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, (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

The coordination numbers of \(\mathrm{Al}^{3+}\) ions in the given compounds are: (a) In \(\mathrm{AlF}_{3}\), the \(\mathrm{Al}^{3+}\) ion has a coordination number of 6. (b) In \(\mathrm{Al}_{2} \mathrm{O}_{3}\), the \(\mathrm{Al}^{3+}\) ion has a coordination number of 6. (c) In AlN, the \(\mathrm{Al}^{3+}\) ion has a coordination number of 4.

Step-by-step solution

(a) Coordination number of \(\mathrm{Al}^{3+}\) in \(\mathrm{AlF}_{3}\)

Since the fluoride ions are two-coordinate, this means that each fluoride ion is bonded to two Al atoms. Therefore, each \(\mathrm{Al}^{3+}\) ion must be bonded to at least two fluoride ions to maintain the two-coordinate nature of the fluoride ion. Since the fluoride ions maintain a charge of \(-1\) each, the \(\mathrm{Al}^{3+}\) ion will be bonded to three fluoride ions \((2 \times 3 = 6)\), making the coordination number for the \(\mathrm{Al}^{3+}\) ion in \(\mathrm{AlF}_{3}\) equal to six.

(b) Coordination number of \(\mathrm{Al}^{3+}\) in \(\mathrm{Al}_{2} \mathrm{O}_{3}\)

In this compound, each oxygen ion is six-coordinate, meaning it is bonded to six Al atoms. The oxygen atom has a charge of \(-2\), which means that it must be bonded to two \(\mathrm{Al}^{3+}\) ions to maintain charge balance. Therefore, each \(\mathrm{Al}^{3+}\) ion is bonded to three oxygen ions \((2 \times 3 = 6)\) making the coordination number for the \(\mathrm{Al}^{3+}\) ion in \(\mathrm{Al}_{2} \mathrm{O}_{3}\) equal to six.

(c) Coordination number of \(\mathrm{Al}^{3+}\) in AlN

In this case, the nitride ions are four-coordinate, which means that each nitride ion is bonded to four Al atoms. The nitride ion has a charge of \(-3\), so it must be bonded to one \(\mathrm{Al}^{3+}\) ion to maintain charge balance. Therefore, the coordination number for the \(\mathrm{Al}^{3+}\) ion in AlN is equal to four.

Key concepts

Coordination Chemistry

Coordination chemistry involves the study of compounds formed between metal ions and organic or inorganic ligands. One important aspect of coordination chemistry is the coordination number, which defines the number of ligand donor atoms, or anions, surrounding a central metal ion. This number can influence the geometry, electronic properties, and reactivity of the coordination compound.

In the context of the exercise, the coordination number of the \( \mathrm{Al}^{3+} \) ion is being evaluated in three different compounds: \( \mathrm{AlF}_{3} \), \( \mathrm{Al}_{2} \mathrm{O}_{3} \), and AlN. This involves understanding how many atoms directly attach to the central aluminum ions in each compound.

• For \( \mathrm{AlF}_{3} \), fluoride ions being two-coordinate implies each fluoride links with two aluminum ions, which means the \( \mathrm{Al}^{3+} \) ion links with three fluoride ions, resulting in a coordination number of six.
• In \( \mathrm{Al}_{2} \mathrm{O}_{3} \), since oxygen ions are six-coordinate, every oxygen connects to two \( \mathrm{Al}^{3+} \) ions. This arrangement implies each aluminum is surrounded by three oxygen atoms, maintaining a coordination number of six.
• For AlN, with nitride ions four-coordinate, each nitride associates with one aluminum because each nitride ion must stay balanced with its charge, giving the \( \mathrm{Al}^{3+} \) ion a coordination number of four.

Ionic Compounds

Ionic compounds consist of ions held together by electrostatic forces. These compounds typically form between metal cations and non-metal anions, leading to a crystal lattice structure. The coordination number helps define how ions are arranged around a central cation within the lattice.

The exercise shows how the coordination number can provide insight into the spatial arrangement of ions in compounds like \( \mathrm{AlF}_{3} \), \( \mathrm{Al}_{2} \mathrm{O}_{3} \), and AlN. Understanding these arrangements explains why certain physical properties like melting points and solubilities are observed.

In \( \mathrm{AlF}_{3} \), the lattice is influenced by fluoride's two-coordinate reference, creating a coordination of three fluoride ions around aluminum. With \( \mathrm{Al}_{2} \mathrm{O}_{3} \), oxygen's ability to coordinate with six aluminum ions influences the lattice structure significantly, maintaining its stability. Lastly, AlN's nitride ions stabilize the lattice by forming a four-coordinate arrangement with the \( \mathrm{Al}^{3+} \) ions.

Chemical Bonding

Chemical bonding plays a crucial role in determining the structure and stability of compounds. In coordination chemistry and ionic compounds, bonding involves interactions between ions, through coordinate covalent bonds or ionic bonds, that stabilize the overall structure.

For coordination compounds, the bond between metal ions and ligands is often termed a coordinate covalent bond. Such arrangements lead to definable coordination number as depicted in the provided examples:

• In \( \mathrm{AlF}_{3} \), coordinate bonds form between \( \mathrm{Al}^{3+} \) ions and fluoride ion pairs, leading to complex stabilization through a coordination number of six.
• \( \mathrm{Al}_{2} \mathrm{O}_{3} \) relies on coordinate bond formation between aluminum and oxygen ions, maintaining charge neutrality and structure through its six-coordinate arrangement.
• In AlN, the association of \( \mathrm{Al}^{3+} \) and nitride ions exemplifies stable bond formation through a coordination number of four.

By understanding these bond types and arrangements, the chemical behavior of complex compounds can be better explained, reflecting on characteristics such as reactivity and interaction with other molecular entities.