Question

LiF is less soluble in water than \(\mathrm{KF}\) because (1) LiF is more covalent than \(\mathrm{KF}\). (2) LiF has more lattice energy than KF. (3) LiF has higher enthalpy of hydration than \(\mathrm{KF}\). (4) Li- ions are not extensively hydrated as \(\mathrm{K}^{+}\).

Short answer

LiF is less soluble in water than KF because LiF has more lattice energy than KF.

Step-by-step solution

Analyze solubility factors

Solubility of ionic compounds in water depends on both lattice energy and hydration energy.

Understand lattice energy

Lattice energy is the energy required to separate one mole of a solid ionic compound into gaseous ions. Higher lattice energy means stronger ionic bonds, making the compound less soluble.

Compare lattice energies

LiF has a smaller cation (Li+) compared to K+ in KF. This smaller size leads to a higher lattice energy in LiF compared to KF.

Evaluate hydration energy

Hydration energy is the energy released when ions are solvated by water molecules. Smaller cations like Li+ are more hydrated than larger cations like K+.

Compare enthalpy of hydration

Although Li+ is more extensively hydrated, the lattice energy is a more determining factor for solubility. The higher lattice energy of LiF makes it less soluble than KF.

Conclusion

LiF is less soluble in water than KF primarily due to its higher lattice energy.

Key concepts

Lattice Energy

To understand why LiF is less soluble in water than KF, we need to consider lattice energy. Lattice energy is the energy required to separate one mole of an ionic solid into its gaseous ions. Higher lattice energy indicates a stronger force holding the ions together in the solid state.
Because Li+ is smaller than K+, the ions in LiF are more tightly packed. This leads to stronger attractions between ions, resulting in higher lattice energy for LiF compared to KF.
Higher lattice energy makes it harder for the compound to dissolve since more energy is needed to break these strong ionic bonds.

Hydration Energy

Hydration energy is the energy released when ions are surrounded by water molecules. This process is exothermic because energy is released.
Smaller ions, like Li+, have higher hydration energies because they are more strongly attracted to water molecules due to their higher charge density.
Though Li+ has a higher hydration energy than K+, this is not the main factor determining its solubility in this context. The lattice energy has a greater impact on LiF being less soluble.

Ionic Bonds

Ionic bonds form between positively charged cations and negatively charged anions. The strength of these bonds depends on the charges of the ions and their sizes.
Larger ions generally form weaker ionic bonds compared to smaller ions with similar charges.
In the case of LiF and KF, the bond strength in LiF is stronger because Li+ is smaller than K+, which contributes to the higher lattice energy of LiF.

Cation Size

The size of the cation plays a crucial role in determining the lattice energy and hydration energy.
Smaller cations like Li+ are more densely charged, leading to higher lattice energy and stronger hydration energy.
This means that while Li+ interacts more strongly with water molecules, leading to higher hydration energy, the higher lattice energy of LiF makes it less soluble compared to KF, which has the larger K+ ions.

Enthalpy of Hydration

The enthalpy of hydration refers to the heat change when one mole of ions dissolves in water.
While Li+ has a higher enthalpy of hydration than K+ due to the smaller size and higher charge density, this contribution is lesser compared to the dominant effect of lattice energy in determining solubility.
Thus, despite the higher enthalpy of hydration, LiF remains less soluble because its higher lattice energy requires more energy to dissociate into individual ions in water.