Problem 76 - Chemistry: The Central Science

Question

Would you expect AlN to have a lattice energy that is larger or smaller than ScN? Explain.

Step-by-Step Solution

Answer

Aluminum Nitride (AlN) is expected to have a larger lattice energy compared to Scandium Nitride (ScN) because Aluminum (Al³⁺) has a smaller ionic radius than Scandium (Sc³⁺), while the ionic charges between the two compounds are the same. According to Coulomb's law, the lattice energy is larger when the ionic radii are smaller, and the charge difference is larger, making AlN have a larger lattice energy.

Step 1: Understand what lattice energy is

Lattice energy refers to the energy required to break a crystal lattice, in other words, to separate the ions in a crystal and turn it into a gas. Factors affecting lattice energy include ionic radii and ionic charges. The smaller the ionic radii and the larger the ionic charge difference, the larger the lattice energy (according to Coulomb's law).

Step 2: Compare the ionic size/radii of AlN and ScN

Comparing the ionic radii of Aluminum and Scandium ions, Aluminum (Al³⁺) is smaller than Scandium (Sc³⁺) due to having fewer electron shells (Aluminum is in the 3rd Period while Scandium is in the 4th Period). Nitride ion, N³⁻, is the same in both compounds. Smaller ionic radii are associated with higher lattice energy.

Step 3: Compare the ionic charges of AlN and ScN

For Aluminum Nitride (AlN), Aluminum ion (Al³⁺) has a charge of +3, and Nitride ion (N³⁻) has a charge of -3. For Scandium Nitride (ScN), Scandium ion (Sc³⁺) has a charge of +3, and Nitride ion (N³⁻) has a charge of -3. It can be concluded that both AlN and ScN have the same magnitude of ionic charges. Hence, the charge difference between the two compounds does not play a significant role in the comparison of their lattice energies.

Step 4: Conclusion

Based on the analysis of ionic radii and charges of both compounds, Aluminum Nitride (AlN) is expected to have a larger lattice energy compared to Scandium Nitride (ScN). The reasoning is that Aluminum (Al³⁺) has a smaller ionic radius than Scandium (Sc³⁺), while the ionic charges between the two compounds are the same. According to Coulomb's law, the lattice energy is larger when the ionic radii are smaller, and the charge difference is larger, making AlN have a larger lattice energy.

Key Concepts

Ionic Radii

Ionic radii refer to the apparent measure of the size of an ion. It is an important factor when discussing lattice energy. Smaller ions can pack more closely together in a crystal lattice. This proximity allows the ions to exert stronger electrostatic attractions between each other. As a result, compounds with smaller ionic radii typically exhibit larger lattice energies.

For example, consider Aluminum (Al³⁺) and Scandium (Sc³⁺). The Al³⁺ ion is smaller than the Sc³⁺ ion due to fewer electron shells. Aluminum is in the third period of the periodic table, whereas Scandium is in the fourth. The Nitride (N³⁻) ion remains constant in both AlN and ScN. Because of the smaller ionic radius of Al³⁺, AlN is expected to have a larger lattice energy than ScN.

• Smaller ionic radii result in higher lattice energy.
• More packed ions increase electrostatic attraction.

Understanding ionic radii helps in predicting and comparing lattice energies of different compounds.

Ionic Charges

Ionic charges are integral in determining lattice energy. The charge on an ion represents how many electrons were lost or gained to form the ion, resulting in its positive or negative charge. Higher ionic charges generally mean stronger electrostatic attractions in the crystal lattice, leading to higher lattice energy.

In both AlN and ScN, Aluminum ion (Al³⁺) and Scandium ion (Sc³⁺) both have a charge of +3. Similarly, the Nitride ion (N³⁻) has a charge of -3 in both cases. The magnitude of ionic charges in AlN and ScN is the same, meaning this factor does not differentiate the lattice energies of these compounds.

• Equal ionic charges result in similar contributions to lattice energy.
• The difference in lattice energy is not influenced by ionic charge in this comparison since they are the same.

Ionic charge is crucial, but in this scenario, both compounds carry equal ionic charges.

Coulomb's Law

Coulomb's Law is a scientific principle used to calculate the force between two charged particles. It states that the force of attraction between two points is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. When applied to lattice energy:

\[ F = rac{{k imes |q_1 imes q_2|}}{{r^2}} \]
In this equation, \( F \) represents the force of attraction, \( k \) is a constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the ion centers. Stronger forces indicate larger lattice energies. When comparing AlN and ScN, the smaller ionic radius in AlN reduces \( r \), thus increasing the force and ultimately the lattice energy. Although the ionic charges are identical, the smaller distance between ions in AlN makes its lattice energy larger.

• Smaller \( r \) (distance between ions) increases lattice energy.
• Coulomb’s Law explains the relationship between ionic charges and radii on lattice energy.

Coulomb's Law provides a basis for understanding the interplay between ion size and charge when assessing lattice energy.