Problem 29 - A Complete Resource Book in Chemistry for JEE Main

Question

In \(\mathrm{NaCl}\), the chloride ions occupy the space in a fashion of (a) \(\mathrm{BCC}\) (b) \(\mathrm{FCC}\) (c) both (d) none

Step-by-Step Solution

Answer

Chloride ions in NaCl occupy a FCC structure.

Step 1: Understand the Problem

We are asked to determine the arrangement of chloride ions in a sodium chloride crystal lattice, specifically choosing from the given options of body-centered cubic (BCC), face-centered cubic (FCC), both, or none.

Step 2: Identify the Crystal Structure of NaCl

Sodium chloride (NaCl) has a specific crystal structure known as the rock-salt structure. In this structure, the chloride ions form a cubic arrangement, which typically corresponds to a face-centered cubic (FCC) lattice.

Step 3: Analyze FCC Lattice in NaCl

In FCC structures, particles are located at each corner and in the center of each face of the cube. In NaCl, chloride ions occupy these positions, creating an FCC lattice.

Step 4: Conclusion

Based on the crystal structure of NaCl, the chloride ions are arranged in a face-centered cubic (FCC) configuration.

Key Concepts

Face-Centered Cubic (FCC)

In a face-centered cubic (FCC) crystal structure, each unit cell is a cube where particles such as atoms or ions are located at each of the cube's corners and the centers of all cube faces. This arrangement allows for the optimization of space and provides high packing efficiency.

In FCC structures, each particle interacts with multiple neighbors. This gives the structure excellent stability and strength. Common materials, including metals like aluminum, copper, and silver, crystallize in this manner.

• Each cube edge contains a series of corners where particles are located.
• Additionally, the center of each of the six cube faces has a particle.
• The repeating pattern extends in three dimensions.

This arrangement not only optimizes packing, allowing for minimal wasted space, but it also imparts unique properties like material ductility. In the context of \(\text{NaCl}\), chloride ions specifically occupy this face-centered cubic arrangement.

Rock-Salt Structure

The rock-salt structure, synonymous with \(\text{NaCl}\) crystals, is a specific arrangement of ions that forms a type of FCC lattice. In this structure, sodium ions and chloride ions alternately form a 3D regular grid.

The rock-salt structure can be visualized as two interpenetrating face-centered cubic lattices:

• One FCC lattice is created by the chloride ions.
• The second is a bit offset and formed by sodium ions.

This complex formation results in each ion being surrounded by six ions of the opposite charge. This coordination leads to a neutral charge balance throughout the crystal. The robustness of this structure helps explain the hardness and high melting point of \(\text{NaCl}\) crystals. Typical salt crystals exhibit a cubic shape easily identifiable under a microscope.

Chloride Ion Arrangement

In sodium chloride crystals, the chloride ions play a crucial role in determining the overall crystal structure. These ions are positioned in a face-centered cubic (FCC) configuration, which contributes to the stability and balance of the crystal.

Each chloride ion within the \(\text{NaCl}\) lattice is surrounded by a framework of six sodium ions, creating a balanced and neutral environment. This coordinated system ensures that the electrostatic forces between the positive sodium ions and negative chloride ions are evenly distributed within the lattice.

• Chloride ions sit at the corners and centers of cube faces.
• This symmetrical arrangement allows for efficient packing of the ions.

The overall result is a highly ordered and symmetrical crystal lattice that exhibits stability, leading to the characteristic properties of common table salt, such as its crystalline appearance and ability to easily dissolve in water.