Problem 98 - Chemistry The Molecular Science

Question

Which ionic compound has the largest lattice energy? Explain your choice. \(\begin{array}{lll}\mathrm{MgS} & \mathrm{RbI} & \mathrm{Li}_{2} \mathrm{~S}\end{array}\)

Step-by-Step Solution

Answer

MgS has the largest lattice energy due to high charges and small ionic radii.

Step 1: Understanding Lattice Energy

Lattice energy is the energy required to separate one mole of an ionic compound into its gaseous ions. It is an indicator of the strength of the forces holding the ions together in the solid.

Step 2: Factors Affecting Lattice Energy

The lattice energy depends on two main factors: the charges of the ions and the distance between the ions (ionic radii). Higher charges and smaller distances result in higher lattice energy.

Step 3: Analyze MgS

In MgS, magnesium \((\text{Mg}^{2+})\) and sulfur \((\text{S}^{2-})\) both carry a double charge. The ionic radii are relatively small, leading to a strong attraction between ions.

Step 4: Analyze RbI

In RbI, rubidium \((\text{Rb}^{+})\) and iodine \((\text{I}^{-})\) have single charges. Both ions are relatively large, resulting in weaker attraction compared to ions with higher charge density.

Step 5: Analyze Li2S

In Li2S, lithium \((\text{Li}^{+})\) has a single charge while sulfur \((\text{S}^{2-})\) has a double negative charge. The lattice energy is influenced by the presence of the doubly charged sulfur, but it is typically lower than MgS due to the single charge of lithium.

Step 6: Conclusion about Largest Lattice Energy

Considering the factors of ionic charge and radius, MgS has the largest lattice energy among the given compounds due to the double charges on both its ions and relatively small ionic radius, which results in a strong electrostatic interaction.

Key Concepts

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons to achieve a stable electron configuration. Usually, this involves a metal donating electrons to a non-metal, resulting in the formation of positive and negative ions.

• Metals, like magnesium (Mg), lose electrons to form positive ions, known as cations.
• Non-metals, like sulfur (S), gain electrons to form negative ions, called anions.

In the solid state, these ions arrange themselves into a regular, repeating pattern known as a lattice structure. This structure is stabilized by the electrostatic forces, or electrostatic attractions, between the oppositely charged ions. The stability and properties of an ionic compound, such as its lattice energy, heavily depend on the nature of these forces.

Electrostatic Forces

Electrostatic forces are fundamental to the behavior of ionic compounds. These forces result from the attraction between positively and negatively charged ions. The strength of electrostatic forces plays a crucial role in determining the lattice energy of an ionic compound. When ions have stronger electrostatic attractions:

• The lattice energy is higher, which leads to a more stable compound.
• The melting and boiling points of the compound are usually higher.

Two main factors influence these electrostatic forces: - **Ionic charges**: Greater charges result in stronger attractions. - **Ionic radius**: Smaller ions allow charges to be closer, increasing the force.

Ionic Charges

The charge on an ion profoundly influences the lattice energy of an ionic compound. The rule of thumb is: the greater the charges of the ions, the higher the lattice energy. For example:

• In MgS, both ions (Mg²⁺ and S^2-) have double charges, making their electrostatic forces highly significant.
• In RbI, Rb⁺ and I^- have single charges, resulting in weaker interactions compared to ions with higher charges.
• In Li₂S, the sulfur ion has a double negative charge (S^2-), but the lithium ion has only a single positive charge (Li⁺), which reduces overall attraction compared to compounds like MgS.

Ionic charge is a primary factor in understanding why different compounds have varying lattice energies.

Ionic Radius

Ionic radius refers to the size of an ion in a crystal lattice. The size of an ion influences how close ions can get to each other, affecting their electrostatic forces and, consequently, the lattice energy.

• Smaller ionic radii allow ions to be closer, increasing the strength of the electrostatic attractions.
• Larger ionic radii result in weaker attractions due to increased distances between ions.

For instance: - In MgS, both magnesium and sulfur have relatively small ionic radii, which contributes to strong ionic bonds and high lattice energy. - In RbI, both rubidium and iodine ions are larger, decreasing the strength of the interactions. Understanding ionic radii helps explain why MgS possesses larger lattice energy compared to RbI and Li₂S.