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Structure of a mixed oxide is cubic clos...

Structure of a mixed oxide is cubic close packed the cubic unit cell of mixed oxide is composed of oxide ions. One fourth of the tetrahedral voids are occupied by divalent metal.A and the octahedral voids are occupied by a monvalent metal `B`. The formula of the oxide is :

A

`ABO_(2)`

B

`A_(2)BO_(2)`

C

`A_(2)B_(3)O_(4)`

D

`AB_(2)O_(2)`

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To determine the formula of the mixed oxide based on the given information, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Structure**: - The structure is cubic close packed (CCP), which means that the oxide ions (O²⁻) occupy the lattice points. 2. **Determine the Number of Oxide Ions**: - In a cubic close packed structure, there are 4 oxide ions per unit cell. 3. **Tetrahedral and Octahedral Voids**: - In a CCP structure, there are 8 tetrahedral voids and 4 octahedral voids. 4. **Occupancy of Tetrahedral Voids**: - According to the problem, one-fourth of the tetrahedral voids are occupied by divalent metal A (A²⁺). - Therefore, the number of tetrahedral voids occupied by A²⁺ = (1/4) × 8 = 2. - Thus, there are 2 A²⁺ ions in the unit cell. 5. **Occupancy of Octahedral Voids**: - The octahedral voids are occupied by monovalent metal B (B⁺). - Since all octahedral voids are occupied, the number of octahedral voids occupied by B⁺ = 4. - Thus, there are 4 B⁺ ions in the unit cell. 6. **Count the Total Ions**: - We have: - 2 A²⁺ ions - 4 B⁺ ions - 4 O²⁻ ions 7. **Write the Empirical Formula**: - The empirical formula can be written based on the number of each type of ion: - The formula is A₂B₄O₄. 8. **Simplify the Formula**: - We can simplify the formula by dividing all subscripts by 2: - This gives us the simplest formula: AB₂O₂. ### Final Answer: The formula of the oxide is **AB₂O₂**. ---
To determine the formula of the mixed oxide based on the given information, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Structure**: - The structure is cubic close packed (CCP), which means that the oxide ions (O²⁻) occupy the lattice points. 2. **Determine the Number of Oxide Ions**: ...
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