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

The coordination numbers are 8 for calcium and 4 for fluoride, which matches option (d).

Step 1: Understand the Structure

Calcium fluoride (CaF₂) has a crystal structure known as the fluorite structure. In this structure, calcium ions (Ca²⁺) form a face-centered cubic (fcc) lattice.

Step 2: Coordination Number of Calcium

In the fluorite structure, each calcium ion (Ca²⁺) is surrounded by 8 fluoride ions (F⁻), which means the coordination number of calcium is 8.

Step 3: Coordination Number of Fluoride

Each fluoride ion (F⁻) is surrounded by 4 calcium ions (Ca²⁺) in the fluorite structure, meaning the coordination number of fluoride is 4.

Step 4: Match the Coordination Numbers

Compare the coordination numbers of calcium and fluoride ions to the given options to find the correct match.

Key Concepts

Calcium Fluoride

Calcium fluoride (CaF₂) is an ionic compound composed of calcium ions (Ca²⁺) and fluoride ions (F⁻). The unique arrangement of these ions within its structure is what grants calcium fluoride its notable properties. One of the most important aspects of calcium fluoride is its crystal architecture, resulting in a very stable compound used in various applications such as in the production of specialty glasses and optics. - **Ionic Composition:** - Comprises positive calcium ions - Comprises negative fluoride ions The interaction between these ions forms a lattice that gives calcium fluoride its characteristic hardness and high melting point. It's mostly used in industries that require materials that can withstand thermal stress and physical wear.

Fluorite Structure

The fluorite structure is named after the mineral fluorite, which is composed of calcium fluoride. This structure is a highly symmetric cubic arrangement that is central to understanding the behavior and properties of calcium fluoride. In the fluorite structure: - **Calcium Ions:** - Form a face-centered cubic (fcc) lattice, creating a very stable foundation - **Fluoride Ions:** - Occupy the tetrahedral sites The structure results in the calcium ions being coordinated by eight fluoride ions, while each fluoride ion is coordinated by four calcium ions. This specific arrangement provides the compound with distinct features: - **Stability**: The symmetric cubic pattern contributes to its thermal stability - **Optical Properties**: This structure is crucial for its use in lenses and other optical devices due to its transparency and low refraction Understanding the fluorite structure elucidates why calcium fluoride can be so resilient and effective in specialized applications.

Face-Centered Cubic (fcc)

A key component of the calcium fluoride structure is the face-centered cubic (fcc) arrangement of the calcium ions. The fcc lattice is one of the most efficient ways to pack spheres in three-dimensional space, leading to dense and stable structures. Characteristics of the fcc arrangement: - **Efficient Packing:** - Every face of the cube is centered with an atom, maximizing the number of neighboring atoms - This results in a high coordination number and efficient space use - **High Coordination Number**: - For calcium, this means each calcium ion is surrounded by eight fluoride ions The fcc structure is not just applicable to calcium fluoride; it is also seen in several metals and other ionic compounds. Its presence in calcium fluoride highlights the geometric principles that govern crystal stability and density in materials science, explaining why such structures are preferred in a variety of technological applications.