The crystalline structure of sodium chloride can be...

The crystalline structure of sodium chloride can be described by two interpenetrating face-centered cubic structures (see Figure 29.18a) with four formula units per unit cell. Given that the length of a unit cell is $564.1 \mathrm{pm}$ at $20^{\circ} \mathrm{C}$, calculate the density of $\mathrm{NaCl}(\mathrm{s})$. The literature value is $2.163 \mathrm{~g} \cdot \mathrm{cm}^{-3}$.

Key Concepts

Lattice Parameters and Unit Cell Volume

Lattice parameters refer to the dimensions of a unit cell, typically described by the edge lengths and angles between edges in the crystal lattice. For cubic systems, the unit cell volume is computed by cubing the edge length. Accurate knowledge of the lattice parameter is essential for calculating the volume needed in density determinations.

Density Calculation in Crystalline Solids

The density of a crystalline solid is calculated by dividing the total mass contained within one unit cell, which includes the contributions of all the individual atoms or formula units, by the volume of the unit cell. This method requires knowledge of the number of formula units per cell, the molar mass of the compound, and the conversion of molar quantities to individual particle masses using Avogadro's number.

Avogadro's Number

Avogadro's number is a fundamental constant that links the macroscopic and microscopic worlds by specifying the number of entities, such as atoms or molecules, present in one mole of a substance. This constant is crucial for converting between the molar mass of a substance and the mass of the individual constituents in a crystal lattice.

Unit Cell

The unit cell is the smallest repeating structural unit of a crystal lattice that preserves the overall structure's symmetry and properties. It serves as the building block from which the entire crystalline structure is built by periodic repetition in three-dimensional space.

Face-Centered Cubic (FCC) Structure

The FCC structure is a specific arrangement within a crystal lattice where atoms are positioned at each corner and the centers of all the faces of a cube. This configuration leads to efficient packing of atoms and is a common arrangement in many metals and ionic compounds, influencing properties such as density and coordination number.

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