Given that the density of KBr is 2.75 g ·cm^-3 and that the length of an edge of a cubic unit c

step 1 In answering this question, we need to recall that density is equal to mass divided by the volum

Given that the density of KBr is 2.75 g ·cm^-3 and that the...

Given that the density of $\mathrm{KBr}$ is $2.75 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ and that the length of an edge of a cubic unit cell is $654 \mathrm{pm}$, determine how many formula units of KBr there are in a unit cell. Does the unit cell have a $\mathrm{NaCl}$ or a CsCl structure? (See Figure 29.18.)

Key Concepts

Unit Cell and Crystal Lattice

A unit cell is the smallest repeating structural unit in a crystalline solid that, when stacked together, recreates the entire crystal lattice. Its geometry, including the edge length in cubic cells, is fundamental to determining other properties like volume, and it plays a vital role in understanding how atoms or ions are arranged in the crystal structure.

Density and Unit Cell Calculations

The density of a crystalline material links the mass of the unit cell to its volume. By using the measured density and the calculated volume from the unit cell’s edge length, one can determine the total mass contained within the cell. This enables the calculation of the number of formula units per unit cell by comparing the actual mass with the molar mass, effectively bridging macroscopic measurements with microscopic structure.

Ionic Crystal Structures (NaCl vs. CsCl)

Ionic compounds crystallize in different structural arrangements, with the NaCl and CsCl structures being two common types. The NaCl structure is characterized by a face?centered cubic lattice where typically four formula units are present per unit cell, whereas the CsCl structure involves a simple cubic arrangement with two formula units per cell. Recognizing these structures is critical in correlating calculated values such as density and unit cell dimensions with the underlying structural motif.

Formula Unit Count in a Unit Cell

The concept of a formula unit in a crystal refers to the smallest ratio of ions that represents the compound's chemical composition. Determining the number of formula units per unit cell is essential for understanding how the ions are organized in the crystal lattice. This count is derived from the structural arrangement of the ions, as each specific ionic crystal structure, like those of NaCl or CsCl, has a characteristic number of formula units per unit cell.

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