Problem 24 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following statements about the \(\mathrm{NaCl}\) crystal is correct? (a) Cl ions are present at the corners and \(\mathrm{Na}^{+}\)ions at the body- centre (b) \(\mathrm{Cl}\) ions adopt bcc arrangement (c) Cl ions are packed following ABC ABC pattern of hexagonal close packing (d) \(\mathrm{Na}^{+}\)ions are at the edge centres only

Step-by-Step Solution

Answer

None of the provided options correctly describe the NaCl crystal structure.

Step 1: Understand the Crystal Structure of NaCl

The crystal structure of sodium chloride (NaCl) is known as a face-centered cubic (FCC) structure for the chloride ions. Sodium ions fill the octahedral voids in this arrangement. Neither the chloride ions nor the sodium ions alone form a body-centered cubic (BCC) structure in NaCl.

Step 2: Analyze Option (a)

Option (a) states Cl ions are at the corners, and Na+ ions at the body-centre. This is incorrect because NaCl adopts the FCC structure with Cl at the face-center, not a BCC structure with Na+ ions at the body-center.

Step 3: Analyze Option (b)

Option (b) suggests that Cl ions adopt BCC arrangement. This statement is false, as Cl ions in NaCl are arranged in a face-centered cubic structure, not in a BCC arrangement.

Step 4: Analyze Option (c)

Option (c) describes Cl ions packed in an ABC ABC pattern of hexagonal close packing. This is incorrect, as the Cl ions in NaCl are in a cubic close packing arrangement, not a hexagonal one.

Step 5: Analyze Option (d)

Option (d) claims Na+ ions are at the edge-centres only. This is false; in the face-centered cubic lattice of NaCl, Na+ ions occupy the octahedral holes, not located only at the edge centers.

Key Concepts

Face-Centered Cubic Structure

The face-centered cubic (FCC) structure is a common crystalline arrangement that you will encounter in various materials, including the \(\text{NaCl}\) crystal structure. In simple terms, this structure involves atoms positioned at each of the eight corners of a cube and at the center of each of the cube's six faces. This kind of arrangement ensures that each atom is surrounded closely by others, maximizing density.

• Key Characteristics: An FCC structure in metals and ionic crystals like NaCl provides high packing efficiency, meaning the space within the crystal is used efficiently.
• Atom Interaction: This packing allows each chloride ion to be surrounded by six sodium ions, and vice versa, establishing a stable ionic compound.

In NaCl's face-centered cubic structure, the chloride ions occupy the face-centered positions, forming the primary scaffolding of the crystal. Meanwhile, sodium ions fill in the gaps between these chloride ions, specifically locating themselves in the octahedral voids, maintaining the crystal's integrity.

Octahedral Voids

Octahedral voids are the spaces or gaps in a crystal structure where smaller ions or atoms can sit. In a face-centered cubic arrangement like in \(\text{NaCl}\), these voids are located among atoms that form the corners and the centers of the cube's faces. This is crucial for accommodating ions like sodium in the NaCl crystal.

• Structure Formation: In the NaCl lattice, each octahedral void is surrounded by six different ions, making it suitable for hosting sodium ions, given their size and charge.
• Ion Positioning: In NaCl, sodium ions fill these octahedral sites, thus each sodium ion is equidistant from six chloride ions. This arrangement helps maintain the electrical neutrality and stability of the crystal.

Understanding where these voids are located and how they are filled allows us to appreciate how the individual particles fit together to create the larger structure.

Cubic Close Packing

Cubic close packing (CCP) is another term that describes the arrangement of atoms in a face-centered cubic structure. This concept stems from the efficient and dense packing of spherical entities, similar to stacking oranges in a crate. Within materials science, it's crucial to understand how atoms arrange themselves to opt for stability and efficiency.

• Layer Patterns: In cubic close packing, the layers of atoms stack in a sequence denoted as ABCABC. This means that the placement of one layer will repeat every third layer, promoting dense packing.
• Ion Distribution: For NaCl, the \(\text{Cl}^-\) ions adopt this cubic close packing arrangement, with \(\text{Na}^+\) ions fitting into the structured gaps or the octahedral voids produced.

This arrangement not only enhances the overall stability of the crystalline structure but also maximizes space efficiency, allowing a large number of atoms to occupy a given volume.