Problem 105 - Chemistry: Atoms First

Question

Which compound in each of the following pairs has the larger lattice energy? Note: \(\mathrm{Mg}^{2+}\) and \(\mathrm{Li}^{+}\) have similar radii; O \(^{2-}\) and \(\mathrm{F}^{-}\) have similar radii. Explain your choices. (a) MgO or MgSe (b) LiF or MgO (c) \(\mathrm{Li}_{2} \mathrm{O}\) or \(\mathrm{LiCl}\) (d) Li_se or MgO

Step-by-Step Solution

Answer

The compound with the larger lattice energy in each pair is: (a) MgO, (b) MgO, (c) Li2O, (d) MgO.

Step 1 - Understanding Lattice Energy Patterns

The lattice energy of an ionic compound depends on both the charge magnitude of its ions and the distance between the ion centers (often associated with the ionic radii). Higher charges and smaller radii typically give rise to larger lattice energies, because the electrostatic forces between the ions are stronger.

Step 2 - Analyzing MgO vs. MgSe

For comparing MgO and MgSe, note that Mg is the same in both compounds, but O and Se are different. Both O and Se are in the same group with O above Se, leading to O having a smaller size. Also, O has a 2- charge compared to the 2- charge of Se. As both charge and size favor O, MgO will have a larger lattice energy than MgSe.

Step 3 - Comparing LiF with MgO

For LiF and MgO, the key difference is in the cations. Mg has a 2+ charge whereas Li has a 1+ charge. F and O have the same 1- and 2- charges respectively, but since the charges on Mg and O are both higher than those on Li and F, MgO will have a larger lattice energy than LiF.

Step 4 - Comparing Li2O with LiCl

In the case of Li2O vs. LiCl, we must understand that Cl has a 1- charge while O has a 2- charge. Although the compounds have a similar structure, the larger charge on O will mean that Li2O has a larger lattice energy than LiCl.

Step 5 - Comparing Li2Se with MgO

To compare Li2Se with MgO, we should look at both the cations and anions. Mg has a 2+ charge compared to Li's 1+, and O has a 2- charge compared to Se's 2-. Even though Li+ and Mg2+ have similar radii, the higher charge on Mg2+ gives MgO a larger lattice energy than Li2Se.

Key Concepts

Ionic Compound

An ionic compound is a chemical compound composed of ions held together by electrostatic forces termed ionic bonding. These ions are atoms or molecules that have gained or lost electrons, resulting in a net charge. Ionic compounds typically form when a metal reacts with a non-metal, transferring electrons from the metal to the non-metal.

For example, in table salt (sodium chloride), sodium (Na) donates an electron to chlorine (Cl), resulting in Na⁺ and Cl^- ions. The positive and negative charges attract each other, creating a solid lattice structure. Ionic compounds have high melting and boiling points, are typically solid at room temperature, and conduct electricity when melted or dissolved in water due to the mobility of ions.

Ionic Radii

The term ionic radii refers to the measure of an ion's size. Specifically, it describes the distance from the center of the nucleus to the outer boundary of the surrounding cloud of electrons. The size of an ion can affect the properties of an ionic compound, including its lattice energy.

Factors Affecting Ionic Radii

• Atomic Number: As the atomic number increases, additional electrons and orbitals are added, which can increase the size of the ion.
• Charge: Positive ions (cations) lose electrons and consequently, their ionic radii are smaller compared to their neutral atoms as the electron cloud shrinks. In contrast, negative ions (anions) gain electrons, which increases the electron-electron repulsion and leads to a larger ionic radius compared to the neutral atom.
• Electron Configuration: Ions with similar electron configurations may vary in size due to differing nuclear charges.

Comparing ionic radii is crucial in determining the strength of the electrostatic forces between ions in a compound and therefore the compound's lattice energy.

Electrostatic Forces

In the context of ionic compounds, electrostatic forces are the attractions or repulsions that occur between charged particles. These forces are described by Coulomb's Law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Electrostatic forces are responsible for the strong attraction between positively charged cations and negatively charged anions in an ionic lattice. The magnitude of these forces can determine the lattice energy of a compound. For example, an ionic compound with higher charged ions will have a stronger electrostatic force, leading to a greater lattice energy—meaning it takes more energy to separate the ions.

Ionic Charges

The concept of ionic charges is fundamental to understanding ionic compounds and lattice energy. Ions are atoms or groups of atoms that have lost or gained electrons, thus acquiring a charge. Cations are positively charged ions, while anions are negatively charged ions.

In ionic compounds, the total positive charge must balance the total negative charge to maintain electrical neutrality. The type and magnitude of the ionic charges influence the strength of the interactions within the crystal lattice of an ionic compound and consequently its lattice energy. The greater the charge of the interacting ions, the stronger the bond between them and the higher the lattice energy. This effect can be seen when comparing the lattice energies of different ionic compounds in chemical reactions.