Select the correct statement (s) :

Options

A. When solid `CaCl_(2)` is added to liquid water , the boiling point temperature rises
B. When solid `CaCl_(2)` is added to ice at `0^(@)C`, then freezing point temperature falls
C. Both (a) and (b)
D. None of these

Answer

To solve the question regarding the correct statements about the effects of adding solid calcium chloride to water and ice, we will analyze each statement step by step using colligative properties.

### Step-by-Step Solution:

1. **Understanding the First Statement**:
- The first statement claims that when solid calcium chloride (CaCl₂) is added to liquid water, the boiling point temperature rises.
- To analyze this, we use the formula for boiling point elevation:
\[ \Delta T_b = i \cdot K_b \cdot m \]
where:
- \(\Delta T_b\) is the change in boiling point,
- \(i\) is the van 't Hoff factor (number of particles the solute dissociates into),
- \(K_b\) is the ebullioscopic constant of the solvent (water in this case),
- \(m\) is the molality of the solution.

2. **Calculating the Effect on Boiling Point**:
- When CaCl₂ is dissolved in water, it dissociates into three ions: one calcium ion (Ca²⁺) and two chloride ions (Cl⁻). Thus, \(i = 3\).
- Since \(K_b\) and molality \(m\) are both positive values, the product \(i \cdot K_b \cdot m\) is also positive.
- Therefore, the boiling point of the solution will be:
\[ T_b = T_{b0} + \Delta T_b \]
which indicates that the boiling point increases.
- **Conclusion**: The first statement is **correct**.

3. **Understanding the Second Statement**:
- The second statement claims that when solid calcium chloride is added to ice at 0 degrees Celsius, the freezing point temperature falls.
- We use the formula for freezing point depression:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- \(\Delta T_f\) is the change in freezing point,
- \(K_f\) is the cryoscopic constant of the solvent (again, water).

4. **Calculating the Effect on Freezing Point**:
- Similar to before, when CaCl₂ is added, it dissociates into three ions, so \(i = 3\).
- The formula for the final freezing point becomes:
\[ T_f = T_{f0} - \Delta T_f \]
Since \(\Delta T_f\) is positive, the final freezing point \(T_f\) will be less than the initial freezing point \(T_{f0}\).
- **Conclusion**: The second statement is also **correct**.

5. **Final Conclusion**:
- Since both statements are correct, the third option stating that both A and B are correct is also correct.

### Final Answer:
Both statements A and B are correct.

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