Consider the given plots of vapour pressure (VP) vs temperature (T/K). Which amongst the following options is correct graphical representation  showing  $$\Delta T_f,$$  depression in the freezing point of a solvent in a solution?

1. Vapor Pressure Lowering:

   The addition of a non-volatile solute lowers the vapor pressure of the liquid solvent. Therefore, at any given temperature, the vapor pressure curve of the solution always lies below the vapor pressure curve of the pure liquid solvent.

2. Definition of Freezing Point:

   The freezing point is the specific temperature at which the liquid phase and the solid phase of a substance coexist in dynamic equilibrium, meaning they have the exact same vapor pressure.

3. Intersection Points on the Graph:

   • The freezing point of the pure solvent ($$T_f^0$$) is determined by the intersection of the liquid solvent curve with the frozen (solid) solvent curve.
   • The freezing point of the solution ($$T_f$$) is determined by the intersection of the solution curve with the frozen (solid) solvent curve.

Deducing the Correct Graph:

Because the solution curve lies below the pure liquid solvent curve, its intersection with the steep frozen solvent line occurs at a lower temperature compared to the pure liquid solvent:

$$T_f < T_f^0$$

The depression in freezing point ($$\Delta T_f$$) is the horizontal distance between these two temperatures on the temperature ($$T/K$$) axis:

$$\Delta T_f = T_f^0 - T_f$$

The correct graph must clearly show three distinct lines: the pure liquid solvent (top curve), the solution (bottom curve), and the frozen solvent (steep intersecting line), with $$\Delta T_f$$ representing the drop in freezing temperature along the x-axis.