Understanding Coordination Number in NaCl Lattice

The question asks about the coordination number of the sodium ions (Na⁺) and chloride ions (Cl⁻) in the sodium chloride (NaCl) crystal lattice structure. The coordination number is a fundamental concept in solid-state chemistry, describing the number of nearest neighbors surrounding a central atom or ion in a crystal lattice.

What is a Coordination Number?

In crystallography, the coordination number refers to the number of atoms, ions, or molecules that a central atom or ion holds as its nearest neighbors in a crystal structure. It is a key characteristic of the lattice structure and the bonding within the crystal.

Structure of NaCl Crystal Lattice

The NaCl structure is a face-centered cubic (FCC) lattice for both the Na⁺ and Cl⁻ ions, offset from each other. You can think of it in two ways:

• A FCC lattice of Cl⁻ ions with Na⁺ ions in all the octahedral holes.
• A FCC lattice of Na⁺ ions with Cl⁻ ions in all the octahedral holes.

Both perspectives describe the same arrangement.

Coordination Number of Na⁺ in NaCl

Let's consider a central Na⁺ ion in the NaCl lattice. This Na⁺ ion is located at a position like the center of an edge or the center of the unit cell (if we place Cl⁻ at corners and face centers). In this structure, a Na⁺ ion is surrounded by Cl⁻ ions.

• Each Na⁺ ion is surrounded by 6 Cl⁻ ions.
• These 6 Cl⁻ ions are located at equal distances from the central Na⁺ ion, positioned along the three perpendicular axes (like at the center of the faces of a cube if the Na⁺ is at the body center, or at the corners of an octahedron centered on Na⁺).
• Therefore, the coordination number of Na⁺ in the NaCl lattice is 6.

Coordination Number of Cl⁻ in NaCl

Now, let's consider a central Cl⁻ ion in the NaCl lattice. Similar to the Na⁺ ion, a Cl⁻ ion is surrounded by ions of the opposite charge, which are Na⁺ ions.

• Each Cl⁻ ion is surrounded by 6 Na⁺ ions.
• These 6 Na⁺ ions are located at equal distances from the central Cl⁻ ion, again forming an octahedral arrangement around the Cl⁻ ion.
• Therefore, the coordination number of Cl⁻ in the NaCl lattice is also 6.

Summary of Coordination Numbers

In the NaCl crystal lattice, both the cation (Na⁺) and the anion (Cl⁻) have the same coordination number because of the lattice's symmetrical structure (it's a 1:1 stoichiometry compound in a specific type of cubic lattice where both sublattices are FCC and occupy each other's octahedral holes).

The coordination number of Na⁺ is 6.

The coordination number of Cl⁻ is 6.

So the coordination numbers of Na⁺ and Cl⁻ ions in the NaCl lattice are 6 and 6, respectively.

Revision Table: NaCl Lattice Details

Additional Information: Common Crystal Structures

Understanding coordination number is crucial for different ionic crystal structures. Here are a few other common types and their coordination numbers:

• CsCl structure: Cesium Chloride (CsCl) lattice is a body-centered cubic (BCC) type arrangement, but with one ion at the center and the other at the corners. The coordination number for both Cs⁺ and Cl⁻ is 8.
• ZnS structure (Zinc Blende): Zinc Sulfide (ZnS) structure has an FCC lattice of one ion type (say S²⁻) with the other ion type (Zn²⁺) in half of the tetrahedral holes. The coordination number for both Zn²⁺ and S²⁻ is 4.
• CaF₂ structure (Fluorite): Calcium Fluoride (CaF₂) has an FCC lattice of Ca²⁺ ions with F⁻ ions in all the tetrahedral holes. The coordination number for Ca²⁺ is 8, and for F⁻ is 4.

These examples show that the coordination number depends directly on the specific arrangement of ions in the crystal lattice structure.