Question

The lattice energies of \(\mathrm{FeCl}_{3}, \mathrm{FeCl}_{2},\) and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) are (in no particular order) \(-2631,-5359,\) and \(-14,774 \mathrm{kJ} / \mathrm{mol}\) . Match the appropriate formula to each lattice energy. Explain.

Short answer

Fe₂O₃ has a lattice energy of -14,774 kJ/mol, because it has the highest product of charges (+6). FeCl₂ has a lattice energy of -2,631 kJ/mol, as it has the lowest product of charges (+2). FeCl₃ has a lattice energy of -5,359 kJ/mol, with an intermediate product of charges (+3).

Step-by-step solution

Identify the charges of the ions in each compound

We need to determine the charges of the ions in each compound: FeCl₃: Fe has a charge of +3 and Cl has a charge of -1. FeCl₂: Fe has a charge of +2 and Cl has a charge of -1. Fe₂O₃: Fe has a charge of +3 and O has a charge of -2.

Calculate the product of the charges and distances

We don't need to calculate the actual distances between ions since we're only comparing the lattice energies. We just need to focus on the differences in the magnitude of ionic charges. FeCl₃: The ionic charges are +3 and -1, so their product is +(3×1) = +3. FeCl₂: The ionic charges are +2 and -1, so their product is +(2×1) = +2. Fe₂O₃: The ionic charges are +3 and -2, so their product is +(3×2) = +6. Now we can analyze the magnitudes of these products to determine which lattice energy value corresponds to which compound.

Match the products of charges with the lattice energy values

Since lattice energy is directly proportional to the product of charges, the compound with the highest product of charges should have the highest lattice energy value, and the compound with the lowest product of charges should have the lowest lattice energy value. - Fe₂O₃: The product of charges is +6. This compound should have the highest lattice energy value, which is -14,774 kJ/mol. - FeCl₂: The product of charges is +2. This compound should have the lowest lattice energy value, which is -2,631 kJ/mol. - FeCl₃: The product of charges is +3. This compound should have the intermediate lattice energy value, which is -5,359 kJ/mol. So, we can conclude that: Fe₂O₃ has a lattice energy of -14,774 kJ/mol. FeCl₂ has a lattice energy of -2,631 kJ/mol. FeCl₃ has a lattice energy of -5,359 kJ/mol.

Key concepts

ionic compounds

Ionic compounds are an essential part of chemistry, particularly in the study of materials. These compounds are formed when atoms transfer electrons to achieve a more stable, energetically favorable electronic configuration. Essentially, they involve ions—atoms possessing an electric charge due to the loss or gain of electrons.

In ionic compounds:

• Atoms become ions by either losing or gaining electrons: metals typically lose electrons, becoming positively charged cations, whereas non-metals generally gain electrons, becoming negatively charged anions.
• Cations and anions interact to form a strong electrostatic attraction, known as an ionic bond, which holds the compound together in a structured lattice.
• Examples include NaCl (table salt), where sodium (Na) loses an electron to become Na⁺ and chlorine (Cl) gains an electron to become Cl⁻.

Ionic compounds are characterized by their high melting and boiling points, as well as their ability to conduct electricity when molten or dissolved in water.

charge of ions

In the world of ionic compounds, the charge of ions plays a key role in determining many of their properties, including lattice energy. Ions are atoms or molecules that have gained or lost electrons, resulting in a net charge.

Understanding ion charges:

• A metal atom loses electrons and forms a positively charged ion, known as a cation. For example, iron (Fe) can lose electrons to form Fe²⁺ or Fe³⁺.
• A non-metal atom gains electrons and forms a negatively charged ion, known as an anion. Chlorine (Cl), for instance, gains an electron to form Cl⁻.
• The number of electrons lost or gained determines the magnitude of the ion's charge.

The charge of ions directly affects the formation and strength of ionic bonds, as well as the resultant compound's lattice energy, due to the electrostatic forces between oppositely charged ions.

relationship between charges and lattice energy

Lattice energy is a measure of the strength of the forces holding ions together in an ionic solid. This is a crucial concept in understanding the stability of ionic compounds.

Here's how charge affects lattice energy:

• Lattice energy is influenced by both the magnitude of the charges and the distance between the ions.
• The greater the charges on the ions, the stronger the attractive forces, and hence, the higher the lattice energy.
• For instance, compounds with higher charged ions like Fe₂O₃ (Fe³⁺ and O²⁻) have higher lattice energies compared to FeCl₂ (Fe²⁺ and Cl⁻).

Essentially, lattice energy increases with increasing ion charge, making it a direct proportional relationship. This understanding helps in predicting and comparing the stability and properties of different ionic compounds.

comparison of lattice energies

Comparing lattice energies helps us understand differences in stability and strength of ionic bonds in various compounds. The comparison is primarily based on the product of ion charges within each compound.

Understanding lattice energy comparisons:

• The higher the product of the charges, the more negative the lattice energy, indicating a stronger bond and greater lattice stability.
• For example, among FeCl₂ (+2 × -1), FeCl₃ (+3 × -1), and Fe₂O₃ (+3 × -2), Fe₂O₃ has the highest product (+6), hence the most negative lattice energy (-14,774 kJ/mol).
• This comparison directly traces back to the electrostatic principles governing ionic interactions.

Therefore, when comparing lattice energies of ionic compounds, the greater the charged products, the stronger and more stable the ionic structure.