Question

Aluminium oxide crystallizes with aluminium ions in 2/3 of the line octahedral and 1/3 octahedral holes remaining vacant in a closest packed array of oxide ions. What is the formula of aluminium oxide?

Answer 1

Oxide ions are involved in forming packing structure.

Let, number of oxide ions $=n$

Number of octahedral voids $=n$

i.e, Number of Aluminum ions $=\frac{2}{3}n$

Now, $A{l}^{3+}:O^{2-}\Rightarrow A{l}^{3+}:O^{2-}$

$\frac{2}{3}n:n\Rightarrow$ $2$ $:$ $3$

So, formula is $A{l}_2{O}_3$