During depression in freezing point in a solution, the following are in equilibrium:

Liquid solvent, solid solvent

The correct answer is option 1. Liquid solvent, solid solvent.

When a non-volatile solute is added to a solvent, the freezing point of the solvent decreases. This phenomenon is known as freezing point depression and is a colligative property, which depends on the number of solute particles in the solution rather than the type of solute.

Understanding the Equilibrium: In a solution where freezing point depression occurs, the system reaches equilibrium between the following two phases:

Liquid Solvent: The solvent in its liquid state, where the molecules are in a fluid arrangement.

Solid Solvent: The solvent in its solid state, where the molecules are arranged in a crystalline lattice.

When a solute is added to the solvent, the freezing point of the solvent decreases. This happens because the solute particles disrupt the formation of the solid lattice structure of the solvent. As a result, the temperature needs to be lowered further for the solvent to solidify.

Equilibrium Dynamics:

At any given temperature below the freezing point of the pure solvent:

Liquid Solvent: This is the phase present in the solution due to the lowered freezing point.

Solid Solvent: This is the solid phase that would be present if the temperature were further reduced to reach the new freezing point.

The equilibrium here is between the liquid and solid phases of the solvent. The presence of the solute prevents the solvent from freezing at its original freezing point, thus lowering the temperature at which the solid phase forms.

Why Other Options Are Not Correct:

1. Liquid Solvent, Solid Solute: This option refers to the phases involving the solute, which is not relevant to the freezing point depression of the solvent.

2. Liquid Solute, Solid Solute: This describes the phases of the solute, not the solvent, which is central to the concept of freezing point depression.

3. Liquid Solute, Solid Solvent: This describes a situation where the solute is liquid and the solvent is solid, which is not related to the freezing point depression of the solvent.

Summary: The correct description for the equilibrium involved in freezing point depression is: Liquid solvent, Solid solvent.

This equilibrium highlights the interaction between the liquid and solid phases of the solvent in the presence of a solute, which affects the temperature at which the solvent transitions to its solid phase.