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A spinel is an important class of oxid...

A spinel is an important class of oxide consisting two types of metal ions with the oxide ions arranged in ccp layers . The normal spinel has one -eight of the tetrahedral holes occupied by one type of metal ions and one- half of the octahedral holes occupied by another type of metal ion. Such a spine is formed by `Mg^(2+), Al^(3+) and O^(2-)` . The neutrality of the crystal is being maintained.
Type of hole occupied by `Al^(3+)` ions is:

A

(a) tetrahedral

B

(b) octahedral

C

(c) both (a) and (b)

D

(d) None of these

Text Solution

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The correct Answer is:
To determine the type of hole occupied by Al³⁺ ions in the spinel structure formed by Mg²⁺, Al³⁺, and O²⁻, we will follow these steps: ### Step 1: Understand the Structure of Spinel Spinel structures are characterized by the arrangement of oxide ions in a cubic close-packed (CCP) lattice. In this structure: - The number of atoms per unit cell (Z) is 4. - The number of tetrahedral voids is 8 (2 times the number of atoms). - The number of octahedral voids is 4 (equal to the number of atoms). ### Step 2: Identify the Occupancy of Voids According to the problem: - One-eighth of the tetrahedral voids are occupied by one type of metal ion (let's assume this is Mg²⁺). - One-half of the octahedral voids are occupied by another type of metal ion (assumed to be Al³⁺). ### Step 3: Calculate the Number of Ions Occupying the Voids - **Tetrahedral Voids**: Total = 8. If 1/8 of these are occupied by Mg²⁺, then: \[ \text{Number of Mg²⁺ ions} = \frac{1}{8} \times 8 = 1 \] - **Octahedral Voids**: Total = 4. If 1/2 of these are occupied by Al³⁺, then: \[ \text{Number of Al³⁺ ions} = \frac{1}{2} \times 4 = 2 \] ### Step 4: Charge Neutrality To maintain charge neutrality in the spinel structure: - The total negative charge from O²⁻ ions is: \[ \text{Total negative charge} = 4 \text{ (O²⁻ ions)} \times 2 = 8 \] - The total positive charge must also equal +8. If we assume: - 1 Mg²⁺ contributes +2 - 2 Al³⁺ contribute \(2 \times 3 = 6\) Thus, the total positive charge is: \[ \text{Total positive charge} = 2 + 6 = 8 \] ### Step 5: Conclusion Since Al³⁺ occupies the octahedral voids, the type of hole occupied by Al³⁺ ions is **octahedral**. ### Final Answer The type of hole occupied by Al³⁺ ions is **octahedral**. ---
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