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

The chloride ions in NaCl occupy the space in an FCC structure.

Step 1: Understanding Crystal Structures

A Body Centered Cubic (BCC) structure has atoms at the corners and a single atom in the center of the cube. A Face Centered Cubic (FCC) structure has atoms at each corner and one atom centered on each face of the cube. We need to determine which structure NaCl forms.

Step 2: Analyzing NaCl Structure

NaCl forms a crystal structure where each ion forms a cubic lattice. More specifically, it adopts a Face Centered Cubic (FCC) structure for both the sodium (Na) and chloride (Cl) ions. They alternate in the lattice structure, filling octahedral holes.

Step 3: Identifying the Correct Answer

Given that NaCl adopts an FCC structure, we identify that chloride ions occupy the space in a fashion of FCC. Thus, the answer to the question is option (b).

Key Concepts

Face Centered Cubic (FCC)

The Face Centered Cubic (FCC) structure is a type of crystal lattice where each cell consists of atoms at each of the eight corners and one in the center of each of the six faces of the cube. This arrangement allows for a very efficient packing, leading to a high coordination number.

• High Packing Efficiency: In FCC, each atom is surrounded by 12 nearest neighbors, making it one of the most closely packed structures. This high coordination number (12) results from the strategic placement of each atom within the lattice.
• Commonly Found in Metals: This structure is often observed in metals like copper, aluminum, and also halides like NaCl, where both types of ions (sodium and chloride in NaCl) are organized in an interpenetrating FCC structure.

The FCC arrangement is critical for the stability and density of the crystal. In substances like NaCl, this setup ensures that each sodium ion is surrounded by six chloride ions and vice versa, optimizing ionic interaction and bond strength.

Body Centered Cubic (BCC)

The Body Centered Cubic (BCC) structure is another type of lattice where atoms are positioned at each corner of the cube with an additional atom located at the center of the cube. This differs from FCC by its internal composition and packing efficiency.

• Lower Packing Efficiency: Compared to FCC, BCC has a lower packing efficiency, with each atom in contact with 8 neighbors, giving it a coordination number of 8.
• Difference in Application: BCC structures are typical in metals such as iron at room temperature, chromium, and tungsten. This structure does not support the same level of packed density as FCC, which is why it's not as common in ionic compounds like NaCl.

The distinctive feature of BCC is the central atom in each cell that imparts unique mechanical properties. This configuration is less suited to compounds requiring close ionic interaction, making it unsuitable for describing NaCl's structure.

Octahedral Holes

In the context of crystal lattices, octahedral holes are the spaces created between atoms in close-packed structures. Specifically, they are the interstitial sites located between six atoms, forming an octahedral geometry.

• Formation: Octahedral holes occur in FCC and BCC lattices. In FCC, these holes are larger compared to BCC due to higher atom packing.
• Occupancy in NaCl: In the NaCl structure, chloride ions form the FCC lattice, while the sodium ions occupy these octahedral holes, ensuring a stable and consistent distribution throughout.

The filling of octahedral holes is crucial in ionic crystals to maintain charge neutrality and optimal ionic bonds. In NaCl, each ion fits into the available spaces perfectly, maintaining a strong electrostatic bond that characterizes its solid structure.