Chapter 12: Problem 66

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.

Short Answer

Expert verified

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 by step solution

(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.

(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.

(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.

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Short Answer

Step by step solution

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

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

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

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