Problem 129 - Chemistry The Molecular Science

Question

Use Coulomb's law to predict which substance in each of these pairs has the larger lattice energy. (a) \(\mathrm{CaO}\) or \(\mathrm{Kl}\) (b) \(\mathrm{CaF}_{2}\) or \(\mathrm{BaF}_{2}\) (c) \(\mathrm{KCl}\) or \(\mathrm{LiBr}\)

Step-by-Step Solution

Answer

(a) CaO, (b) CaF2, (c) LiBr have larger lattice energies.

Step 1: Understanding Coulomb's Law

Coulomb's Law is used to calculate the force of attraction or repulsion between two charged particles. In lattice energy, it expresses the energy required to separate an ionic compound into its gaseous ions. Coulomb's Law can be stated as: \[ F = k \frac{|q_1 q_2|}{r^2} \] where \(F\) is the force, \(k\) is Coulomb's constant, \(q_1\) and \(q_2\) are the charges on the ions, and \(r\) is the distance between the centers of the ions.

Step 2: Analyzing Pair (a) CaO vs KI

For CaO, calcium has a charge of +2 and oxygen has a charge of -2, resulting in a stronger attraction. For KI, potassium has a charge of +1 and iodine has a charge of -1. The charges in CaO are higher than in KI, meaning CaO will have a larger lattice energy due to the increased attraction between ions.

Step 3: Analyzing Pair (b) CaF2 vs BaF2

Both compounds have fluoride ions with a charge of -1. However, in CaF2, calcium has a charge of +2, whereas in BaF2, barium also has a charge of +2. The primary difference is the ion size; calcium ions are smaller than barium ions, leading to shorter distances between ions in CaF2 and thus greater lattice energy due to stronger attraction.

Step 4: Analyzing Pair (c) KCl vs LiBr

Both compounds involve ions with "+1" and "-1" charges. Comparing ionic sizes, lithium ions are smaller than potassium ions, and bromine atoms are larger than chlorine atoms. However, the smaller cation size and therefore shorter distance between ions in LiBr suggest that LiBr has a larger lattice energy than KCl.

Key Concepts

Lattice Energy

Lattice energy refers to the energy required to separate a solid ionic compound into its individual gaseous ions. This concept is important because it helps us understand the stability and strength of ionic bonds in a compound. High lattice energy implies strong ionic bonds, making the compound more stable.
To determine lattice energy, we often use Coulomb's Law. This law states that the force of attraction or repulsion between charged particles is directly proportional to the product of the charges' magnitudes ( (q_1 q_2) ) and inversely proportional to the square of the distance between them ( (r^2) ).
Lattice energy increases with:

• Greater ionic charge: Higher charges mean stronger forces of attraction, thus higher lattice energy.
• Smaller ionic size: Shorter distances between ions increase attraction, boosting lattice energy.

Understanding lattice energy allows us to predict various properties of ionic compounds such as melting points, solubility, and hardness.

Ionic Compounds

Ionic compounds are chemical compounds composed of ions held together by electrostatic forces. These ions are atoms or molecules that have gained or lost electrons, resulting in a net charge. Typically, ionic compounds are formed between metals and nonmetals:

• Metals, like sodium or calcium, lose electrons to become positively charged cations.
• Nonmetals, like chlorine or oxygen, gain electrons to become negatively charged anions.

The compounds form a regular crystalline structure known as a lattice. This ordered arrangement results in the significant strength and durability of ionic compounds. The lattice structure also contributes to the high melting and boiling points often observed in ionic substances.
Ionic compounds conduct electricity when dissolved in water or melted, due to the mobility of the ions. This makes them distinct from covalent compounds, which do not readily conduct electricity. Overall, the unique structure and interactions within ionic compounds greatly influence their chemical and physical properties.

Ionic Bonding

Ionic bonding occurs when one atom transfers electrons to another, resulting in the formation of ions. This transfer can be understood through the concepts of electronegativity and electron affinity.
The process typically involves a metal, which easily loses electrons, and a nonmetal, which has a strong tendency to gain electrons. Once electrons are transferred:

• The metal becomes a positively charged cation.
• The nonmetal becomes a negatively charged anion.
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The attraction between the oppositely charged ions forms the ionic bond.
This bond is incredibly strong, which explains why ionic compounds appear as rigid, crystalline solids. The strength of ionic bonds makes them resistant to phase changes, giving ionic compounds high melting and boiling points. Additionally, as these bonds are not directional like covalent bonds, ions in ionic compounds can form large, repeating lattices, contributing to their hardness and brittleness.
Ionic bonding is a fundamental concept in chemistry, highlighting the interplay between electron exchange and mutual attraction that shapes the behaviors and characteristics of numerous substances.