Question

Lithium salts are often much less soluble in water than the corresponding salts of other alkali metals. For example, at \(18^{\circ} \mathrm{C}\). the concentration of a saturated LiF solution is \(1.0 \times 10^{-2} \mathrm{M}\) whereas that of a saturated KF solution is \(1.6 M .\) How can you explain this behavior?

Short answer

LiF is less soluble due to its higher lattice energy compared to KF, even though both have favorable solvation energies.

Step-by-step solution

Understand the Problem

Lithium salts like LiF are much less soluble in water compared to salts of other alkali metals, such as KF. The given concentrations of saturated solutions are 1.0 x 10^{-2} M for LiF and 1.6 M for KF.

Analyze Lattice Energy

Consider the lattice energy, which is the energy required to separate the ions in an ionic solid. Lithium ions (Li+) are smaller in size compared to potassium ions (K+), which means the lattice energy of LiF is higher than that of KF.

Solvation Energy

Think about the solvation energy, which is the energy released when ions are solvated by water molecules. Smaller ions like Li+ also have higher solvation energy when compared to larger ions like K+.

Compare Lattice and Solvation Energies

The solubility of an ionic compound in water depends on the competition between lattice energy and solvation energy. Despite the higher solvation energy for smaller ions, the much higher lattice energy of LiF (because Li+ is very small) limits its solubility. For KF, the lower lattice energy relative to its solvation energy makes it more soluble.

Conclusion

Thus, the higher lattice energy of LiF compared to KF results in its much lower solubility despite the favorable solvation energy.

Key concepts

Lattice Energy

Lattice energy is a crucial factor influencing the solubility of ionic compounds. It is the energy released when oppositely charged ions in the gas phase come together to form an ionic solid. Smaller ions tend to release more energy when they form a lattice, which means their lattice energy is higher.

For lithium salts like LiF, the lithium ion (Li⁺) is much smaller compared to a potassium ion (K⁺). This small size leads to a high lattice energy because the ions can pack closely together, increasing the attraction between them.

High lattice energy makes it harder for the ionic compound to dissolve because more energy is required to break apart the solid crystal lattice into individual ions.

Solvation Energy

Solvation energy is the energy released when ions from an ionic compound are surrounded by solvent molecules, in this case, water.

Generally, smaller ions like Li⁺ exhibit higher solvation energies because they are more attracted to the polar water molecules. This attraction results in the release of more energy when they are solvated. For example, Li⁺'s smaller size allows it to interact more closely with the water molecules, enhancing the solvation process.

Despite the higher solvation energy, in some cases, this is not sufficient to overcome the lattice energy, affecting the ionic compound's overall solubility.

Ionic Compounds Solubility

The solubility of ionic compounds in water is a balancing act between lattice energy and solvation energy.

For salts like LiF, the high lattice energy due to the small size of Li⁺ ions means that a lot of energy is required to disrupt the solid structure. Even though Li⁺ ions have a high solvation energy, it often isn't enough to overcome the large lattice energy, leading to lower solubility.

Conversely, in salts like KF, K⁺ ions are larger, resulting in lower lattice energy. The energy required to separate K⁺ and F⁻ ions is less, and although the solvation energy of K⁺ is lower compared to Li⁺, it is adequate to dissolve more KF in water.

In summary, the solubility of ionic compounds is determined by the relative magnitudes of lattice energy and solvation energy.