) and \(d_{z^2}\) align along the axes, making them less involved in low-energy hybridization like \(d^2sp^3\).

Each d orbital can carry a maximum of two electrons, and their relative energy levels and symmetry greatly influence the chemical bonding and properties of metal complexes. This orbital orientation helps minimize electron repulsion and ensures proper mixing with other atomic orbitals to facilitate hybridization tailored for specific geometries like octahedral complexes.