Problem 73 - Chemistry

Question

Order the following compounds according to their expected lattice energies: \(\mathrm{AlBr}_{3}, \mathrm{MgBr}_{2}, \mathrm{LiBr}, \mathrm{CaO}\).

Step-by-Step Solution

Answer

The order from highest to lowest lattice energy is: CaO > AlBr₃ > MgBr₂ > LiBr.

Step 1: Understand Lattice Energy

Lattice energy is the energy released when ions in the gas phase form an ionic solid. It primarily depends on the charges of the ions and the distance between them. A higher charge and smaller ionic radius generally result in greater lattice energy.

Step 2: Analyze Compounds

List the ions and their charges for each compound:1. \(\mathrm{AlBr}_{3}\) involves \(\mathrm{Al}^{3+}\) and \(\mathrm{Br}^{-}\).2. \(\mathrm{MgBr}_{2}\) involves \(\mathrm{Mg}^{2+}\) and \(\mathrm{Br}^{-}\).3. \(\mathrm{LiBr}\) involves \(\mathrm{Li}^{+}\) and \(\mathrm{Br}^{-}\).4. \(\mathrm{CaO}\) involves \(\mathrm{Ca}^{2+}\) and \(\mathrm{O}^{2-}\).

Step 3: Determine Ion Charges and Sizes

Identify the charges and consider size:1. In \(\mathrm{AlBr}_{3}\), Aluminum has a charge of 3+ and Bromine is 1-.2. In \(\mathrm{MgBr}_{2}\), Magnesium is 2+ and Bromine is 1-.3. In \(\mathrm{LiBr}\), Lithium is 1+ and Bromine is 1-.4. In \(\mathrm{CaO}\), Calcium is 2+ and Oxygen 2-.

Step 4: Lattice Energy Relationship

Recall that lattice energy increases with greater ion charge and decreases with larger ionic radii. Therefore, compounds with higher charged ions and small ions tend to have higher lattice energies.

Step 5: Rank Compounds by Lattice Energy

Compare based primarily on charge, and consider the size:- \(\mathrm{CaO}\) likely has the highest lattice energy due to 2+ and 2- charges.- \(\mathrm{AlBr}_{3}\) follows with 3+ but disperses among three larger bromides.- \(\mathrm{MgBr}_{2}\) has moderate charges (2+) with larger bromide ions.- \(\mathrm{LiBr}\) is last, with 1+ and 1- charges, thus being lowest.

Key Concepts

Ionic Compounds

Ionic compounds form when atoms transfer electrons, resulting in ions with opposite electrical charges that attract each other. These compounds are typically formed between metals and nonmetals. Metal atoms lose electrons to become positively charged ions (cations), whereas nonmetals gain electrons to become negatively charged ions (anions).
For example:

• In the compound \(\mathrm{LiBr}\), Lithium (\(\mathrm{Li}\)) loses one electron, becoming \(\mathrm{Li}^{+}\), and Bromine (\(\mathrm{Br}\)) gains that electron, becoming \(\mathrm{Br}^{-}\).
• Similarly, \(\mathrm{CaO}\) contains Calcium (\(\mathrm{Ca}\)), which loses two electrons to form \(\mathrm{Ca}^{2+}\), and Oxygen (\(\mathrm{O}\)), which gains these two electrons to form \(\mathrm{O}^{2-}\).

Ionic compounds are characterized by high melting and boiling points, and they conduct electricity when dissolved in water or melted because ions are free to move.

Ionic Charges

The ionic charge is crucial in determining the properties of ionic compounds, including lattice energy. The charge of an ion arises from the loss or gain of electrons. This charge can heavily influence the strength of the ionic bond.

• In \(\mathrm{AlBr}_{3}\), Aluminum as \(\mathrm{Al}^{3+}\) has a charge of 3+, which is significant in strengthening the bond between it and the Bromide ions (\(\mathrm{Br}^{-}\), 1- each).
• Meanwhile, \(\mathrm{MgBr}_{2}\) contains Magnesium (\(\mathrm{Mg}^{2+}\)) at 2+, and \(\mathrm{CaO}\) features Calcium (\(\mathrm{Ca}^{2+}\)) with 2+, a strong charge that pairs with Oxygen at 2- (\(\mathrm{O}^{2-}\)).

Larger ion charges generally increase a compound's lattice energy, as the electrostatic forces between ions are stronger.

Ionic Radii

The ionic radius is a measure of the size of an ion. It significantly affects the lattice energy of an ionic compound. Smaller ionic radii typically result in higher lattice energy because the ions can pack closely together, increasing the strength of the ionic bonds.
For instance:

• In \(\mathrm{LiBr}\), the \(\mathrm{Li}^{+}\) ion is quite small, allowing a reasonably compact lattice structure. However, its charge is only 1+, which doesn't greatly enhance the lattice energy.
• Conversely, \(\mathrm{AlBr}_{3}\) involves a small \(\mathrm{Al}^{3+}\) ion with high positive charge that can strongly attract the larger \(\mathrm{Br}^{-}\) ions.

Additionally, \(\mathrm{CaO}\) benefits from relatively small ions, \(\mathrm{Ca}^{2+}\) and \(\mathrm{O}^{2-}\), contributing to its high lattice energy due to compact ion packing.

Chemical Bonding

Chemical bonding describes how atoms stick together in compounds, underpinning the structure of matter. Ionic bonding, specifically, involves the electrostatic attraction between oppositely charged ions, such as those in ionic compounds.
These strong bonds are why ionic compounds exhibit properties like high melting points and brittleness.

• Ionic bonds form because metals donate electrons, becoming cations, while non-metals accept electrons, becoming anions.
• In \(\mathrm{MgBr}_{2}\), the Magnesium ion \(\mathrm{Mg}^{2+}\) forms ionic bonds with two Bromide ions \(\mathrm{Br}^{-}\), as it donates its two valence electrons.
• The bond strength reflects in lattice energies: with \(\mathrm{CaO}\) having a particularly high lattice energy due to its highly charged ions \(\mathrm{Ca}^{2+}\) and \(\mathrm{O}^{2-}\).

Understanding these bonds helps explain why certain compounds have higher lattice energies and different physical properties.