Question

For each pair, choose the compound with the smaller lattice energy, and explain your choice: (a) NaF or \(\mathrm{NaCl}\) (b) \(\mathrm{K}_{2} \mathrm{O}\) or \(\mathrm{K}_{2} \mathrm{~S}\)

Short answer

NaCl and K2S have smaller lattice energies.

Step-by-step solution

Understand Lattice Energy

Lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions. It depends on the charges of the ions and the distance between them.

Compare Charges of Ions

For both pairs, the charges on the ions are identical: +1 and -1 for NaF and NaCl, and +1 and -2 for K2O and K2S.

Analyze Ionic Radii

Look at the size of the anions. For NaF vs. NaCl, compare F- and Cl- ions. For K2O vs. K2S, compare O2- and S2- ions. Larger ionic radii will decrease lattice energy.

Identify Smaller Anion

Among the pair NaF and NaCl, F- has a smaller radius than Cl-. Between K2O and K2S, O2- has a smaller radius than S2-.

Determine Lattice Energy

Smaller anions lead to smaller interionic distances, resulting in higher lattice energy. Therefore, NaCl and K2S, both having larger anions, will have smaller lattice energies compared to NaF and K2O respectively.

Key concepts

Ionic Compounds

Ionic compounds are formed when atoms transfer electrons to or from other atoms, resulting in ions. These ions are held together by strong electrostatic forces known as ionic bonds. In an ionic compound, the positive ion (cation) and the negative ion (anion) attract each other to form a stable structure. Common examples of ionic compounds include table salt (NaCl) and potassium oxide (K2O). Ionic compounds generally have high melting and boiling points because of the strong attraction between the ions. They also tend to dissolve in water, where they can conduct electricity due to the formation of free-moving ions.
For example, NaCl is made up of Na⁺ and Cl^- ions. When NaCl dissolves in water, the Na⁺ and Cl^- ions move freely, allowing the solution to conduct electricity.

Ionic Radii

The ionic radius is the measure of the size of an ion. It plays a crucial role in determining the properties of an ionic compound, including its lattice energy. The size of the ion influences the distance between the ions in the crystal lattice. Smaller ions can pack more closely together, leading to stronger attractions and higher lattice energies.
For instance, in NaF and NaCl, the F^- ion is smaller than the Cl^- ion. This results in a stronger attraction between Na⁺ and F^- compared to Na⁺ and Cl^-. Therefore, NaF has a higher lattice energy than NaCl.
As a general rule, as you move down a group in the periodic table, the ionic radius increases due to additional electron shells. This reduces the lattice energy because the ions are further apart, weakening their attraction.

Ion Charges

Ion charges are another critical factor affecting lattice energy. The charge on an ion is determined by the number of electrons lost or gained. Ions with higher charges create stronger electrostatic forces, resulting in higher lattice energies.
For example, in K2O and K2S, we see charges of +1 on K⁺ and -2 on O^2-, compared to +1 on K⁺ and -2 on S^2-. The K⁺ and O^2- combination leads to a stronger attraction and higher lattice energy than the combination of K⁺ and S^2- due to the smaller ionic radius of O^2-.
In summary, higher ion charges mean greater forces of attraction between the ions, resulting in higher lattice energy. Conversely, lower charges will result in lower lattice energy due to weaker attractions.