Which of the following is/are ture?

Options

A. For the same solution, elevation in boiling point =depression in freezing point.
B. The Van't Hoff factor for a dilute solution of `BaCl_(2)` is `3`.
C. The elevation in boiling point is due to increase in vapour pressure.
D. The depression in freezing point is due to decrease in vapour pressure.

Explanation

To determine which of the given statements are true, let's analyze each option step by step.

### Step 1: Analyze Option A
**Statement**: For the same solution, elevation in boiling point equals depression in freezing point.

**Explanation**:
- The elevation in boiling point (\( \Delta T_B \)) and depression in freezing point (\( \Delta T_F \)) can be expressed as:
\[ \Delta T_B = i \cdot K_B \cdot m \]
\[ \Delta T_F = i \cdot K_F \cdot m \]
- Here, \( i \) is the van 't Hoff factor, \( K_B \) is the ebullioscopic constant, \( K_F \) is the cryoscopic constant, and \( m \) is the molality of the solution.
- For the same solution, since \( i \), \( K_B \), and \( K_F \) are constants, we can conclude that \( \Delta T_B \) can be equal to \( \Delta T_F \) under certain conditions. Thus, this statement is **true**.

### Step 2: Analyze Option B
**Statement**: The van 't Hoff factor for a dilute solution of BaCl2 is 3.

**Explanation**:
- BaCl2 dissociates in solution as follows:
\[ \text{BaCl}_2 \rightarrow \text{Ba}^{2+} + 2 \text{Cl}^- \]
- This means one formula unit of BaCl2 produces 3 particles (1 Ba²⁺ and 2 Cl⁻).
- Therefore, the van 't Hoff factor \( i \) for BaCl2 is indeed 3. Thus, this statement is **true**.

### Step 3: Analyze Option C
**Statement**: The elevation in boiling point is due to an increase in vapor pressure.

**Explanation**:
- The elevation in boiling point occurs because the vapor pressure of the solution is lower than that of the pure solvent. As a result, a higher temperature is required to reach the boiling point.
- Therefore, the statement that the elevation in boiling point is due to an increase in vapor pressure is incorrect. Thus, this statement is **false**.

### Step 4: Analyze Option D
**Statement**: The depression in freezing point is due to a decrease in vapor pressure.

**Explanation**:
- The depression in freezing point occurs because the vapor pressure of the solution is lower than that of the pure solvent. This decrease in vapor pressure leads to a lower freezing point.
- Thus, this statement is **true**.

### Conclusion
After analyzing all options:
- **True Statements**: A, B, and D
- **False Statement**: C

### Final Answer
The true statements are **A, B, and D**.

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