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Chapter 12: Problem 60

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

Expert verified
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

01

(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.
02

(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.
03

(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.

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