Solubility of a substance is its maximum amount that can be dissolved in a specified amount of solvent at a specified temperature. Solubility of a substance depends upon the nature of solute and solvent as well as temperature and pressure. A saturated solution is a solution that is in equilibrium with an excess of solid at a given temperature. A solution that contains a high concentration of solute than does a saturated solution is known as supersaturated solution. If a small crystal of solute is added to a supersaturated solution, the solid will at once crystallize out and an equilibrium will be established. This is known as seeding. More the dielectric constant of a solvent, more is the solubility of polar covalent or ionic compounds in it. Some covalent compounds dissolve in water due to hydrolysis while some other covalent solids dissolve in water due to hydrogen bonding. Ionic compounds dissolve in polar solvents while covalent compounds dissolve in non-polar solvents and this is known as like dissolves like.

The solubilities of ionic compounds often but not always increase with temperature, because energy is required to pull the molecules or ions away from the crystal lattice (lattice energy) \(\Delta H_L\).

Energy is also liberated due to solvation of the solute particles. If the solvent is water, the energy liberated due to solvation is known as hydration energy \(\Delta H_h\).

The energy change when one mole of ionic compound dissolves in water is \(\Delta H_{sol}\).

\[\Delta H_{sol} = \Delta H_h - \Delta H_L\]

Since the hydration energies of the ions and the lattice energy are exothermic changes, they have a negative sign. If \(\Delta H_h\) is more than \(\Delta H_L\), then \(\Delta H_{sol}\) will be negative and the ionic crystal dissolves exothermically.

A solid dissolves in water if

Lattice energy is less than hydration energy

The correct answer is option 2. Lattice energy is less than hydration energy

Let us delve into detail:

Lattice Energy:

Lattice energy is the energy required to break the bonds within the crystal lattice of a solid. It is an indicator of the strength of the forces holding the particles together in the solid state.

For ionic compounds, like salts, the lattice energy is associated with the electrostatic forces between positively and negatively charged ions in the crystal structure.

Hydration Energy:

When a solute dissolves in water, it interacts with water molecules. The energy released when these interactions occur is known as hydration energy.

Water is a highly polar molecule, and it can surround and stabilize ions or polar molecules, reducing the overall energy of the system.

Dissolution Process:

When a solid dissolves in water, it involves breaking the bonds within the solid (requiring energy) and forming new interactions with water molecules (releasing energy).

If the energy required to break the bonds in the solid (lattice energy) is less than the energy released when the solute interacts with water (hydration energy), the overall process is exothermic and favorable.

Explanation for Option 2: Lattice Energy is Less than Hydration Energy:

If the lattice energy is relatively low (indicating weaker bonds in the solid) compared to the hydration energy (indicating strong interactions between the solute and water molecules), then the overall process is energetically favorable.

In this case, the attractive forces between the solute particles are overcome by the interactions with water molecules, leading to the dissolution of the solid in water.

In Summary:

If the lattice energy is less than the hydration energy, the overall process of dissolution is favorable, and the solid will dissolve in water.

If the lattice energy is greater than the hydration energy, the process is not energetically favorable, and the solid may not dissolve in water under normal conditions.

Dissolution being exothermic (Option 4) is a common characteristic, but it's not the decisive factor. The relative magnitudes of lattice energy and hydration energy determine whether a solid will dissolve in water.

Here's why the other options are incorrect:

1. Lattice energy is greater than hydration energy: If the energy required to break apart the crystal lattice (lattice energy) is greater than the energy released when the ions interact with water molecules (hydration energy), the solid will not dissolve. The strong attraction between ions in the lattice will overcome the weaker attraction of water molecules.

3. Lattice energy is equal to hydration energy: This is a rare situation where the opposing energies cancel each other out, and the solid might be in equilibrium with its saturated solution. However, it wouldn't readily dissolve.

4. Dissolution is exothermic: While an exothermic dissolution process (releasing heat) is generally favorable, it's not the sole criterion for solubility. An endothermic process (absorbing heat) can also occur if the hydration energy significantly outweighs the lattice energy.

Therefore, for a solid to dissolve in water, the energy gained from hydration (interaction with water) must be greater than the energy required to overcome the crystal lattice forces. This means the lattice energy must be less than the hydration energy.