One crystalline form of silica (SiO) has a cubic unit cell,...

One crystalline form of silica (SiO_) has a cubic unit cell, and from X-ray diffraction data it is known that the cell edge length is $0.700 \mathrm{nm}$. If the measured density is $2.32 \mathrm{g} / \mathrm{cm}^{3},$ how many $\mathrm{Si}^{4+}$ and $\mathrm{O}^{2-}$ ions are there per unit cell?

Key Concepts

Unit Cell

The unit cell is the smallest repeating structural unit of a crystal. Its dimensions and geometry define the entire crystal lattice and are used to calculate properties such as volume and density, which are fundamental in determining the number of atoms or ions within the crystal structure.

Density in Crystallography

In crystallography, density relates the mass contained within a unit cell to its volume. By knowing the density, the unit cell volume, and the molar mass of the material, one can determine how many formula units are present in one unit cell, establishing a link between macroscopic measurements and the atomic-level structure.

Formula Units and Stoichiometry

The chemical formula of a compound represents the ratio of its constituent ions or atoms in a single formula unit. When the number of formula units per unit cell (often denoted as Z) is determined, it helps in calculating the total number of each type of ion or atom in the entire unit cell while reflecting the stoichiometric relationships in the compound.

Avogadro's Number

Avogadro's number is the constant that represents the number of particles (atoms, ions, or molecules) in one mole of a substance. This conversion factor is essential for bridging the gap between the macroscopic mass measured in experiments and the microscopic count of the individual particles within a crystal.

Transcript

Please give Ace some feedback