Potassium bromide (KBr) has a density of 2.75 ×10^3 kg / m^3 and the same crystal structure as

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Potassium bromide (KBr) has a density of 2.75 ×10^3 kg /...

Potassium bromide (KBr) has a density of $2.75 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ and the same crystal structure as $\mathrm{NaCl}$. The mass of potassium is $6.49 \times 10^{-26} \mathrm{~kg},$ and that of bromine is $1.33 \times 10^{-25} \mathrm{~kg}$. (a) Calculate the average spacing between adjacent atoms in a $\mathrm{KBr}$ crystal. (b) Compare the spacing for $\mathrm{KBr}$ with the spacing for $\mathrm{NaCl}$ (See the preceding problem.) Is the relationship between these two values qualitatively what you would expect? Explain your reasoning.

Key Concepts

Atomic Mass Contribution

Each atom contributes its own mass to the overall mass of the unit cell. By using the provided atomic masses and accounting for the number of each type of atom within the cell, one can calculate the total mass present. This total mass, when combined with the unit cell volume, directly yields the crystal's density.

Density Calculation in Crystals

Density is defined as the mass of the material per unit volume. For a crystal, this involves summing the masses of all atoms (or formula units) within a unit cell and then dividing by the unit cell’s volume. This method links microscopic properties of the unit cell to the macroscopic property of density.

Unit Cell Volume

The unit cell volume is derived from the dimensions of the unit cell, often calculated as the cube of the edge length in cubic systems. This volume is used in density calculations where the mass contained within one unit cell is spread over this volume to determine mass per unit volume.

Atomic Spacing and Lattice Parameters

Atomic spacing is the distance between adjacent atoms in a crystal lattice, and it is closely related to the dimensions of the unit cell. For many cubic crystals, the edge length of the cell can be determined from the spacing between atoms. These lattice parameters are fundamental in calculating the volume of the unit cell, which directly impacts density computations.

Crystal Lattice Structure

This concept involves understanding that crystalline materials are made up of a regularly repeating arrangement of atoms. The arrangement forms a unit cell—a small, representative volume that, when repeated in space, creates the entire crystal. In the context of density calculations, knowing the unit cell structure (for example, whether it is cubic, face?centered, body?centered, etc.) is essential because it dictates how many atoms or formula units are contained within one cell.

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