Consider 0.1 M solutions of two solutes X and Y. The solute X behaves as univalent electrolyte, while the solute Y dimerises in solution. Select correct statement(s) regarding these solutions:

Options

A. The boiling point of solution of 'X' will be higher than that of 'Y'
B. The osmotic pressure of solution of 'Y' will be lower than that of 'X'
C. The freezing point of solution of 'X' will be lower than that of 'Y'
D. The relative lowering of vapour pressure of both the solution will be the same

Answer

To solve the problem regarding the 0.1 M solutions of solutes X and Y, we need to analyze their behavior based on the information provided. Let's break down the solution step by step.

### Step 1: Understand the nature of solutes
- **Solute X**: It behaves as a univalent electrolyte, meaning it dissociates into one positive ion and one negative ion. Therefore, for every 1 mole of X, it produces 1 mole of ions.
- **Solute Y**: It dimerizes in solution, meaning two molecules of Y combine to form one dimer (Y2). This means that for every 2 moles of Y, it produces 1 mole of dimer.

### Step 2: Determine the Van't Hoff factor (i)
- For **solute X**: Since it dissociates completely into 2 ions (1 positive and 1 negative), the Van't Hoff factor (i) for X is:
\[ i_X = 2 \]

- For **solute Y**: When dimerization occurs, if we start with 1 mole of Y, it will produce 0.5 moles of dimer (Y2). Thus, the effective number of particles in solution will be:
\[ i_Y = \frac{1}{2} \]

### Step 3: Analyze colligative properties
Colligative properties depend on the number of solute particles in solution, which is influenced by the Van't Hoff factor (i).

#### Boiling Point Elevation (ΔTb)
- The elevation in boiling point is given by:
\[ \Delta T_b = K_b \cdot m \cdot i \]
- For solute X:
\[ \Delta T_{bX} = K_b \cdot 0.1 \cdot 2 \]
- For solute Y:
\[ \Delta T_{bY} = K_b \cdot 0.1 \cdot \frac{1}{2} \]
- Since \( \Delta T_{bX} > \Delta T_{bY} \), the boiling point of solution X will be higher than that of Y.

#### Osmotic Pressure (π)
- The osmotic pressure is given by:
\[ \pi = C \cdot R \cdot T \cdot i \]
- For solute X:
\[ \pi_X = 0.1 \cdot R \cdot T \cdot 2 \]
- For solute Y:
\[ \pi_Y = 0.1 \cdot R \cdot T \cdot \frac{1}{2} \]
- Since \( \pi_X > \pi_Y \), the osmotic pressure of solution Y will be lower than that of X.

#### Freezing Point Depression (ΔTf)
- The depression in freezing point is given by:
\[ \Delta T_f = K_f \cdot m \cdot i \]
- For solute X:
\[ \Delta T_{fX} = K_f \cdot 0.1 \cdot 2 \]
- For solute Y:
\[ \Delta T_{fY} = K_f \cdot 0.1 \cdot \frac{1}{2} \]
- Since \( \Delta T_{fX} > \Delta T_{fY} \), the freezing point of solution X will be lower than that of Y.

#### Relative Lowering of Vapor Pressure
- The relative lowering of vapor pressure is given by:
\[ \text{Relative lowering} = \frac{P_0 - P}{P_0} = i \cdot \frac{C}{C_0} \]
- Since \( i_X > i_Y \), the relative lowering of vapor pressure will not be the same for both solutions.

### Conclusion
Based on the analysis, the correct statements regarding the solutions are:
1. The boiling point of solution X will be higher than that of Y.
2. The osmotic pressure of solution Y will be lower than that of X.
3. The freezing point of solution X will be lower than that of Y.
4. The relative lowering of vapor pressure of both the solutions will not be the same.

### Summary of Correct Statements
- The boiling point of solution X is higher than that of Y. (Correct)
- The osmotic pressure of solution Y is lower than that of X. (Correct)
- The freezing point of solution X is lower than that of Y. (Correct)
- The relative lowering of vapor pressure of both solutions will not be the same. (Incorrect)