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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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Suppose the number of oxide ions `(O^(2-))` in the packing = n.
`:.` Number of octahedral voids = n.
As 2/3rd of the octahedral voids are occupied by ferric ions, therefore, number of ferric ions present
`(2)/(3)xxn = (2n)/(3)`
`:.` Ratio of `Fe^(3+) : O^(2-) = (2n)/(3): n = 2:3`
Hence, the formula of ferric oxide is Fe `""_(2)O_(3)`.
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