Question

Aluminum oxide \(\left(\mathrm{Al}_{2} \mathrm{O}_{3}\right)\) is a widely used industrial abrasive (known as emery or corundum), for which the specific application depends on the hardness of the crystal. What does this hardness imply about the magnitude of the lattice energy? Would you have predicted from the chemical formula that \(\mathrm{Al}_{2} \mathrm{O}_{3}\) is hard? Explain.

Short answer

The high lattice energy of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) implies that it is hard. Based on the formula, the strong electrostatic interactions between \(\mathrm{Al}^{3+}\) and \(\mathrm{O}^{2-}\) predict this hardness.

Step-by-step solution

Understand Hardness and Lattice Energy

Hardness in a crystal implies that the atoms are strongly bonded together. In ionic compounds, this strong bonding is a result of a high lattice energy. Lattice energy is the energy required to separate one mole of an ionic solid into its constituent ions.

Determine the Lattice Energy of \(\mathrm{Al}_{2} \mathrm{O}_{3}\)

To assess the magnitude of the lattice energy for \(\mathrm{Al}_{2} \mathrm{O}_{3}\), consider the charge and sizes of the ions. Aluminum forms \(\mathrm{Al}^{3+}\) ions, and oxygen forms \(\mathrm{O}^{2-}\) ions. Due to the high charges (3+ and 2-), \(\mathrm{Al}_{2} \mathrm{O}_{3}\) is expected to have a high lattice energy based on Coulomb’s law, which states that lattice energy is directly proportional to the product of the charges of the ions and inversely proportional to the sum of the radii of the ions.

Predict Hardness from the Chemical Formula

Given the high lattice energy due to the high charges on the \(\mathrm{Al}^{3+}\) and the \(\mathrm{O}^{2-}\) ions, it can be predicted that \(\mathrm{Al}_{2} \mathrm{O}_{3}\) will be hard. The strong electrostatic attraction between these ions forms a hard and stable ionic lattice.

Conclusion

Based on the chemical formula, \(\mathrm{Al}_{2} \mathrm{O}_{3}\) can be predicted to be hard due to its high lattice energy, resulting from the strongly bonded \(\mathrm{Al}^{3+}\) and \(\mathrm{O}^{2-}\) ions in the crystal lattice.

Key concepts

hardness of ionic compounds

When we talk about the hardness of ionic compounds, we mean how resistant they are to being scratched or deformed. Hardness in these compounds is all about the crystal structure. The ions are arranged in a specific pattern, creating a strong, solid framework. The strength of the bonds between these ions determines how hard the compound is.
Ionic compounds, like aluminum oxide \(\text{Al}_2O_3\), are typically very hard. Why? Because the ions are held together by strong electrostatic forces. This is often due to the high lattice energy – the energy needed to separate the ions.
This tight bond makes it difficult to break or scratch the crystal, giving it its hardness. So, a high hardness often means high lattice energy.

lattice energy

Lattice energy is a key concept when talking about ionic compounds. It's the amount of energy needed to pull apart one mole of an ionic solid into its individual ions. Think of it like a measure of how tightly the ions are bound to each other in the lattice.
Several factors influence lattice energy:

• Charges of the ions: Higher charges mean stronger attraction.
• Sizes of the ions: Smaller ions mean they can pack closely together.
• The arrangement of the ions in the lattice

For aluminum oxide \(\text{Al}_2O_3\), the \(\text{Al}^{3+}\) ions and the \(\text{O}^{2-}\) ions have high charges. This high charge leads to a strong attraction and, consequently, high lattice energy. Since lattice energy is inversely proportional to the sum of the radii of the ions, smaller radii will further increase this energy.

Al2O3 properties

Aluminum oxide \(\text{Al}_2O_3\) is a fascinating and versatile compound. Here are some key properties:

• Hardness: As previously explained, it's very hard, often used as an abrasive.
• Melting Point: High melting point, due to the strong ionic bonds.
• Stability: Very stable, resistant to weathering and wear.
• Electrical Insulator: Does not conduct electricity in solid state, because the ions are not free to move.

These properties stem from the strong ionic bonds between the \(\text{Al}^{3+}\) and \(\text{O}^{2-}\) ions. This makes \(\text{Al}_2O_3\) a highly valued material in various industrial applications.

ionic bonds

Ionic bonds are the glue holding ionic compounds together. These bonds form when one atom donates an electron to another, creating ions. One ion becomes positively charged (a cation) and the other becomes negatively charged (an anion).
The electrostatic attraction between these oppositely charged ions forms the ionic bond. In aluminum oxide \(\text{Al}_2O_3\), aluminum \(\text{Al}^{3+}\) loses three electrons and oxygen \(\text{O}^{2-}\) gains electrons to fill its valence shell. This results in a very strong attraction between \(\text{Al}^{3+}\) and \(\text{O}^{2-}\) ions, creating a robust ionic bond.
These bonds not only determine the compound's structure but also its properties, like high lattice energy and hardness.