Problem 160 - A Complete Resource Book in Chemistry for JEE Main

Question

The solubilities of carbonates decrease down the magnesium group due to thedecrease in [2003] (a) inter ionic interaction (b) lattice energies of solids (c) entropy of solution formation (d) hydration energies of cations

Step-by-Step Solution

Answer

(d) hydration energies of cations

Step 1: Understand Ionic Solubility

The solubility of ionic compounds in water involves two primary energies: lattice energy and hydration energy. Lattice energy is the energy needed to separate the ions in a solid lattice to an infinite distance apart. Hydration energy is the energy released when ions are surrounded by water molecules.

Step 2: Identify the Trend

As you move down the magnesium group (Mg, Ca, Sr, Ba), the size of the cations increases. Larger ions have lower charge density, affecting both lattice energy and hydration energy differently.

Step 3: Analyze Lattice and Hydration Energies

Lattice energy generally decreases as cation size increases because the larger ions do not pack as closely together. However, hydration energy decreases more significantly for larger ions, as they are not as strongly attracted to water molecules.

Step 4: Determine Dominant Factor

Between the two influences, the decrease in hydration energy down the group is the dominant factor in reducing the overall solubility of carbonates. While both lattice and hydration energies change, hydration energy has a greater impact on solubility trends.

Step 5: Choose the Correct Answer

Given the options, the dominant reason for the decrease in solubility of carbonates down the magnesium group is the decrease in hydration energies of the cations.

Key Concepts

Lattice Energy

Lattice energy plays a critical role in the formation of ionic compounds. It is the energy required to completely separate a mole of a solid ionic compound into its gaseous ions. Essentially, lattice energy relates to the strength of the ionic bonds within a crystal lattice. A high lattice energy indicates strong forces holding the ions together, making it harder for the compound to dissolve. This energy differs based on:

• The charges of the ions: Higher charges result in higher lattice energies due to stronger attractions.
• The size of the ions: Smaller ions lead to closer packing and thus higher lattice energies.

As you move down the magnesium group (Mg, Ca, Sr, Ba), ions become larger and the spacing between them in the lattice increases. This results in a decrease in lattice energy, as larger ions experience weaker forces of attraction due to their increased distance. Although lattice energy decreases with larger ions, its impact on solubility is not as dominant as hydration energy.

Hydration Energy

Hydration energy refers to the amount of energy released when ions in the gaseous state become surrounded by water molecules, forming a hydration shell. It significantly affects the solubility of ionic compounds. Strong attractions between the ions and water molecules result in high hydration energy, facilitating dissolution.

• Larger ions have lower hydration energy. They have more diffuse charge distributions, resulting in weaker interactions with water.
• The charge of the ion also affects hydration energy. Ions with higher charges generally exhibit stronger attraction to water.

In the case of alkali earth metals (like those in the magnesium group), as you move down the group, the cation size increases. Larger cations interact less strongly with water molecules, leading to decreased hydration energy. This reduction in hydration energy is more significant than changes in lattice energy and is the primary factor affecting solubility trends within the group.

Ionic Solubility

Ionic solubility is fundamentally about the ability of a compound to dissolve in a solvent, like water. For ionic substances, solubility is influenced by a balance between lattice and hydration energies. The solubility process can be understood through these steps:

• The ionic compound dissociates in the solvent, a process primarily counteracted by the strength of lattice energy.
• The dissociated ions become surrounded by water molecules, releasing energy termed as hydration energy.

The solubility of carbonates in the magnesium group decreases as you move down the group. This is largely attributed to the decrease in hydration energy, which overpowers the corresponding decrease in lattice energy. Even though larger ions mean lower lattice energy and reduced packing efficiency, the decrease in hydration energy has a greater effect, resulting in reduced solubility.

Magnesium Group Elements

The magnesium group consists of alkaline earth metals: magnesium (Mg), calcium (Ca), strontium (Sr), and barium (Ba). These elements exhibit clearly defined trends across the group based on their position in the periodic table.

• Size of Cations: As you go down the group, the cation size increases. Larger cations have a lower charge density.
• Chemical Reactivity: Reactivity tends to increase with size increase. Barium is more reactive than magnesium.
• Solubility Trends: Down the group, their carbonates become less soluble in water. This is due to decreasing hydration energy of the larger ions, as previously explained.

Understanding these trends within the magnesium group helps explain many chemical behaviors, including the challenges and limitations associated with their industrial and biological applications.