The crystal structure of CO2 is cubic, with a cell edge length of 5.540 A. A diagram of the cell

step 1 In this problem, we're taking a look at the unit cell of carbon dioxide. So if we take a look at

The crystal structure of CO2 is cubic, with a cell edge...

The crystal structure of $\mathrm{CO}_{2}$ is cubic, with a cell edge length of 5.540 A. A diagram of the cell is shown in Figure $13-31$ a. (a) What is the number of molecules of $\mathrm{CO}_{2}$ per unit cell? (b) Is this structure face-centered cubic? How can you tell? (c) What is the density of solid $\mathrm{CO}_{2}$ at this temperature?

The crystal structure of $\mathrm{CO}_{2}$ is cubic, with a cell edge length of 5.540 A. A diagram of the cell is shown in Figure $13-31$ a.
(a) What is the number of molecules of $\mathrm{CO}_{2}$ per unit cell?
(b) Is this structure face-centered cubic? How can you tell?
(c) What is the density of solid $\mathrm{CO}_{2}$ at this temperature?

Key Concepts

Unit Cell

The unit cell is the smallest repeating entity in a crystalline solid that captures the entire symmetry and structure of the material. It defines the lattice parameters, such as edge lengths and angles, and serves as the building block of the overall crystal structure when it is periodically repeated in three dimensions.

Face-Centered Cubic (FCC) Structure

A face-centered cubic structure is a type of crystal lattice where atoms or molecules are located at each of the corners and the centers of all the faces of the cube. This arrangement is known for its high symmetry and efficient packing, and it is characterized by a specific number of entities per unit cell that results from contributions from these lattice points.

Molecular Packing in Crystals

Molecular packing refers to the way in which molecules are arranged and distributed within the unit cell. The counting of molecules within a unit cell involves accounting for the contributions from atoms or molecules placed at different positions, such as corners (which are shared among several cells) and face centers (which are shared by adjacent cells). This concept helps in determining the overall composition and repeating unit of the crystal.

Density Calculation in Crystallography

Density in a crystalline solid is calculated by dividing the mass of the atoms or molecules contained in the unit cell by the volume of the unit cell. This requires an accurate count of the number of entities per unit cell, their individual molecular or atomic masses, and the precise measurements of the cell dimensions. This calculation ties the microscopic arrangement of particles to the macroscopic property of density.

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