Formula of Aluminium Oxide (Al₂O₃)

Aluminium oxide (Al₂O₃) is an ionic compound composed of aluminium ions (Al³⁺) and oxide ions (O^2-). The arrangement of oxide ions in the compound is in a hexagonal close packing (hcp) structure. Let's understand how the formula of aluminium oxide is derived based on the given information.

1. Understanding Hexagonal Close Packing (HCP)

Hexagonal close packing is a type of crystal lattice structure where spheres (ions) are arranged in a closely packed manner. In an hcp structure, each sphere is surrounded by six spheres of its first layer, three spheres above it, and three spheres below it. This arrangement results in two types of voids - tetrahedral voids and octahedral voids.

2. Aluminium Ions in Octahedral Voids

In the given oxide of aluminium, the aluminium ions (Al³⁺) occupy 2/3 of the octahedral voids. Octahedral voids are formed by the arrangement of six spheres in a hexagonal close packing. Since aluminium ions have a charge of +3, they can occupy these voids.

3. Ratio of Aluminium Ions to Oxide Ions

In an ionic compound, the total positive charge of cations must balance the total negative charge of anions. Each aluminium ion (Al³⁺) has a charge of +3, and each oxide ion (O^2-) has a charge of -2. Therefore, the ratio of aluminium ions to oxide ions should be chosen in such a way that the charges are balanced.

4. Deriving the Formula

Since aluminium ions occupy 2/3 of the octahedral voids, the ratio of aluminium ions to oxide ions is 2:3. This means, in the formula, there are 2 aluminium ions for every 3 oxide ions.

Therefore, the formula of the oxide of aluminium is Al₂O₃. This formula ensures that the total positive charge of the aluminium ions (+6) balances the total negative charge of the oxide ions (-6).

Summary:

The formula of the oxide of aluminium is Al₂O₃. This is derived based on the arrangement of oxide ions in hexagonal close packing (hcp) and the fact that aluminium ions occupy 2/3 of the octahedral voids. The ratio of aluminium ions to oxide ions is chosen in such a way that the charges of cations and anions balance each other in the ionic compound.