Cryoscopic constant of a liquid is:

Options

A. decreases in freezing point when 1 gram of solute is dissolved per kg of the solvent
B. decreases in the dreezing point when 1 mole of solute is dissolved per kg of the solvent
C. the elevation for 1 molar solution
D. a factor used for calculation of elevation in boiling point

Explanation

To solve the question regarding the cryoscopic constant of a liquid, we need to understand the definition and significance of the cryoscopic constant (Kf). The cryoscopic constant is a property of a solvent that indicates how much the freezing point of the solvent will decrease when a solute is added.

### Step-by-Step Solution:

1. **Understanding Cryoscopic Constant (Kf)**:
- The cryoscopic constant (Kf) is defined as the decrease in the freezing point of a solvent when one mole of solute is dissolved in one kilogram of that solvent.
- Mathematically, this is represented as:
\[ \Delta T_f = K_f \times m \]
where \(\Delta T_f\) is the depression in freezing point and \(m\) is the molality of the solution.

2. **Analyzing the Options**:
- **Option A**: Decrease in freezing point when one gram of solute is dissolved per kg of solvent.
- **Option B**: Decrease in freezing point when one mole of solute is dissolved per kg of solvent.
- **Option C**: Elevation of one molar solution, a factor used for calculation of elevation in boiling point.
- **Option D**: Not applicable as it refers to boiling point.

3. **Eliminating Incorrect Options**:
- **Option C** is incorrect because it refers to boiling point elevation, which is not related to the cryoscopic constant (Kf).
- **Option D** is also incorrect as it pertains to boiling point rather than freezing point.
- **Option A** is incorrect because the cryoscopic constant is defined per mole of solute, not per gram.

4. **Identifying the Correct Option**:
- **Option B** is correct because it accurately describes the cryoscopic constant: it is the decrease in freezing point when one mole of solute is dissolved per kg of solvent.

### Final Answer:
The cryoscopic constant of a liquid is the decrease in freezing point when one mole of solute is dissolved per kg of solvent.

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