consider 0.1 M solutions of two solutes X and Y. The behaves as a univalent electrolyte while the solute Y dimerises in solution. Which of the following statement are correct regarding these solutions?
(1) The boiling point of the solution of X will be higher than that of Y
(2) The osmotic pressure of the solution of Y will be lower than that of X
(3) The freezing point of the solition of X will be lower than that of Y
(4) The relative lowering of vapour pressure of both the solutions will be the same
(a)1, 2 and 3
(b)2, 3 and 4
(c)1, 2 and 4
(d)1, 3 and 4

Options

A. 1, 2 and 3
B. 2, 3 and 4
C. 1, 2 and 4
D. 1, 3 and 4

Answer

To solve the problem, we need to analyze the properties of the two solutions based on the information given about solutes X and Y.

### Step-by-Step Solution:

1. **Identify the Van't Hoff Factor (i)**:
- For solute X, which behaves as a univalent electrolyte, the Van't Hoff factor (i) is 1.
- For solute Y, which dimerizes in solution, the Van't Hoff factor (i) is 0.5 (since one molecule of Y produces two particles in solution).

2. **Analyze the First Statement**:
- The boiling point elevation is given by the formula:
\[ \Delta T_b = i \cdot K_b \cdot m \]
- Since i for X is 1 and for Y is 0.5, the elevation in boiling point for X will be greater than that for Y.
- **Conclusion**: The boiling point of the solution of X will be higher than that of Y. **(True)**

3. **Analyze the Second Statement**:
- The osmotic pressure (π) is given by the formula:
\[ \pi = i \cdot C \cdot R \cdot T \]
- Here, C is the concentration, R is the gas constant, and T is the temperature.
- Since i for X is 1 and for Y is 0.5, the osmotic pressure for X will be higher than that for Y.
- **Conclusion**: The osmotic pressure of the solution of Y will be lower than that of X. **(True)**

4. **Analyze the Third Statement**:
- The freezing point depression is given by the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
- Again, since i for X is 1 and for Y is 0.5, the depression in freezing point for X will be greater than that for Y.
- This means the actual freezing point of X will be lower than that of Y.
- **Conclusion**: The freezing point of the solution of X will be lower than that of Y. **(True)**

5. **Analyze the Fourth Statement**:
- The relative lowering of vapor pressure is given by:
\[ \text{Relative lowering of vapor pressure} = \frac{i \cdot C}{C_0} \]
- Since the Van't Hoff factors are different (1 for X and 0.5 for Y), the relative lowering of vapor pressure will also be different.
- **Conclusion**: The relative lowering of vapor pressure of both the solutions will not be the same. **(False)**

### Final Conclusion:
The correct statements are:
1. The boiling point of the solution of X will be higher than that of Y. **(True)**
2. The osmotic pressure of the solution of Y will be lower than that of X. **(True)**
3. The freezing point of the solution of X will be lower than that of Y. **(True)**
4. The relative lowering of vapor pressure of both solutions will be the same. **(False)**

Thus, the correct answer is **(a) 1, 2, and 3**.