Question

Specify which compound in each of the following pairs of ionic compounds should have the higher lattice energy: (a) \(\mathrm{KCl}\) or \(\mathrm{MgO},\) (b) \(\mathrm{LiF}\) or \(\mathrm{LiBr}\), (c) \(\mathrm{Mg}_{3} \mathrm{~N}_{2}\) or NaCl. Explain your choice.

Short answer

(a) MgO, (b) LiF, (c) Mg3N2 have higher lattice energies.

Step-by-step solution

Understanding Lattice Energy

Lattice energy is the energy required to completely separate a mole of a solid ionic compound into its gaseous ions. It is influenced by the charge and size of the ions, with higher charge and smaller ionic radii leading to higher lattice energy due to stronger electrostatic attractions.

Analyzing Pair (a): KCl vs MgO

In the pair \((\mathrm{KCl}\) vs \(\mathrm{MgO}\)), both compounds are ionic. \(\mathrm{KCl}\) is formed by \(\mathrm{K}^+\) and \(\mathrm{Cl}^-\), whereas \(\mathrm{MgO}\) is formed by \(\mathrm{Mg}^{2+}\) and \(\mathrm{O}^{2-}\). The charges are higher in \(\mathrm{MgO}\), as they involve +2 and -2 as opposed to +1 and -1 in \(\mathrm{KCl}\). Higher charges generally lead to stronger attractions and higher lattice energy, so \(\mathrm{MgO}\) should have the higher lattice energy.

Analyzing Pair (b): LiF vs LiBr

In the pair \(\mathrm{LiF}\) vs \(\mathrm{LiBr}\)), both have the same cation \(\mathrm{Li}^+\) but different anions: \(\mathrm{F}^-\) and \(\mathrm{Br}^-\). \(\mathrm{F}^-\) is smaller in size compared to \(\mathrm{Br}^-\), which increases the ionic charge density and results in stronger attraction in \(\mathrm{LiF}\). Therefore, \(\mathrm{LiF}\) should have the higher lattice energy.

Analyzing Pair (c): Mg3N2 vs NaCl

In the pair \((\mathrm{Mg}_{3} \mathrm{N}_{2})\) vs \(\mathrm{NaCl}\)), \(\mathrm{Mg}_{3} \mathrm{N}_{2}\) has cations \(\mathrm{Mg}^{2+}\) and anions \(\mathrm{N}^{3-}\), significantly increasing the lattice energy compared to \(\mathrm{NaCl}\) with \(\mathrm{Na}^+\) and \(\mathrm{Cl}^-\). The higher charge of both ions in \(\mathrm{Mg}_{3} \mathrm{N}_{2}\) results in much stronger ionic bonds, indicating a higher lattice energy.

Key concepts

Ionic Compounds

Ionic compounds are fascinating substances made up of ions, which are atoms or molecules that have gained or lost electrons. This charge difference creates a strong force that holds the ions together. When atoms form ionic compounds, they create a three-dimensional lattice structure.
Each ion in the lattice structure is surrounded by ions of opposite charge, resulting in a stable and neutral substance. The strength of this structure is one reason ionic compounds have high melting and boiling points.

• Formed by the complete transfer of electrons.
• Typically occur between metals and non-metals.
• Construct lattices that are highly organized.

The arrangement in ionic compounds means they are brittle; they tend to shatter rather than bend when stressed. This is because shifting any of the ions causes similar charges to align, leading to repulsion.

Electrostatic Attraction

Electrostatic attraction plays a critical role in maintaining the integrity of ionic compounds. It is the force that pulls together oppositely charged particles, like the positive and negative ions in an ionic lattice. This attraction is described by Coulomb's Law, which explains how the potential energy is proportional to the product of the charges and inversely proportional to the distance between them.
The higher the charge of the ions, the stronger the electrostatic attraction. This is why ionic compounds tend to have very stable structures. Electrostatic attraction is also responsible for many of the physical properties of ionic compounds, such as:

• High melting and boiling points due to the strong forces holding the lattice together.
• Brittleness, as symmetry disruption can misalign ions and cause repulsion.

Understanding this force helps explain why changes in ion size and charge can vastly affect lattice energy.

Ion Charge and Size

The charge and size of ions are pivotal when predicting lattice energy. The lattice energy of an ionic compound is significantly influenced by how these two factors interact. Higher ionic charges result in a stronger force of attraction, which contributes to a higher lattice energy.
Similarly, the size of the ions matters too: smaller ions can pack more closely together. This proximity increases the strength of electrostatic attraction between the ions.

• Higher charges mean stronger attraction.
• Smaller ions typically have higher lattice energy due to closer packing.

Consider the example: In \( \mathrm{MgO} \) vs \( \mathrm{KCl} \). Mg and O ions have charges of +2 and -2, compared to +1 and -1 in K and Cl ions. This dramatically increases the lattice energy in \( \mathrm{MgO} \).

Ionic Bonds

Ionic bonds are the result of the electrostatic forces that hold charged particles within ionic compounds together. These bonds form when one atom donates one or more electrons to another, resulting in positively-charged cations and negatively-charged anions. The strength of an ionic bond is determined by the magnitude of the charge on the ions and the distance between them.
Ionic bonds are generally strong, which leads to the many characteristic properties of ionic compounds like high melting points, electrical conductivity in the liquid state, and solubility in water. Ionic bonds form a lattice that is a highly structured arrangement ensuring stability and uniformity throughout the compound.

• There, the electron donor usually becomes a cation, while the receiver becomes an anion.
• Depends on both ion charge and distance between ions.
• Larger charges or smaller distances lead to stronger bonds.

Consider how \( \mathrm{LiF} \) forms, there is a tight bond due to the strong attraction between \( \mathrm{Li^+} \) and \( \mathrm{F^-} \), resulting in a high lattice energy.