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In a certain type of spinel oxide, oxide ions (O²-) are in a cubic close-packed (ccp) arrangement. Fe²+ cations occupy 1/8th of the tetrahedral voids and Fe³+ cations occupy half of the octahedral voids. What is the formula of this spinel?

1. Fe2O3
2. Fe3O4
3. FeO
4. Fe4O5

Correct answer: Fe3O4

Solution

A ccp unit cell contains 4 formula units of O²-, 8 tetrahedral voids, and 4 octahedral voids. Fe²+ occupies 1/8 of tetrahedral voids = 1 per unit cell. Fe³+ occupies 1/2 of octahedral voids = 2 per unit cell. Total formula: Fe(1+2)O4 = Fe3O4, which is magnetite — a well-known mixed-valence iron oxide spinel.

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