Question

Ionic Solids One of these compounds crystallizes in the fluorite structure. Which one and why? $$\mathrm{Rb}_{2} \mathrm{O}, \mathrm{CaS}, \mathrm{BaF}_{2}$$

Short answer

BaF2 crystallizes in the fluorite structure because it has the correct AX2 stoichiometry, which is typical for compounds with this structure.

Step-by-step solution

Understanding the Fluorite Structure

The fluorite structure is characterized by a face-centered cubic arrangement with anions located at each corner and the center of each face of the cube. Cations fill the tetrahedral holes within this structure. The formula of a fluorite structure compound is typically AX2, where A represents the cation and X represents the anion.

Determining the Stoichiometry

Look for a compound with the formula AX2 among the given options. Rb2O has a stoichiometry of A2X, CaS has AX, and BaF2 has the desired AX2 stoichiometry.

Identifying the Compound

Since BaF2 has the correct AX2 stoichiometry and forms a structure similar to the cubic fluorite structure, it is the compound that crystallizes in the fluorite structure.

Key concepts

Ionic Solids

Ionic solids are a class of compounds made up of ions bound together by strong electrostatic forces known as ionic bonds. These forces arise from the attraction between positively charged cations and negatively charged anions. In an ionic solid, ions are arranged in a highly ordered structure called a crystal lattice. This arrangement minimizes the potential energy of the system, leading to a stable and often brittle material.

Each ionic compound has a characteristic crystal structure that depends on the size, charge, and coordination number of its ions. Coordination number refers to the number of nearest neighbor ions surrounding a given ion within the crystal. The fluorite structure, mentioned in the exercise, is one such crystal structure that specifically accommodates ions in a particular ratio and spatial configuration.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It also pertains to the ratio of atoms and ions in compounds, as well as their molecular or empirical formulas. Understanding stoichiometry is crucial when examining the chemical formula of compounds to determine their structure. For example, in the context of the given exercise, recognizing the AX2 stoichiometry is key to identifying compounds with the fluorite structure.

In the fluorite structure, the stoichiometry AX2 indicates that for every cation (A), there are two anions (X). This specific ratio is necessary to maintain charge neutrality and to fit into the spatial arrangement of the crystal lattice characteristic of the fluorite structure. Incorrect stoichiometry would result in a different crystal structure. The exercise provided outlines the importance of stoichiometry in concluding that BaF₂ is the one that crystallizes in the fluorite structure, due to its matching AX2 stoichiometry.

Crystal Lattice

A crystal lattice is the regular, repeating three-dimensional arrangement of atoms, ions, or molecules in a crystalline solid. The lattice embodies not just the physical position of these particles but also defines the geometric shape of the crystal. Crystal lattices are described by unit cells, which are the smallest repeating units of the lattice and define its symmetry and structure.

The fluorite structure is a classic example of a face-centered cubic lattice, where the anions form a cubic arrangement with anions at the corners and the centers of each cube face, and the cations occupying the tetrahedral holes. Understanding the geometric constraints and coordination preferences of ions in the crystal lattice is fundamental to determining the type of structure a compound will adopt. As indicated in the solution, recognizing that BaF₂ fits into this arrangement allows us to resolve that it is the compound that illustrates the fluorite structure.