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Ferric oxide crystallises in a hexagonal...

Ferric oxide crystallises in a hexagonal close packed array of oxide ions with two out of every three octahedral holes occupied by ferric ions. Derive the formula of the ferric oxide.

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There is one octahedral hole for each atom in hexagonal closed packed arrangement. If the number of oxides ions `(O^(2-))` per unit cell is x, then
Number of `Fe^(3+)` ions `=2//3xx` octahedral holes
`=(2)/(3) xx x=(2x)/(3)`
`:.` Ratio of `Fe^(3+) : O^(2-) =(2x)/(3) : x=2:3`
Thus, formula of compound`=Fe_(2)O_(3)`
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