The correct option is Cryoscopic constant.
Explanation
Colligative properties are properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution. One such property is the depression of the freezing point, which occurs when a non-volatile solute is added to a solvent. The magnitude of this depression is proportional to the molality of the solution.
Analysis of Options
- Cryoscopic constant is correct: The proportionality constant that relates the molality of a solution to the depression in its freezing point is called the Cryoscopic constant (represented as \(K_f\)). It is also referred to as the molal freezing point depression constant. The term is derived from the Greek word "kryos," meaning cold or frost.
- Ebullioscopic constant is incorrect: The Ebullioscopic constant (\(K_b\)) is the molal boiling point elevation constant. It relates the molality of a solution to the elevation in its boiling point.
- Osmotic constant is incorrect: The Osmotic constant is a quantity used in physical chemistry to characterize the deviation of a solvent from ideal behavior, specifically regarding osmotic pressure, but it is not the standard term for the freezing point depression constant.
- Hydraulic constant is incorrect: Hydraulic constant is a term generally associated with fluid mechanics and hydraulic conductivity, unrelated to the thermodynamic properties of solutions.
Key Takeaway: The Cryoscopic constant (\(K_f\)) relates to freezing point depression, while the Ebullioscopic constant (\(K_b\)) relates to boiling point elevation.