Problem 78 - A Complete Resource Book in Chemistry for JEE Main

Question

In calcium fluoride structure, the coordination numbers of calcium and fluoride ions respectively are (a) 6 and 8 (b) 8 and 8 (c) 4 and 8 (d) 8 and 4

Step-by-Step Solution

Answer

(d) 8 and 4

Step 1: Identify the Structure

Calcium fluoride (aF_2) is known to crystallize in a fluorite structure. In this structure, a^{2+} ions form a face-centered cubic (FCC) lattice.

Step 2: Determine Coordination for Calcium

In the fluorite structure, each calcium ion a^{2+} is surrounded by 8 fluoride ions ^{-}, forming a cubic arrangement. Therefore, the coordination number for calcium is 8.

Step 3: Determine Coordination for Fluorine

Each fluoride ion ^{-} is surrounded by 4 calcium ions a^{2+}. Hence, the coordination number for fluorine is 4.

Step 4: Match Results with Options

Based on the given options: - (a) 6 and 8 - (b) 8 and 8 - (c) 4 and 8 - (d) 8 and 4 Match the coordination numbers: 8 for calcium and 4 for fluoride, which corresponds to option (d).

Key Concepts

Coordination Number

In solid-state chemistry, the term "coordination number" refers to the number of ions or atoms that surround a central atom in a crystal lattice. It is a critical indicator of how tightly packed the atoms are within a structure.
For calcium fluoride ( CaF_2 ), the calcium ions ( Ca^{2+} ) are surrounded by 8 fluoride ions ( F^{-} ), giving calcium a coordination number of 8. Meanwhile, each fluoride ion is surrounded by 4 calcium ions, resulting in a coordination number of 4 for fluoride.
Coordination numbers help understand material stability and packing efficiency, influencing the physical properties of the substance.

Fluorite Structure

The fluorite structure is a common type of crystal structure, particularly for compounds like calcium fluoride. In this arrangement, calcium ions ( Ca^{2+} ) form a face-centered cubic (FCC) lattice, with fluoride ions habiting the tetrahedral gaps of this lattice.
This structure is renowned for its symmetry and dense packing, which ensures strong ionic bonding between the calcium and fluoride ions. The fluorite structure leads to unique physical properties such as transparency and hardness, making it important in material science and various industrial applications.

Face-Centered Cubic Lattice

A face-centered cubic (FCC) lattice is one of the most efficient ways of arranging atoms in three-dimensional space. In such a lattice, atoms are located at each of the cube's eight corners, with an additional atom in the center of each of the six cube faces.
For calcium fluoride ( CaF_2 ), the calcium ions ( Ca^{2+} ) form this FCC lattice. This organization allows for optimal space usage, providing the necessary stability for the compound. The FCC structure is significant in understanding how materials can pack together tightly while maintaining strength and stability.

Solid State Chemistry

Solid state chemistry is the study of the composition, structure, and properties of solid materials. This field explores how the arrangement of atoms affects the overall properties of materials.
Insights from solid state chemistry are crucial for developing new materials and understanding existing ones, such as calcium fluoride. By analyzing its fluorite structure and its coordination numbers, scientists can predict its physical properties, such as electrical conductivity and thermal stability.

Solid state chemistry plays a critical role in:
• Developing new technologies
• Understanding material durability
• Improving industrial manufacturing processes

Through these principles, solid state chemistry helps us develop materials that are fundamental to technological advancements.