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.

Which of the following represents a metastable system?

a supersaturated solution

The correct answer is option 4. a supersaturated solution.

Let us delve into the concept of metastable systems and explore why a supersaturated solution fits this description.

1. Dilute Solution: A dilute solution contains a relatively small amount of solute compared to the solvent. It may or may not be metastable, depending on the specific solute-solvent interaction and concentration. For instance, if we have a dilute solution of sugar in water, it may not necessarily be metastable; it could reach equilibrium depending on the conditions.

2. Unsaturated Solution: An unsaturated solution is in equilibrium with undissolved solute. It's stable in its current state, as it has not reached its maximum capacity for holding solute at a given temperature and pressure.

3. Saturated Solution: A saturated solution is in a state of dynamic equilibrium, where the rate of dissolution equals the rate of precipitation of solute. It's stable because any attempt to add more solute would result in immediate precipitation.

4. Supersaturated Solution: A supersaturated solution is formed when a solution contains more solute than it can normally hold at a given temperature and pressure. It's created by dissolving solute at an elevated temperature and then cooling the solution slowly, preventing precipitation. In this state, the solution is metastable because it's poised to crystallize if disturbed, such as by adding a seed crystal or shaking.

Metastability implies that a system is in a state that could easily transition to a more stable state with a slight change in conditions. In the case of a supersaturated solution, this transition occurs when the solution is disturbed, causing the excess solute to precipitate out, returning the solution to a saturated state.

So, while all the options provided are related to solutions, only the supersaturated solution fits the definition of a metastable system.