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) \(\mathrm{d}_{x^{2}-y^{2}} d_{z^{2}}\) (b) \(d_{x x^{\prime}}, d_{x^{2}-y^{2}}\) (c) \(\mathrm{d}_{z^{2}}, \mathrm{~d}_{\mathrm{xz}}\) (d) \(\mathrm{d}_{x y}, d_{y z}\)

Step-by-Step Solution

Answer

The correct pair involved in \( \mathrm{d}^{2} \mathrm{sp}^{3} \) hybridization for an octahedral structure is (a) \( \mathrm{d}_{x^{2}-y^{2}}, \mathrm{d}_{z^{2}} \).

Step 1: Understanding d2sp3 Hybridization

In an octahedral complex with \( \mathrm{d}^{2} \mathrm{sp}^{3} \) hybridization, the \( \mathrm{d} \) orbitals involved are typically the inner \( \mathrm{d} \) orbitals. The process involves the mixing of two \( \mathrm{d} \) orbitals with one \( \mathrm{s} \) and three \( \mathrm{p} \) orbitals, forming six equivalent degenerate orbitals.

Step 2: Identifying Suitable d Orbitals

For the inner d orbitals in \( \mathrm{d}^{2} \mathrm{sp}^{3} \) hybridization in an octahedral complex, the orbitals involved are those lying in the plane of symmetry. Particularly, \( \mathrm{d}_{x^{2}-y^{2}} \) and \( \mathrm{d}_{z^{2}} \) are the most common because they are oriented along the axes of the coordinate system, aligning perfectly with the octahedral ligands.

Step 3: Comparing Given Options

Now consider the options: (a) \( \mathrm{d}_{x^{2}-y^{2}} \) and \( \mathrm{d}_{z^{2}} \)(b) \( \mathrm{d}_{x x^{\prime}} \) and \( \mathrm{d}_{x^{2}-y^{2}} \)(c) \( \mathrm{d}_{z^{2}} \) and \( \mathrm{d}_{xz} \)(d) \( \mathrm{d}_{xy} \) and \( \mathrm{d}_{yz} \).Options (a) reflects the orientation needed for optimal overlap with octahedral ligand fields.

Step 4: Final Selection of Correct Pair

After analyzing the options, the pair of \( \mathrm{d} \) orbitals typically involved in \( \mathrm{d}^{2} \mathrm{sp}^{3} \) hybridization within an octahedral structure is option (a): \( \mathrm{d}_{x^{2}-y^{2}} \) and \( \mathrm{d}_{z^{2}} \). These orbitals are ideal for such hybridization, encompassing alignment required by octahedral symmetry.

Key Concepts

Octahedral Structure

An octahedral structure is defined as a molecular geometry with six atoms or ligands symmetrically arranged around a central atom, forming the shape of an octahedron. Think of it like a six-sided dice where each side has one atom or ligand attached at the vertices. This symmetrical arrangement allows for strong and equal bonding between the central atom and its surrounding atoms. Octahedral structures are common in coordination chemistry where metal ions are often surrounded by six ligands. Examples of octahedral complexes include

• Manganese (Mn) in its hexaquo complex (e.g., [ Mn(H₂O)₆ ]²⁺ )
• Iron (Fe) in [ Fe(CN)₆ ]³⁻

These structures provide stabilization through interactions that ensure minimal electron-pair repulsion. This structure is often linked with certain types of hybridization such as d²sp³ hybridization, where d orbitals of a metal often interact with s and p orbitals to form new hybrid orbitals suitable for bonding.

d Orbitals

In chemistry, particularly when dealing with transition metals and their complexes, understanding d orbitals is crucial. There are five types of d orbitals:

• d_xy (oriented between the axes in a plane)
• d_yz and d_zx (also oriented between the axes in different planes)
• d_x²-y² (oriented along the axes in the xy-plane)
• d_z² (aligned along the z-axis)

These orbitals are crucial in the formation of complex shapes when bonding occurs in coordination compounds. The orientation of these orbitals plays a critical role in determining the type of overlap and the strength of interaction between the central metal and its ligands, leading to varying coordination geometries like octahedral or tetrahedral structures.

Orbital Hybridization

Orbital hybridization is a fascinating concept in chemistry used to explain how atoms like metals in a coordination complex can form equivalent bonds despite having different types of orbitals. In the case of d²sp³ hybridization, the hybridization involves the mixing of d orbitals with s and p orbitals:

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

These combine to form a new set of six hybrid orbitals. These hybrid orbitals align such that they form an octahedral configuration around the central atom. The idea of hybridization helps in predicting molecular geometry and understanding bonding. It's a key tool for chemists when dealing with the formation of complexes and understanding their reactivity and bonding mechanisms.

Inner d Orbitals

In the context of hybridization, particularly in an octahedral field, inner d orbitals have a significant role. When we refer to inner d orbitals, it implies the utilization of the d_x²-y² and d_z² orbitals. These are termed "inner" because they are often used closer to the central metal ion within a coordination compound. These orbitals are preferred in d²sp³ hybridization because:

• They have the best orientation for overlap with ligand orbitals in the octahedral structure.
• They allow for the formation of stable, strong bonds without significant electronic repulsion since they lie along the axes where ligand approach occurs.

Understanding which orbitals hybridize can explain why certain elements and their complexes exhibit specific structural and chemical characteristics.