Generalized solubility rule IV in section 3.2 says that many...

Generalized solubility rule IV in section 3.2 says that many feebly acidic cations and feebly basic anions give insoluble salts. Both $\mathrm{Li}^{+}$and $\mathrm{Ba}^{2+}$ are feebly acidic cations, and $\mathrm{NO}_2^{-}, \mathrm{ClO}_2^{-}, \mathrm{SO}_4{ }^{2-}$, and $\mathrm{SeO}_4{ }^{2-}$ are all feebly basic anions. Although $\mathrm{BaSO}_4$ and $\mathrm{BaSeO}_4$ are indeed insoluble, $\mathrm{Ba}\left(\mathrm{NO}_2\right)_2$, $\mathrm{Ba}\left(\mathrm{ClO}_2\right)_2, \mathrm{Li}_2 \mathrm{SO}_4$, and $\mathrm{Li}_2 \mathrm{SeO}_4$ are all soluble. Can you explain this?

Key Concepts

Ionic Size and Charge Density Effects

The size of an ion and its charge density are key factors affecting both lattice and hydration energies. Smaller ions or those with higher charge density tend to have stronger interactions with water molecules, often resulting in high hydration energies that can promote solubility. Conversely, larger ions or those with lower charge densities may contribute to lower hydration energies and possibly higher lattice energies, impacting solubility. These factors help explain differences in solubility even among salts formed from ions with similar acid–base characteristics.

Hydration Energy

Hydration energy is the energy released when ions interact with water molecules as they become solvated. When the hydration energy is high enough to overcome the lattice energy of the salt, the ions are released into solution, leading to higher solubility. The balance between lattice energy and hydration energy is critical in determining whether a particular salt will dissolve in water.

Acid?Base Properties of Ions

Ions can display weak acidic or basic behavior in water, which influences their interaction with other species. Feebly acidic cations and feebly basic anions tend to form salts that might be expected to be insoluble due to their reluctance to further interact with water. However, other factors such as lattice energy and hydration can override these tendencies, leading to unexpected solubility behavior in some cases.

Generalized Solubility Rules

These rules provide empirical guidelines for predicting whether an ionic compound will dissolve in water. They are based on common trends observed for different combinations of ions but have exceptions. In practice, the overall solubility of a salt depends on a balance of forces, and while the rules serve as a starting point, factors such as lattice energy and hydration energy often dictate the final outcome.

Lattice Energy

Lattice energy is the energy released when oppositely charged ions come together to form a solid crystal lattice. High lattice energies make a salt more energetically stable as a solid and typically reduce its solubility because a greater amount of energy is required to separate the ions in water. Variations in lattice energy among compounds can explain why some salts are insoluble despite following general solubility rules.

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