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

Question

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

Step-by-Step Solution

Answer

(b) FCC

Step 1: Understand the Terms

To solve this exercise, we need to understand what BCC (Body-Centered Cubic) and FCC (Face-Centered Cubic) mean. These are types of crystal lattice structures that describe how ions are arranged in a solid. In a BCC lattice, every unit cell has one atom at each corner and one atom in the center of the cell, whereas in an FCC lattice, there is one atom at each corner and one atom in the center of each face of the cube.

Step 2: Analyze NaCl Structure

NaCl, known as sodium chloride or common table salt, has a specific crystal structure. The chloride ions ( Cl-) in NaCl form a face-centered cubic (FCC) lattice. Each chloride ion is surrounded closely by sodium ions (Na+), occupying the octahedral interstices formed in the FCC lattice of chloride ions.

Step 3: Determine the Correct Answer

Based on the identified structure of NaCl, we conclude that the chloride ions create an FCC arrangement. This implies that in the compound NaCl, the anions (chloride ions) arrange themselves in the Face-Centered Cubic (FCC) lattice pattern.

Key Concepts

face-centered cubic lattice

A face-centered cubic (FCC) lattice is a common arrangement found in many solid substances, including the crystal structure of sodium chloride (NaCl). This arrangement allows the atoms—or in the case of NaCl, ions—to pack closely together in a symmetrical and efficient manner. In an FCC lattice, each unit cell consists of atoms at all eight corners of a cube and an additional atom at the center of each of the six faces.
This arrangement can be visualized as atoms occupying key positions within a cube. Each corner atom is shared amongst eight neighboring cubes, which means each atom at the corners contributes effectively only one-eighth of its volume to any single cube. Similarly, the atoms located at the faces share half of their volume with each adjacent unit cell, making the FCC arrangement particularly dense and stable.
When considering ionic compounds like NaCl, the FCC structure refers to the spatial organization of one type of ion, such as the chloride ions. These create a repeating symmetrical pattern, essential for the stable formation of the salt crystal.

crystal lattice structures

A crystal lattice structure defines the three-dimensional geometric arrangement of particles, be they atoms, molecules, or ions, in a crystalline solid. Each particle is called a lattice point, and these lattice points are systematically arranged over long distances, creating the solid's architecture.
There are several types of crystal lattice structures, including body-centered cubic (BCC), face-centered cubic (FCC), and simple cubic. These all differ in terms of complexity, density, and atomic positions within the unit cell.

• A simple cubic lattice has particles located only at the eight corners of a cube.
• In BCC, besides the corner particles, there is one at the center of the cube.
• FCC, as previously explained, includes additional points at the centers of each face.

Understanding crystal lattice structures is crucial for grasping how different physical properties arise, such as hardness, melting point, and conductivity. For ionic solids like NaCl, conceptualizing how the ions are ordered gives insight into their stability and behavior as materials.

ionic arrangements in solids

Ionic arrangements in solids deal with how ions organize themselves in crystal lattices to form stable structures. In ionic compounds like sodium chloride (NaCl), these arrangements determine the solid's overall stability and its distinct properties.
In NaCl, the structure is best described by thinking of a face-centered cubic (FCC) lattice of chloride ions, where sodium ions fit into the gaps or voids that occur within this lattice. Specifically, sodium ions occupy the octahedral interstices. These are the spaces between ions where atoms naturally place themselves based on size and charge balance.

• Ions in such structures often maximize electrostatic interaction by arranging in a pattern that allows opposite charges to be as close as possible, while like charges are kept at a distance.
• The balance achieved minimizes the potential energy of the solid, giving the compound its characteristic robustness.

Understanding these patterns explains why NaCl is so stable as a solid and why it dissolves in water to break into free ions. This organized arrangement is what facilitates its efficient dissolution, as the interaction with water molecules disrupts the ionic lattice.