Question

The coordination number for the \(\mathrm{Al}^{3+}\) ion is typically between four and six. Use the anion coordination number to determine the \(\mathrm{Al}^{3+}\) coordination number in the following compounds: (a) AlF_ \(_{3}\) where the fluoride ions are two coordinate, (b) \(\mathrm{Al}_{2} \mathrm{O}_{3}\) where the oxygen ions are six coordinate, (c) AlN where the nitride ions are four coordinate.

Short answer

For the given compounds, the coordination numbers of \(\mathrm{Al}^{3+}\) ions are: (a) AlF\(_3\): 6, (b) \(\mathrm{Al}_2\mathrm{O}_3\): 4, and (c) AlN: 4.

Step-by-step solution

Determine the ratio between cations and anions

In AlF\(_3\) compound, we have 1 Al atom and 3 F atoms in its formula unit. We need to find the ratio of \(\mathrm{Al}^{3+}\) ions to F\(^-\) ions. For every 1 Al atom, we have 3 F atoms, so the ratio between cations and anions is 1:3. Since each F\(^-\) ion is two coordinate, this means it bonds with two Al cations.

Find the coordination number of Al using the given information

As we know that each F\(^-\) ion is two coordinate and F\(^-\) ions are three times \(\mathrm{Al}^{3+}\) ions, so we can find the coordination number of Al as: Al coordination number = 2 (F\(^-\) ions to Al ratio) = 2 × 3 = 6 Moving to (b), \(\mathrm{Al}_2\mathrm{O}_3\):

Determine the ratio between cations and anions

In \(\mathrm{Al}_2\mathrm{O}_3\) compound, we have 2 Al atoms and 3 O atoms in its formula unit. We need to find the ratio of \(\mathrm{Al}^{3+}\) ions to O\(^{2-}\) ions. For every 2 Al atoms, we have 3 O atoms, so the ratio between cations and anions is 2:3. We are given that the O\(^{2-}\) ions are six coordinate.

Find the coordination number of Al using the given information

Since the O\(^{2-}\) ions are six coordinate and the O\(^{2-}\) ions to Al ratio is 3:2, we can find the coordination number of Al as: Al coordination number = 6 (O\(^{2-}\) ions to Al ratio) = 6 × (2/3) = 4 Finally, we will consider (c), AlN:

Determine the ratio between cations and anions

The compound AlN has 1 Al atom and 1 N atom in its formula unit. We need to find the ratio of \(\mathrm{Al}^{3+}\) ions to N\(^{3-}\) ions. For every Al atom, we have 1 N atom, so the ratio between cations and anions is 1:1. We are given that the N\(^{3-}\) ions are four coordinate.

Find the coordination number of Al using the given information

Since the N\(^{3-}\) ions are four coordinate and the N\(^{3-}\) ions to Al ratio is 1:1, we can find the coordination number of Al as: Al coordination number = 4 (N\(^{3-}\) ions to Al ratio) = 4 × (1/1) = 4 Finally, we have found the coordination numbers of \(\mathrm{Al}^{3+}\) ions in each compound: a) AlF\(_3\): 6 b) \(\mathrm{Al}_2\mathrm{O}_3\): 4 c) AlN: 4

Key concepts

Understanding Chemical Bonding

Chemical bonding is the process that holds atoms together in compounds. It's fundamental to the study of chemistry as it explains how atoms combine to form molecules and ultimately, the materials we encounter in our daily lives. In ionic bonds, atoms donate or accept electrons to achieve a stable electron configuration, resulting in the formation of positively charged cations and negatively charged anions.

For students trying to grasp these concepts, considering real-world examples, such as table salt (sodium chloride), can be helpful. In sodium chloride, sodium (Na) donates an electron to chlorine (Cl), forming a bond between Na⁺ and Cl⁻ ions. This exchange of electrons leads to the attraction between oppositely charged ions, illustrating the very essence of ionic bonding.

Exploring Ionic Compounds

Ionic compounds are formed from the strong electrostatic attractions between cations and anions. These attractions, known as ionic bonds, create a regular lattice structure, which is a distinctive characteristic of many ionic compounds. To make the concept of ionic compounds clearer, we can compare them to a closely knit community, where every member has a specific place and connects with neighbors in a defined arrangement. This concept of structure and organization helps students visualize atomic positions within a compound.

When teaching about ionic compounds, using visual aids like diagrams of lattice structures can significantly enhance understanding. Students should know that properties such as melting point, boiling point, and hardness are related to the strength of the attractions within the lattice.

Deciphering the Cation-to-Anion Ratio

The cation-to-anion ratio is crucial to understanding the composition and stability of ionic compounds. This ratio determines how the ions are arranged within the lattice and directly influences the compound's coordination number, which signifies the number of ions of opposite charge that an ion is surrounded by in a crystal lattice.

For instance, in the compound sodium chloride (NaCl), the cation-to-anion ratio is 1:1, meaning each sodium ion is surrounded by six chloride ions, and vice versa, which is reflected in a coordination number of six. To enhance comprehension, students can benefit from interactive simulations that model how changing ratios alter the compound’s structure. By experimenting with different ratios, students can see the immediate effect on the coordination number and deepen their understanding of how ionic compounds form and maintain stability.