Problem 66 - Chemistry: The Central Science in SI Units, Global Edition

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) \(\mathrm{AlF}_{3}\) where the fluoride ions are two coordinate, \((\mathbf{b}) \mathrm{Al}_{2} \mathrm{O}_{3}\) where the oxygen ions are six coordinate, \((\mathbf{c})\) AlN where the nitride ions are four coordinate.

Step-by-Step Solution

Answer

In \(\mathrm{AlF}_{3}\), the coordination number of \(\mathrm{Al}^{3+}\) ions is 1.5, meaning 3 fluoride ions surround an aluminum ion. In \(\mathrm{Al}_{2} \mathrm{O}_{3}\), the coordination number of \(\mathrm{Al}^{3+}\) ions is 3, and in AlN, the coordination number is 4.

Step 1: (a) Determining the coordination number of \(\mathrm{Al}^{3+}\) in \(\mathrm{AlF}_{3}\) with two-coordinate fluoride ions

To determine the coordination number of \(\mathrm{Al}^{3+}\) in \(\mathrm{AlF}_{3}\), we need to use the information that fluoride ions are two-coordinate. This means that: 1. Each fluoride ion (F-) is coordinated to 2 Al3+ ions 2. Since every aluminum ion (\(\mathrm{Al}^{3+}\)) is bonded to 3 fluoride ions, and each fluoride ion can connect 2 aluminum ions: For one fluoride ion (F-), the number of Al3+ connected to one F- is: \(\frac{1}{2} \times 3=1.5\) Thus, the coordination number of \(\mathrm{Al}^{3+}\) ions in \(\mathrm{AlF}_{3}\) is 1.5, which means 3 fluoride ions surround an aluminum ion in this compound.

Step 2: (b) Determining the coordination number of \(\mathrm{Al}^{3+}\) in \(\mathrm{Al}_{2}\mathrm{O}_{3}\) with six-coordinate oxygen ions

Given that oxygen ions are six-coordinate in \(\mathrm{Al}_{2} \mathrm{O}_{3}\), it means that: 1. Each oxygen ion (O2-) is coordinated to 6 Al3+ ions. 2. Since every aluminum ion (\(\mathrm{Al}^{3+}\)) is bonded to 3 oxygen ions, and each oxygen ion can connect 6 aluminum ions: For one oxygen ion (O2-), the number of Al3+ connected to one O2- is: \(\frac{1}{2} \times 6=3\) Therefore, in \(\mathrm{Al}_{2} \mathrm{O}_{3}\), the coordination number of \(\mathrm{Al}^{3+}\) ions is 3.

Step 3: (c) Determining the coordination number of \(\mathrm{Al}^{3+}\) in AlN with four-coordinate nitride ions

Since nitride ions are four-coordinate in AlN, this implies that: 1. Each nitride ion (N3-) is coordinated to 4 Al3+ ions. 2. As the aluminum/nitride ion ratio in AlN is 1:1, and a single nitride ion (N3-) can connect 4 aluminum ions: For one nitride ion (N3-), the number of Al3+ connected to one N3- is: \(\frac{1}{1} \times 4=4\) Thus, the coordination number of \(\mathrm{Al}^{3+}\) ions in AlN is 4.

Key Concepts

Aluminum Ion Coordination

Understanding the concept of aluminum ion coordination involves recognizing how aluminum ions (\[\mathrm{Al}^{3+}\]) form attachments with surrounding ions (or molecules) in a chemical compound. Coordination in chemistry essentially refers to the interaction between a central atom or ion and a surrounding set of molecules or anions - simplifying how compounds are structured.

• In \[\mathrm{AlF}_3\], each \[\mathrm{Al}^{3+}\] ion coordinates with 3 fluoride ions ( \[\mathrm{F}^-\]).
• In \[\mathrm{Al}_2\mathrm{O}_3\], each \[\mathrm{Al}^{3+}\] coordinates with oxygen ions ( \[\mathrm{O}^{2-}\]).
• In AlN, each \[\mathrm{Al}^{3+}\] coordinates with nitride ions ( \[\mathrm{N}^{3-}\]).

Coordination number varies based on the surrounding ions' charge and geometry in compounds. This interplay affects compound properties, like solubility and melting points.

Coordination Number

The coordination number is key in understanding the structure of a compound. It refers to the number of ligand (bonding) atoms that surround a central atom, which in this discussion involves aluminum and different anions.For \[\mathrm{Al}^{3+}\], the coordination numbers can be:

• **In \[\mathrm{AlF}_3\]**: The aluminum ion attaches to 3 fluoride ions, giving a coordination number of 3. This comes from the structure where fluoride ions each connect 2 aluminum ions, thus spanning 3 for every full coordination involving aluminum.
• **In \[\mathrm{Al}_2\mathrm{O}_3\]**: The oxygen ions form a coordination sphere indicating that aluminum bonds to 6 oxygen atoms, however, the structural balance achieves only 3 due to shared connections.
• **In AlN**: The nitride ions share 4 aluminum ions, meaning the entire coordination surrounds aluminum. Hence, the coordination number is 4. This reveals how dense or interconnected the ion packing is around the aluminum ion.

Note that these numbers can vary under different circumstances or material forms, impacting the compound's stability and reactivity.

Anion Coordination

Anion coordination is about how negatively charged ions, or anions, arrange around a central metal ion. This configuration affects the geometry around \[\mathrm{Al}^{3+}\] in various compounds.

• Fluoride ions ( \[\mathrm{F}^-\]) in \[\mathrm{AlF}_3\] typically align to coordinate two aluminum ions, focusing the setup around the anion relationship more than aluminum individually.
• Oxygen ions ( \[\mathrm{O}^{2-}\]) in \[\mathrm{Al}_2\mathrm{O}_3\] tend to coordinate with several aluminum ions indicating a shared network.
• Nitride ions ( \[\mathrm{N}^{3-}\]) within AlN heavily coordinate with four aluminum ions, reinforcing a dense bridging effect.

These configurations showcase the anion's role in determining the geometric structure and stability of a compound. As each anion type targets different coordination styles, they guide the 3D alignment and packing density of the compound's overall structure.