Problem 11 - A Complete Resource Book in Chemistry for JEE Main

Question

In a regular octahedral molecule, \(\mathrm{MX}_{6}\) the number of X-M-X bonds at an angle of \(180^{\circ}\) is (a) three (b) two (c) six (d) four

Step-by-Step Solution

Answer

The number of X-M-X bonds at an angle of 180° is three.

Step 1: Understand the Octahedral Shape

A regular octahedral molecule, such as \( \text{MX}_6 \), has a geometry where one central atom \( M \) is surrounded symmetrically by six atoms \( X \). These six atoms are positioned at the vertices of an octahedron, a shape with eight equilateral triangular faces.

Step 2: Determine the Bond Arrangement

In an octahedron, the six atoms \( X \) around the central atom \( M \) are arranged such that they form 90°, 180°, and sometimes 120° angles with each other. Specifically, any two \( X \) atoms that are directly opposite to each other across the central atom will form bond angles of 180°.

Step 3: Calculate the Number of 180° Angles

In an octahedral configuration, each \( X \) atom is directly opposite to only one other \( X \) atom. Given there are three pairs of opposite \( X \) atoms (6 atoms in total), there are three X-M-X bonds that have angles of 180°.

Key Concepts

Bond Angles

In chemistry, bond angles refer to the angles formed between three atoms across at least two bonds. These angles are crucial for defining the shape and geometry of a molecule. In a regular octahedral molecule, such as \( \text{MX}_6 \), bond angles often appear in the values of 90° and 180°.

Within this geometry:

• Bonds arranged between the central atom \( M \) and adjacent \( X \) atoms create angles of 90°.
• Bonds where two \( X \) atoms are directly opposite across the central \( M \) atom result in an angle of 180°.

Understanding these bond angles is essential because they influence how a molecule interacts with other molecules, impacting its reactivity and properties. For example, the 180° bond angles make certain reactions possible by allowing enough space and correct alignment of molecular orbitals.

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of atoms within a molecule. In an octahedral geometry like \( \text{MX}_6 \), six atoms are symmetrically positioned around a central atom. This forms an octahedron, which is characterized by eight faces and twelve edges.

Key features of octahedral molecular geometry include:

• A central atom \( M \) surrounded by six atoms \( X \).
• Bond angles of either 90° or 180° formed between the atoms.
• A symmetrical layout that often results in the molecule having no dipole moment.

This geometric configuration is not only vital to the stability and shape of the molecule but also affects its chemical behavior and interactive properties. By understanding molecular geometry, students can predict how molecules will interact in reactions or in forming larger molecular complexes.

VSEPR Theory

VSEPR (Valence Shell Electron Pair Repulsion) theory is a model used to predict the geometry of individual molecules based on the repulsion between electron pairs around a central atom. It's a key theory to understand when studying molecular geometries like the octahedral shape.

How VSEPR explains octahedral geometry:

• In \( \text{MX}_6 \), there are six bonding pairs surrounding the central atom \( M \).
• The repulsion between these electron pairs arranges them as far as possible from each other, forming a symmetric shape known as an octahedron.

The application of VSEPR theory enables chemists to predict and explain the three-dimensional structure of molecules, which in turn helps in understanding their physical and chemical properties.