Which one of the following solution has maximum vapour pressure at `27^(@)C` temperature ?

Options

A. `1` `M` `Na_(2)SO_(4)`
B. `1` `M` `AlCl_(3)`
C. `1` `M` `KBr`
D. `1` `M` `MgCl_(2)`

Explanation

To determine which solution has the maximum vapor pressure at 27°C, we need to analyze the given solutions based on their van 't Hoff factor (i), which indicates the number of particles into which a solute dissociates in solution. The higher the value of i, the lower the vapor pressure of the solution, due to the colligative properties of solutions.

### Step-by-Step Solution:

1. **Identify the Solutions**: We have four solutions to consider:
- 1m of Na₂SO₄
- 1m of BaCl₃
- 1m of KBr
- 1m of MgCl₂

2. **Determine the Dissociation of Each Solute**:
- **Na₂SO₄**: Dissociates into 2 Na⁺ and 1 SO₄²⁻, so i = 2 + 1 = 3.
- **BaCl₃**: Dissociates into 1 Ba²⁺ and 3 Cl⁻, so i = 1 + 3 = 4.
- **KBr**: Dissociates into 1 K⁺ and 1 Br⁻, so i = 1 + 1 = 2.
- **MgCl₂**: Dissociates into 1 Mg²⁺ and 2 Cl⁻, so i = 1 + 2 = 3.

3. **List the Values of i**:
- Na₂SO₄: i = 3
- BaCl₃: i = 4
- KBr: i = 2
- MgCl₂: i = 3

4. **Analyze the Relationship Between i and Vapor Pressure**:
- The vapor pressure of a solution decreases as the value of i increases. Therefore, the solution with the lowest i will have the highest vapor pressure.

5. **Compare the Values of i**:
- KBr has the lowest i value of 2, which means it will have the maximum vapor pressure.
- Na₂SO₄ and MgCl₂ both have i = 3.
- BaCl₃ has the highest i value of 4, indicating the lowest vapor pressure.

6. **Conclusion**: The solution with the maximum vapor pressure at 27°C is **1m of KBr**.