Question

When the depression in freezing point is carried out, the equilibrium exist between (a) liquid solvent and solid solvent (b) liquid solute and solid solvent (c) liquid solute and solid solute (d) liquid solvent and solid solute

Short answer

The correct answer is (a) liquid solvent and solid solvent.

Step-by-step solution

Understanding Freezing Point Depression

Freezing point depression occurs when a solute is added to a pure solvent, which results in the lowering of the freezing point of the solvent. This occurs because the solute particles disrupt the formation of the solid phase from the liquid phase, making it harder for the solvent molecules to crystallize into a solid.

Identifying the Correct States of Matter at Equilibrium

At the equilibrium point of freezing point depression, the solvent is trying to freeze. This means there will be a dynamic equilibrium between the solid and liquid phases of the solvent. The solute remains dissolved in the liquid phase and does not participate in the phase change.

Selecting the Correct Option

Based on the explanation above, the correct equilibrium during the freezing point depression exists between the liquid solvent and solid solvent, which is option (a).

Key concepts

Colligative Properties

Colligative properties are characteristics of solutions that depend on the number of dissolved particles in a given amount of solvent, rather than the specific type of particle. Freezing point depression is one such property, along with boiling point elevation, vapor pressure lowering, and osmotic pressure. When a non-volatile solute is added to a solvent, it disrupts the original properties of the pure solvent.

For example, in the case of freezing point depression, adding salt to ice lowers the temperature at which the ice melts, because the solute particles interfere with the ability of the solvent (water) molecules to form a solid structure. Mathematically, this can be expressed using the formula \( \Delta T_f = i \cdot k_f \cdot m \), where \( \Delta T_f \) is the freezing point depression, \( i \) is the van't Hoff factor representing the number of particles the solute breaks into, \( k_f \) is the freezing point depression constant specific to the solvent, and \( m \) is the molality of the solution.

Understanding colligative properties is essential because it allows us to predict how the addition of a solute will affect the freezing point of a solvent, among other properties.

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction's forward and reverse rates are equal, resulting in no net change in the concentration of reactants and products over time. However, it is a dynamic process, meaning that the molecules continue to react, but at a rate that balances out.

In the context of freezing point depression, chemical equilibrium pertains to the solid and liquid phases of the solvent. At the freezing point, a pure solvent would naturally crystallize into a solid. However, when the solute is introduced, it perturbs this equilibrium by preventing the solvent molecules from organizing into a solid structure, hence the freezing point decreases.

While the specific chemical compositions don't change, the physical process is influenced by the introduction of foreign particles. Even in this physical transition, the principles of equilibrium apply: the rate at which solvent molecules join the solid phase equals the rate at which they leave it. The presence of the solute merely shifts the temperature at which this equilibrium exists.

Phase Change

A phase change is a transition of matter from one state to another, such as from a solid to a liquid or from a liquid to a gas. These changes occur due to variations in temperature and pressure. For example, when heat is applied to ice (solid water), it absorbs energy, causing the molecules to move more vigorously, eventually overcoming the bonding forces holding them together, resulting in a phase change to liquid water.

Freezing point depression is directly related to the concept of phase change. By adding a solute to a solvent, we alter the conditions required for a phase change from liquid to solid. The solvent now requires a lower temperature to freeze because the solute molecules disrupt the orderly structure of the crystallizing solvent.

This phase change is tied to equilibrium, as it signifies a balance between the solid and liquid phases at the new, lowered freezing point. The introduction of a solute thus presents a fascinating interplay between colligative properties, chemical equilibrium, and phase changes, each of which is integral to understanding how and why the freezing point depression occurs.