Problem 44 - A Complete Resource Book in Chemistry for JEE Main

Question

In which of the following structures, the cation has maximum coordination number? (a) \(\mathrm{NaCl}\) (b) \(\mathrm{Na}_{2} \mathrm{O}\) (c) zinc blende (d) \(\mathrm{CaF}_{2}\)

Step-by-Step Solution

Answer

The cation in CaF_2 has the maximum coordination number.

Step 1: Understanding Coordination Number

The coordination number in a crystal structure refers to the number of nearest neighboring ions of opposite charge that surround a particular ion. For a cation, it is the number of anions surrounding it.

Step 2: Analyzing Options

Each option represents a different type of crystal structure where the cation's coordination number varies. - In \( ext{NaCl}\), each Na\(^+\) ion is surrounded by 6 Cl\(^{-}\) ions, resulting in a coordination number of 6.- In \( ext{Na}_2 ext{O}\), each Na\(^+\) ion has a coordination number of around 4.- In Zinc Blende (ZnS), the coordination number for Zn\(^{2+}\) is 4.- In \( ext{CaF}_2\), each Ca\(^{2+}\) is surrounded by 8 F\(^-\) ions, giving it a coordination number of 8.

Step 3: Comparison and Conclusion

Comparing the coordination numbers:- NaCl: 6- Na\(_2\)O: 4- Zinc Blende: 4- CaF\(_2\): 8The cation in \( ext{CaF}_2\) has the maximum coordination number.

Key Concepts

Crystal Structure

Crystal structures define how atoms, ions, or molecules are arranged in a material. The main idea is how these particles stack and fit together in space. Each particle's position is crucial since it affects the material's properties and behavior.
In a crystal lattice, the repetitive pattern forms a three-dimensional grid. The particles usually occupy specific sites called lattice points.

• The unique arrangement of atoms in the lattice gives each crystal its specific properties like melting point and hardness.
• Common crystal structures include cubic, hexagonal, and tetragonal systems.

Understanding this framework is important as it influences the interaction between the ions, ultimately affecting properties like coordination number.

Cation Coordination

Cation coordination refers to the arrangement and number of anions surrounding a cation in a crystal structure. The coordination number is an essential metric in this context as it indicates the number of nearest anions positioned around a cation.
The coordination number can vary depending on the structure type and size of the ions involved.

• For instance, in NaCl, where each Na\(^+\) ion interacts with 6 Cl\(^-\) ions, the coordination number is 6.
• Size and charge of the ions can restrict or permit a higher or lower coordination environment.
• In larger crystals like CaF\(_2\), the coordination number increases due to the smaller size and greater number of F\(^-\) ions able to surround each Ca\(^{2+}\) cation.

Thus, the geometry and surrounding neighbors of the cation create significant variations in physical properties.

Anion Coordination

Anion coordination explores the counterpart of cation coordination in crystal structures. It focuses on how cations surround each specific anion in the lattice. This area is equally critical as anion coordination influences the packing and stability of a structure.
The number of cations surrounding an anion defines the effectiveness and strength of the crystal.

• The balance between the charge and size of cations and anions is crucial for maintaining a stable structure.
• For example, in NaCl, this balance results in a harmonious setting where each Cl\(^-\) is also surrounded by 6 Na\(^+\) ions.
• In CaF\(_2\), the arrangement allows every F\(^-\) ion to have a distinct coordination, ensuring strong ionic bonds and enhancing the structure's rigidity.

Understanding this coordination helps explain the mechanical properties and the behavior of the materials under various physical conditions.