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.

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.

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.

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.