Problem 142 - A Complete Resource Book in Chemistry for JEE Main

Question

Sodium sulphate is soluble in water whereas barium sulphate is sparingly soluble because (a) The hydration energy of sodium sulphate is more than its lattice energy (b) The lattice energy of barium sulphate is more than its hydration energy (c) The lattice energy has no role to play in solubility (d) The hydration energy of sodium sulphate is less than its lattice energy.

Step-by-Step Solution

Answer

(b) The lattice energy of barium sulphate is more than its hydration energy.

Step 1: Understanding the Concept of Solubility

Solubility of ionic compounds in water depends on the balance between lattice energy and hydration energy. Lattice energy is the energy required to separate ions in a crystal lattice and hydration energy is the energy released when ions interact with water molecules. Solubility is favored when hydration energy is greater than lattice energy.

Step 2: Analyzing Sodium Sulphate Solubility

Sodium sulphate is soluble in water because the interaction between water molecules and the sodium and sulphate ions (hydration energy) is strong enough to overcome the forces holding the ions together in the solid (lattice energy). Therefore, the hydration energy of sodium sulphate is higher than its lattice energy.

Step 3: Analyzing Barium Sulphate Solubility

Barium sulphate is sparingly soluble because its lattice energy is very high, making it difficult to separate the ions. The hydration energy released when barium and sulphate ions dissolve in water is not sufficient to overcome the high lattice energy. Thus, in this case, the lattice energy of barium sulphate is higher than its hydration energy.

Step 4: Selecting the Correct Option

Based on the above analysis, sodium sulphate's solubility arises because its hydration energy exceeds its lattice energy, while barium sulphate's low solubility is due to its lattice energy being higher than its hydration energy. Therefore, the second option (b) correctly explains why barium sulphate is sparingly soluble.

Key Concepts

Lattice Energy

Lattice energy is a key concept in understanding the solubility of ionic compounds. It refers to the amount of energy required to completely separate a mole of solid ionic compound into its gaseous ions.
This energy is always positive, as it requires energy input to break the attractive forces between the oppositely charged ions.
Stronger attractions between ions result in higher lattice energy. Factors influencing lattice energy include:

• Ion Size: Smaller ions have stronger attractions because they can get closer to each other, increasing lattice energy.
• Ion Charge: Ions with higher charges have stronger attractions, also leading to higher lattice energy. For instance, in comparing \( \text{Ba}^{2+} \) to \( \text{Na}^{+} \), the former has a higher charge, contributing to a higher lattice energy for barium compounds.

In terms of solubility, a high lattice energy can mean that a lot of energy is needed to separate the ions, thus making some compounds, like barium sulphate, less soluble.

Hydration Energy

Hydration energy is essential in determining how well an ionic compound can dissolve in water. It is the energy released when ions are surrounded by water molecules.
Water, being a polar molecule, has a partial positive and a partial negative charge. This allows it to effectively interact with the ions in a compound, stabilizing them in solution. Key aspects of hydration energy:

• Ion Size: Smaller ions are more strongly hydrated because they allow water molecules to approach more closely, releasing more energy.
• Ion Charge: Higher charged ions can attract water molecules more strongly, leading to a higher release of energy upon hydration.

If the hydration energy of a compound, like sodium sulfate, is greater than the lattice energy, the compound is likely to be quite soluble, as the energy needed to separate the ions is compensated for by the energy released upon hydration.

Ionic Compounds

Ionic compounds, known for their characteristic crystal lattice structures, are composed of positively and negatively charged ions.
The overall structure is stabilized by the electrostatic attraction between these ions, giving them unique properties such as high melting points. Attributes of ionic compounds:

• Structure: The rigid and ordered crystal lattice is what gives ionic compounds their solid state at room temperature.
• Solubility: While many ionic compounds can dissolve in water, the solubility is often dependent on the balance between the lattice energy and the hydration energy.

To dissolve, the attractive forces in the crystal lattice must be overcome by hydration energy. When analyzing compounds like sodium sulfate and barium sulfate, understanding this balance explains why some ionic compounds dissolve easily while others are much less soluble.