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) \(\mathrm{CaF}_{2}^{2}\)

Step-by-Step Solution

Answer

The cation in \(\mathrm{CaF}_2\) has the maximum coordination number of 8.

Step 1: Understanding Coordination Number

Coordination number is the number of atoms or ions immediately surrounding a central atom in a complex or crystal structure. It's important to assess the crystal structure of each compound to determine the coordination number of the cation.

Step 2: Analyzing NaCl Structure

In the NaCl structure, sodium (\(\mathrm{Na}^+\)) is surrounded by 6 chloride ions (\(\mathrm{Cl}^-\)). Hence, the coordination number of Na in NaCl is 6.

Step 3: Analyzing Na2O Structure

In \(\mathrm{Na}_2\mathrm{O}\), each Na ion is typically coordinating with oxygen ions. Given its complex crystal structure, the precise coordination may vary, but typically lower than 6 due to the stoichiometry.

Step 4: Analyzing Zinc Blende Structure

In the zinc blende structure, zinc (\(\mathrm{Zn}^{2+}\)) is tetrahedrally coordinated with 4 sulfide ions (\(\mathrm{S}^{2-}\)). Thus, the coordination number in zinc blende is 4.

Step 5: Analyzing CaF2 Structure

In \(\mathrm{CaF}_2\), known as the fluorite structure, calcium (\(\mathrm{Ca}^{2+}\)) is surrounded by 8 fluoride ions (\(\mathrm{F}^-\)). Thus, the coordination number of \(\mathrm{Ca}^{2+}\) is 8.

Step 6: Comparing Coordination Numbers

After analyzing each structure, the arrangement with the highest cation coordination number is \(\mathrm{CaF}_2\) with a coordination number of 8 for \(\mathrm{Ca}^{2+}\).

Key Concepts

Crystal Structure

Crystal structures are the orderly arrangements of atoms in a crystalline material. Each structure is defined by the repetition of a unit cell, which is the smallest repeatable unit that makes up the crystal. The arrangement and space-filling of these unit cells determine the properties of the material. Understanding the coordination number in crystal structures is essential because it's a key factor in defining a material's stability and strength.

• Coordination number: The count of closest neighboring atoms or ions surrounding a central atom in a lattice.
• Unit Cell: The basic building block of the crystal structure that repeats to create the whole material.
• Lattice: A 3D network of points representing positions of atoms.

The way atoms are packed and ordered can vastly alter a material's physical and chemical properties. It's the reason why graphite and diamond, both made of carbon, exhibit vastly different characteristics.

NaCl Structure

The NaCl structure, also known as the rock salt structure, is one of the most common crystalline arrangements. In this structure, each sodium ion (\(\text{Na}^+\)) is surrounded by six chloride ions (\(\text{Cl}^-\)) in an octahedral configuration. This symmetrical arrangement gives the NaCl crystal its cubic structure.

• The coordination number of Na in NaCl is 6.
• Each Cl ion is also surrounded by 6 Na ions, making the coordination reciprocal.

This structural arrangement not only provides high stability but also reflects in NaCl's common cube-shaped crystals and its characteristic properties like high melting and boiling points. The NaCl structure is a vital model for understanding ionic solids.

Zinc Blende Structure

The zinc blende structure, also known as the sphalerite structure, is characterized by its tetrahedral coordination. Here, each zinc ion (\(\text{Zn}^{2+}\)) is coordinated by four sulfide ions (\(\text{S}^{2-}\)), forming a regular tetrahedron. This gives the zinc blende structure its cubic lattice.

• The coordination number of Zn in zinc blende is 4.
• This type of structure is common in semiconductors like GaAs or ZnS.

The tetrahedral arrangement leads to a less dense packing of atoms compared to structures like NaCl, influencing its physical properties. The zinc blende structure is pivotal in semiconductors, where precise atomic arrangements are essential for electronic applications.

CaF2 Structure

The structure of \(\text{CaF}_2\), commonly known as the fluorite structure, is noted for its high coordination number. In this structure, each calcium ion (\(\text{Ca}^{2+}\)) is symmetrically surrounded by eight fluoride ions (\(\text{F}^-\)).

• The coordination number of Ca in CaF2 is 8.
• This leads to a cubic structure where the CaF2 unit cell contains four calcium and eight fluoride ions.

CaF2's structure is known for excellent ionic conductivity, making it useful in a variety of applications. This high coordination number results in a very stable and densely packed crystal lattice, which is essential for materials requiring robust and durable structures.