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

The appropriate lattice energies for each compound are: \(\mathrm{Fe}_{2} \mathrm{O}_{3}: -14,774 \mathrm{~kJ/mol}\), \(\mathrm{FeCl}_{3}: -5359 \mathrm{~kJ/mol}\), and \(\mathrm{FeCl}_{2}: -2631 \mathrm{~kJ/mol}\). This is based on the trend \(\mathrm{Fe}_{2} \mathrm{O}_{3} > \mathrm{FeCl}_{3} > \mathrm{FeCl}_{2}\), as lattice energy generally increases with increasing ionic charge, and \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) has the largest charges on both cation and anion.

Step-by-step solution

Compare charges of the ions in the given compounds

First, we need to determine the charges of the ions in each compound. This will help us understand their potential lattice energies. For \(\mathrm{FeCl}_{3}\): Iron (Fe) has a charge of +3 and Chloride (Cl) has a charge of -1. For \(\mathrm{FeCl}_{2}\): Iron (Fe) has a charge of +2 and Chloride (Cl) has a charge of -1. For \(\mathrm{Fe}_{2} \mathrm{O}_{3}\): Iron (Fe) has a charge of +3 and Oxygen (O) has a charge of -2.

Predict the trend in lattice energies based on ion charges

Recall that lattice energy generally increases with increasing ionic charge. Comparing the charges in the compounds, we can predict the following trend in lattice energies: $$ \mathrm{Fe}_{2} \mathrm{O}_{3} > \mathrm{FeCl}_{3} > \mathrm{FeCl}_{2} $$ This is because in \(\mathrm{Fe}_{2} \mathrm{O}_{3}\), the charges on both the cation and anion are larger than in the other two compounds. In \(\mathrm{FeCl}_{3}\), we have Fe with a larger charge than in \(\mathrm{FeCl}_{2}\), so its lattice energy is expected to be larger than \(\mathrm{FeCl}_{2}\).

Match lattice energies to their respective compounds

Based on our predicted trend in Step 2, we can now match the given lattice energy values to their respective compounds. We are given the following lattice energy values (in kJ/mol): - \(-14,774\) - \(-5359\) - \(-2631\) Since \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is expected to have the largest lattice energy, we match the largest value (\(-14,774\)) to this compound. Similarly, we match the smallest value (\(-2631\)) to \(\mathrm{FeCl}_{2}\), which is expected to have the smallest lattice energy, and the middle value (\(-5359\)) to \(\mathrm{FeCl}_{3}\). So, the matched lattice energies for each compound are: - \(\mathrm{Fe}_{2} \mathrm{O}_{3}: -14,774 \mathrm{~kJ/mol}\) - \(\mathrm{FeCl}_{3}: -5359 \mathrm{~kJ/mol}\) - \(\mathrm{FeCl}_{2}: -2631 \mathrm{~kJ/mol}\)

Key concepts

Ionic Compounds

Ionic compounds are formed when metals and non-metals combine, with metals losing electrons to become positively charged ions, and non-metals gaining electrons to become negatively charged ions. These oppositely charged ions attract each other, creating strong ionic bonds.

Some key characteristics of ionic compounds include:

• High melting and boiling points due to strong attractions between ions.
• Typically soluble in water, allowing the ions to move freely and conduct electricity.
• Form crystalline structures, leading to rigid and brittle materials.

Examples such as \(\mathrm{FeCl}_{3}\), \(\mathrm{FeCl}_{2}\), and \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) showcase these properties as they form from iron and either chloride or oxygen ions.

Ion Charges

Understanding ion charges is crucial when studying ionic compounds. These charges result from the loss or gain of electrons, leading to positively or negatively charged ions. For example, in \(\mathrm{FeCl}_{3}\), iron (Fe) loses three electrons to become \(\mathrm{Fe}^{3+}\), while chloride (Cl) gains one electron to become \(\mathrm{Cl}^{-}\).

In \(\mathrm{Fe}_{2}\mathrm{O}_{3}\), iron forms \(\mathrm{Fe}^{3+}\) ions, and oxygen becomes \(\mathrm{O}^{2-}\) ions. These varying charges influence the strength of the ionic bonds and affect physical properties like lattice energy. Knowing the charges helps us predict how these compounds behave in different chemical reactions.

Lattice Energy Trend

Lattice energy is the energy released when ions in a gaseous state form an ionic solid. It indicates the strength of the ionic bonds, and its magnitude is influenced by the charges and sizes of the ions involved.

Key factors affecting lattice energy include:

• Ion Charge: Greater charges result in stronger attractions and higher lattice energy. For instance, \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) has a higher lattice energy than \(\mathrm{FeCl}_{2}\) due to the higher ionic charges.
• Ion Size: Smaller ions are closer together, increasing attraction and lattice energy.

This concept explains why \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) has the highest lattice energy among the given compounds. Understanding these trends allows chemists to predict the properties and stability of ionic compounds.

Chemical Formulas

Chemical formulas represent the types and numbers of atoms in a compound. They not only show the elemental composition but also provide insight into the charges and bonding patterns.

For example, \(\mathrm{FeCl}_{3}\) informs us that one iron atom combines with three chloride ions, totaling a neutral charge due to \(\mathrm{Fe}^{3+}\) balancing \(\mathrm{Cl}^{-}\) ions.

In the formula \(\mathrm{Fe}_{2}\mathrm{O}_{3}\), two iron ions combine with three oxide ions. The subscript numbers in the formula indicate how many of each type of ion are present. Recognizing how these formulas correlate with ion charges helps in understanding compound formation and reaction behavior, serving as a pivotal skill in chemistry.