Question

BeO is insoluble but \(\mathrm{BaO}\) is soluble as (a) lattice energy of \(\mathrm{BeO}\) is higher than \(\mathrm{BaO}\) due to small size of \(\mathrm{Be}^{2+}\) ion and its covalent nature (b) hydration energy of \(\mathrm{BeO}\) is lower than \(\mathrm{BaO}\) due to small size \(\mathrm{Be}^{2+}\) ion (c) \(\mathrm{BeO}\) is amphoteric in nature while \(\mathrm{BaO}\) is basic (d) BeO forms hydrated salts while \(\mathrm{BaO}\) forms anhydrous salts.

Short answer

BeO is insoluble whereas BaO is soluble primarily because the lattice energy of BeO is higher than that of BaO due to the small size of Be2+ ion and its covalent nature (option a).

Step-by-step solution

Evaluate Solubility Factors

When determining the solubility of ionic compounds, consider both lattice energy and hydration energy. Lattice energy is the energy required to break the ionic bond to dissolve the compound in water, while hydration energy is the energy released when the ions are surrounded by water molecules.

Compare Ionic Radii and Lattice Energy

Since Be has a smaller ionic radius than Ba, the lattice energy of BeO would be higher than that of BaO. This is because the smaller Be2+ ions can be packed more tightly in the lattice, so more energy is required to break the ionic bonds in BeO.

Assess Hydration Energy

The hydration energy depends on the size of the ion; smaller ions have higher charge densities and therefore have higher hydration energies when they interact with water molecules. In this case, even though Be2+ is smaller, its overall hydration energy is not enough to overcome the lattice energy.

Determine the Nature of the Oxides

The nature of the oxide (whether it's amphoteric or basic) does not directly affect solubility as much as lattice and hydration energies do. However, understanding the chemical nature can provide additional insights into the compound's behavior in water.

Conclusion and Selection

Based on the provided options, BeO is insoluble because its high lattice energy due to the small size of Be2+ ions and its covalent character outweighs the hydration energy. Thus, option (a) is the correct reason for the difference in solubility between BeO and BaO.

Key concepts

Lattice Energy

Lattice energy is a key factor in understanding the solubility of ionic compounds. It refers to the amount of energy required to break apart the solid crystal lattice of an ionic compound into its individual ions. This process is crucial when the compound dissolves in water. Higher lattice energy means that the compound’s ions are more strongly attracted to each other in the lattice, making it more difficult for water to break these bonds and dissolve the compound.

For instance, beryllium oxide (BeO) has a higher lattice energy compared to barium oxide (BaO) primarily due to its smaller ionic radii. The smaller size of the Be²⁺ ion allows for a more compact and strongly bonded lattice compared to the larger Ba²⁺ ion. Therefore, more energy is required to dissolve BeO in water, which contributes to its lower solubility.

Hydration Energy

Hydration energy is the energy released when water molecules surround and interact with ions from a dissolved ionic compound. When an ionic compound dissolves in water, its ions become hydrated. The energy released during this process can help to overcome the lattice energy; however, it must be sufficient to do so for the compound to be considered soluble.

Although smaller ions like Be²⁺ have higher charge densities and potentially high hydration energies, in the case of BeO, the hydration energy alone is not enough to offset its substantial lattice energy. This is why BeO has a lower solubility in water. Conversely, since BaO has a lower lattice energy and sufficient hydration energy when dissolved, it is considered soluble.

Ionic Radii

The ionic radius of an ion is the measure of its effective size. Ionic radii are pivotal in determining both lattice energy and hydration energy. Smaller ions generally have higher lattice energies because their charges are closer together, permitting stronger attractions between ions and a more tightly bonded lattice.

In contrast, ions with larger ionic radii have a more spread out charge, generating weaker interactions within the lattice and thus, lower lattice energies. However, for hydration energy, the trend is somewhat inverse; smaller ions with higher charge densities have stronger interactions with water molecules, leading to greater hydration energy. Be²⁺ has a smaller ionic radius than Ba²⁺, influencing both the high lattice and low hydration energies of BeO compared to BaO.

Amphoteric Nature

The amphoteric nature of a substance refers to its ability to behave either as an acid or as a base. In the context of solubility, an amphoteric oxide like BeO can react with both acids and bases to form products that may or may not be soluble in water. This chemical behavior adds complexity to predicting solubility because it depends on the pH of the aqueous environment.

Basic oxides such as BaO, on the other hand, only react with acids. While the amphoteric nature of BeO doesn’t directly influence its solubility in the same manner as lattice and hydration energies, it's an important chemical property that can influence the compound's interactions in different environments and consequently, its solubility in specific conditions.