The cryoscopic constant value depends upon:

Options

A. the molar mass of the solute in the solution
B. the molar mass of the sovent in the solution
C. the enthalpy of fusion of the sovent
D. the freezing point of the solvent

Answer

To determine what the cryoscopic constant value (Kf) depends upon, we can analyze the relationship between the freezing point depression and the properties of the solute and solvent.

### Step-by-step Solution:

1. **Understanding Cryoscopic Constant (Kf)**:
- The cryoscopic constant (Kf) is a property of the solvent that indicates how much the freezing point of the solvent will decrease when a solute is added. It is also known as the molar depression constant.

2. **Freezing Point Depression Formula**:
- The relationship between the freezing point depression (ΔTf), the cryoscopic constant (Kf), and the molality (m) of the solution is given by the formula:
\[ \Delta Tf = Kf \times m \]
- Here, ΔTf is the change in the freezing point, and m is the molality of the solution.

3. **Molality Definition**:
- Molality (m) is defined as the number of moles of solute per kilogram of solvent. It can be expressed as:
\[ m = \frac{\text{Weight of solute (g)}}{\text{Molecular weight of solute (g/mol)} \times \text{Weight of solvent (kg)}} \]

4. **Factors Affecting Kf**:
- The cryoscopic constant (Kf) is influenced by several factors:
- **Molar Mass of the Solute**: Kf depends on the molar mass of the solute because it affects the number of moles present in a given weight of solute.
- **Freezing Point of the Solvent (Tf)**: Kf is also dependent on the freezing point of the pure solvent, as it dictates how much the freezing point will change.
- **Enthalpy of Fusion (ΔHf)**: Kf is influenced by the latent heat of fusion of the solvent, which affects the energy required for the phase change from solid to liquid.

5. **Conclusion**:
- Therefore, the cryoscopic constant (Kf) depends on:
- The molar mass of the solute (A)
- The freezing point of the solvent (C)
- The enthalpy of fusion of the solvent (D)
- It does not depend on the molar mass of the solvent (B).

### Final Answer:
The cryoscopic constant value (Kf) depends on:
- A. Molar mass of the solute
- C. Freezing point of the solvent
- D. Enthalpy of fusion of the solvent