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 CaF2 has the maximum coordination number, which is 8.

Step 1: Understand Coordination Number

The coordination number is the number of nearest neighbors an atom or ion has in a crystal structure. Generally, a higher coordination number indicates a more closely packed structure.

Step 2: Analyzing NaCl Structure

In the rock-salt structure of NaCl, each sodium ion ( ext{Na}^+) is surrounded by 6 chloride ions ( ext{Cl}^-), and vice versa. Hence, the coordination number of the cation in NaCl is 6.

Step 3: Analyzing Na2O Structure

In the antifluorite structure of Na2O, each ext{Na}^+ ion is surrounded by 4 oxide ions ( ext{O}^{2-}). Thus, the coordination number of the sodium cation in Na2O is 4.

Step 4: Analyzing Zinc Blende Structure

In the zinc blende structure (ZnS), each zinc ion is tetrahedrally coordinated by 4 sulfide ions. Hence, the coordination number of the cation in zinc blende is 4.

Step 5: Analyzing CaF2 Structure

In the fluorite structure of CaF2, each calcium ion ( ext{Ca}^{2+}) is surrounded by 8 fluoride ions ( ext{F}^-). Therefore, the coordination number of the cation in CaF2 is 8.

Step 6: Compare Coordination Numbers

Now that we know the coordination numbers are 6 for NaCl, 4 for Na2O, 4 for zinc blende, and 8 for CaF2, we can compare these values. The maximum coordination number among them is 8.

Key Concepts

Coordination Number

The coordination number is a fundamental concept in chemistry and crystallography that refers to the number of nearest neighboring atoms or ions surrounding a central atom or ion in a crystal lattice. This number offers insight into the structure and stability of a crystal. Typically, a higher coordination number suggests a more densely packed arrangement of atoms, which often correlates with increased stability. The coordination number is influenced by several factors:

• Size and charge of the central atom or ion
• Size and charge of the surrounding atoms or ions
• Overall geometry and symmetry of the crystal structure

Understanding coordination numbers can help predict how a crystal will behave and react in a given chemical environment. For example, in an ionic crystal like \({CaF}_{2}\), each calcium ion is surrounded by 8 fluoride ions, defining its coordination number as 8, which indicates a very stable and tightly packed structure.

Crystal Structures

Crystal structures describe the orderly and repeating pattern of atoms or ions in a crystalline solid. These structures are crucial because they define the physical properties of the material, such as its density, hardness, and melting point. There are several types of crystal structures, with some of the most common being:

• Face-Centered Cubic (FCC)
• Body-Centered Cubic (BCC)
• Hexagonal Close-Packed (HCP)

The arrangement in these structures is determined by the balance of attractive and repulsive forces among the atoms or ions. Let's consider the sodium chloride (NaCl) structure, known as the rock-salt structure. Here, each sodium ion is surrounded by 6 chloride ions, and vice versa. This uniform and symmetric packing of ions leads to its high stability and specific physical properties.
Another example is the zinc blende (ZnS) structure, where each zinc ion is surrounded by 4 sulfide ions, resulting in a tetrahedral arrangement which affects its electrical properties, making it useful in semiconductors.

Fluorite Structure

The fluorite structure is a type of ionic crystal structure commonly seen in compounds like \(\text{CaF}_2\). It is characterized by a specific arrangement where each calcium ion is surrounded by eight fluoride ions. This structure is classified as a simple cubic lattice because of its basic repeating pattern.
The fluorite structure features a high coordination number, which means each central atom or ion is encased by many neighboring atoms. This achieves a compact and stable crystal lattice.

• The high coordination number (8) results from the ability of small fluoride ions to easily fit around the larger calcium ions.
• Fluorite structures are highly symmetrical, leading to distinct physical properties like high melting points and good ionic conductivity.

This type of structure is not only important in minerals such as fluorite but also plays a significant role in the functionality of materials used in various applications, including optics and electronics.