Question

Consider two ionic solids, both composed of singly charged ions, that have different lattice energies. (a) Will the solids have the same solubility in water? (b) If not, which solid will be more soluble in water, the one with the larger lattice energy or the one with the smaller lattice energy? Assume that solute-solvent interactions are the same for both solids. [Section 13.1\(]\)

Short answer

(a) No, the two ionic solids will not have the same solubility in water since they have different lattice energies. (b) The ionic solid with the smaller lattice energy will be more soluble in water, as it has weaker ionic attractions and can dissolve more easily.

Step-by-step solution

Understanding Solubility

The solubility of an ionic solid in water mainly depends on the balance between the lattice energy, which holds the solid together, and the solvation energy, which is the energy released when ions are solvated (surrounded by water molecules). In this exercise, we will assume that the solute-solvent interactions are the same for both solids.

Comparing Lattice Energies

We are given that both ionic solids have different lattice energies. Lattice energy is the energy required to separate one mole of an ionic solid into its constituent ions. If an ionic solid has higher lattice energy, it means the attraction between its ions is stronger, which makes it harder to dissolve in water.

Answering (a)

Since the lattice energies are different for both ionic solids, their solubilities in water will also be different. If the lattice energy is higher, it will be harder for the solid to dissolve in water, while a lower lattice energy will result in higher solubility.

Answering (b)

As we concluded in step 2, the solubility of an ionic solid is inversely proportional to the lattice energy. Therefore, the ionic solid with the smaller lattice energy will be more soluble in water, as it has weaker ionic attractions and can dissolve more easily.

Key concepts

Lattice Energy

Lattice energy plays a critical role in understanding the solubility of ionic solids. It represents the energy needed to break the ionic bonds within a crystalline lattice, separating the compound into its individual ions. A high lattice energy indicates a strong attraction between the negatively and positively charged ions, implying that more energy is required to disassemble the lattice structure.

For example, when comparing the solubility of different ionic compounds, those with lower lattice energies are typically more soluble in a solvent like water. This is because less energy is required to overcome the attractions holding the ions in place. When the energy barrier is lower, the solvent molecules can more readily hydrate the ions, leading to increased solubility.

In the context of our exercise, an ionic solid with a lower lattice energy would have higher solubility in water because it's easier for water molecules to separate the ions and dissolve the solid.

Solvation Energy

Solvation energy refers to the energy released when solute particles are surrounded by solvent molecules, a process known as solvation. In an aqueous solution, water molecules exhibit a strong tendency to organize around the ions due to their dipolar nature. This is energetically favorable and results in the release of energy, which is the solvation energy.

When considering ionic solids dissolving in water, the solvation energy works against the lattice energy. If solvation energy is greater than the lattice energy, the compound is likely to dissolve, as there is enough energy being released to compensate for the energy needed to break the lattice apart.

Through understanding the interplay between lattice energy and solvation energy, students can better predict the solubility of ionic solids. For instance, if an ionic solid has a high lattice energy but also has a very high solvation energy when interacting with water, it may still be quite soluble.

Solute-Solvent Interactions

Solute-solvent interactions are the forces that occur between the molecules or ions of the solute and the molecules of the solvent. In an aqueous solution, water molecules interact with solute ions by orienting the partially negative (oxygen) and partially positive (hydrogen) ends toward the oppositely charged ions.

Strong solute-solvent interactions facilitate solvation and can increase solubility. This is crucial in understanding why some ionic solids dissolve better in certain solvents than in others. The 'like dissolves like' principle often guides these interactions: polar solvents generally dissolve polar solutes effectively because of their similar natures.

In our exercise scenario, we are assuming equal solute-solvent interactions for both solids to isolate the effect of lattice energy on solubility. However, in real-world scenarios, differences in these interactions can be just as important as lattice and solvation energies in determining the solubility of an ionic compound in a particular solvent.