Problem 194 - A Complete Resource Book in Chemistry for JEE Main

Question

The maximum number of \(90^{\circ}\) angles between bond pair-bond pair of electrons is observed in \(\quad\) [2004] (a) sp \(^{3} \mathrm{~d}^{2}\) hybridization (b) sp \(^{3}\) d hybridization (c) dsp \(^{3}\) hybridization (d) dsp \(^{2}\) hybridization

Step-by-Step Solution

Answer

The maximum number of 90° angles is observed in sp³d² hybridization (octahedral geometry).

Step 1: Understand the Question

We are asked to identify the type of hybridization that results in the maximum number of \(90^{\circ}\) angles between bond pair-bond pairs of electrons.

Step 2: Identify Hybridization and Geometry

Each type of hybridization corresponds to a specific geometric arrangement: - \(sp^3d^2\) hybridization results in an octahedral geometry.- \(sp^3d\) hybridization results in a trigonal bipyramidal geometry.- \(dsp^3\) hybridization results in a trigonal bipyramidal geometry.- \(dsp^2\) hybridization results in a square planar geometry.

Step 3: Analyze 90° Angles for Each Geometry

For each geometry, consider the 90° angles:- **Octahedral (\(sp^3d^2\))**: All adjacent bonds form 90° angles.- **Trigonal Bipyramidal (\(sp^3d\) and \(dsp^3\))**: Equatorial bonds form 120° angles, and axial-equatorial form 90° angles.- **Square Planar (\(dsp^2\))**: Bonds between adjacent atoms form 90° angles but have fewer such interactions compared to an octahedral geometry.

Step 4: Determine Maximum 90° Angles

The octahedral geometry of \(sp^3d^2\) hybridization has six axes that all form 90° angles with each other, maximizing the number of 90° angles. Therefore, it results in the maximum number of \(90^{\circ}\) angles between bond pairs. The more structures forming 90° angles present, the higher the count.

Key Concepts

Octahedral Geometry

Octahedral geometry is an arrangement of atoms around a central atom in such a way that the bonds form six symmetrical angles. These angles are all 90° apart. This configuration arises from an sp\(^3\)d\(^2\) hybridization.

The classic visualization of an octahedral structure is a shape similar to two square pyramids sharing a common square base. It's characterized by:

• Six vertices, where the atoms are positioned
• All bond angles equal to 90°
• Perfect symmetry and equal spacing for minimizing electron pair repulsion

In an octahedral geometry, the central atom forms exactly six sigma (σ) bonds with surrounding atoms or groups. The equal spacing and 90° angles ensure that electron repulsion is minimized, which stabilizes the molecule.

This geometry is common in compounds having a metal center, with ligands equidistantly placed around it, offering an optimal configuration for stability and symmetry.

90 Degree Bond Angles

Bond angles can influence the stability and reactivity of a molecule. A common angle in molecular geometries is 90°. This angle is pivotal in structures like octahedral geometry, where the electron pair distribution around the atom achieves maximum separation.

90° angles in molecular structures are significant because:

• They help minimize electron pair repulsions by maintaining equal distances between bonding pairs.
• They configure the atom and its bonds into symmetrical shapes, such as squares or cornered geometries.

Various hybridizations lead to these perpendicular angles. For instance, in octahedral formations via sp\(^3\)d\(^2\) hybridization, all bond pair-bond pair interactions form 90° angles.

Understanding these angles is essential for predicting molecular behavior, particularly for reaction mechanisms, and can impact the functional properties of compounds in diverse environments.

Trigonal Bipyramidal Geometry

In trigonal bipyramidal geometry, a central atom is surrounded by five bonds. The bonds diverge into two distinct groups: three are positioned in a plane with each forming 120° angles, while two more are perpendicular to this plane, creating 90° angles. This structure results from sp\(^3\)d hybridization.

The geometric arrangement resembles two triangular pyramids sharing a base, featuring:

• Three equatorial bonds with 120° angles between them
• Two axial bonds at 90° angles to the equatorial plane
• A more complex shape compared to tetrahedral or octahedral configurations

The combination of bond angles and spatial arrangement facilitates potentially lower electron pair repulsions compared to a simple planar shape but can also result in unique molecular vibrations.

Trigonal bipyramidal compounds are often analyzed through molecular orbital theory to understand the distribution of electrons and reactivity, especially in coordination compounds and transition metal chemistry. Connections between axial and equatorial positions play a crucial role in these dynamics.