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 kJ/mol. Match the appropriate formula to each lattice energy. Explain.

Short answer

The appropriate lattice energies for the chemical formulas are: \(\mathrm{Fe}_{2} \mathrm{O}_{3}\): -14,774 kJ/mol, \(\mathrm{FeCl}_{3}\): -5,359 kJ/mol, and \(\mathrm{FeCl}_{2}\): -2,631 kJ/mol. This is determined by analyzing the ionic charges and their relationship to lattice energies; compounds with higher charges generally have higher lattice energy.

Step-by-step solution

1. Understand Lattice Energy

Lattice energy is the energy released when one mole of an ionic compound is formed from its constituent ions. The magnitude of lattice energy is proportional to the product of ionic charges and inversely proportional to the distance between them. This means that the greater the ionic charges, the higher the lattice energy, and the smaller the distance between the ions, the greater the lattice energy.

2. Determine the Ionic Charges

We will begin by determining the ionic charges in each of the given chemical compounds: \(\mathrm{FeCl}_{3}\): Iron(III) chloride, Fe has a +3 charge and Cl has a -1 charge. \(\mathrm{FeCl}_{2}\): Iron(II) chloride, Fe has a +2 charge and Cl has a -1 charge. \(\mathrm{Fe}_{2} \mathrm{O}_{3}\): Iron(III) oxide, Fe has a +3 charge, and O has a -2 charge.

3. Analyze the Relationship Between Lattice Energies and Ionic Charges

Now that we know the ionic charges of each compound, we can make predictions about their lattice energies. Compounds with higher charges generally have higher lattice energy: 1. \(\mathrm{Fe}_{2} \mathrm{O}_{3}\): (+3) * (-2) = -6; highest product 2. \(\mathrm{FeCl}_{3}\): (+3) * (-1) = -3; middle product 3. \(\mathrm{FeCl}_{2}\): (+2) * (-1) = -2; lowest product

4. Match the Compounds with Lattice Energies

We have determined the order of the lattice energies based on the relationship between the ionic charges. Now, we will match the chemical formula with the relevant lattice energy: \(\mathrm{Fe}_{2} \mathrm{O}_{3}\): -14,774 kJ/mol (highest) \(\mathrm{FeCl}_{3}\): -5,359 kJ/mol (middle) \(\mathrm{FeCl}_{2}\): -2,631 kJ/mol (lowest) So, the appropriate lattice energies for the chemical formulas are: \(\mathrm{Fe}_{2} \mathrm{O}_{3}\): -14,774 kJ/mol \(\mathrm{FeCl}_{3}\): -5,359 kJ/mol \(\mathrm{FeCl}_{2}\): -2,631 kJ/mol

Key concepts

Ionic Compounds

Ionic compounds are materials composed of ions, which are atoms or molecules that have gained or lost electrons, resulting in a net charge. These compounds form when metals and nonmetals chemically bond together, with the metal atoms losing electrons to become positively charged cations, and the nonmetals gaining those electrons to become negatively charged anions.

The solid structure of an ionic compound is referred to as a lattice, and it is a highly organized, repeating pattern that maximizes the attraction between oppositely charged ions while minimizing repulsion between ions of the same charge. The strength of this ionic bonding influences various properties of the compound, including melting point, boiling point, and hardness.

Examples of Ionic Compounds

• Table salt (\textnormal{NaCl})
• Calcium fluoride (\textnormal{CaF}\(_2\))
• Magnesium oxide (\textnormal{MgO})

Ionic Charges

Ionic charges arise from the loss or gain of electrons, with the resulting charged atoms being called ions. In an ionic compound, the total positive charge from the cations must balance the total negative charge from the anions, leading to an electrically neutral compound.For transition metals that can form more than one cation with different charges, Roman numerals are used to indicate the ionic charge in the compound’s name. For example:

• Iron(II) indicates an iron ion with a +2 charge (\textnormal{Fe}\(^{2+}\)).
• Iron(III) indicates an iron ion with a +3 charge (\textnormal{Fe}\(^{3+}\)).

Understanding the ionic charges is key in predicting the behavior of compounds, including their reactivity and the strength of the bonds in their lattice structure.

Chemical Formulas

Chemical formulas convey important information about a compound, including the types of atoms present and the ratios in which those atoms combine. In ionic compounds, the chemical formula reflects the simplest ratio of the ions needed to balance the total positive and negative charges, ensuring that the compound is electrically neutral.

Here's how you might decipher a chemical formula:

• The subscript numbers indicate the number of ions of each element in the compound.
• For a compound like \textnormal{FeCl}\(_3\), it means that there is one Fe\(^{3+}\) ion for every three Cl\(^{-}\) ions.

Chemical formulas are essential for understanding stoichiometry, the area of chemistry that deals with the relative quantities of reactants and products in reactions.

Lattice Energy Calculation

Lattice energy is a measure of the strength of the forces holding the ions together in an ionic solid. It is defined as the energy required to separate one mole of a solid ionic compound into its constituent ions in the gaseous state.

The Born-Haber cycle is a common method used to calculate lattice energy using a series of hypothetical steps that include ionization energy, electron affinity, and sublimation energy. However, a simplified approach can be based on Coulomb's Law, where the lattice energy is directly proportional to the product of the charges of the ions (\textnormal{Q}1 × \textnormal{Q}2) and inversely proportional to the distance between their nuclei (\textnormal{r}).

It's important to remember that lattice energy is an indicative measure and can vary depending on the structure of the ionic compound. For example, aluminium oxide (\textnormal{Al}\(_2\)\textnormal{O}\(_3\)) often has a higher lattice energy than sodium chloride (\textnormal{NaCl}), despite both being ionic compounds, due to the higher charges on aluminium and oxygen ions compared to sodium and chloride ions.