Which of the following solutions in water will have the lowest vapour pressure

Options

A. 0.1 M, NaCl
B. 0.1 M, Sucrose
C. `0.1 M, BaCl_(2)`
D. `0.1 M Na_(3)PO_(4)`

Explanation

To determine which of the given solutions in water will have the lowest vapor pressure, we can use the concept of colligative properties. The vapor pressure of a solution decreases with an increase in the number of solute particles in the solution. This is quantified by the van 't Hoff factor (i), which indicates the number of particles the solute dissociates into when dissolved.

### Step-by-Step Solution:

1. **Identify the Solutions**:
We have the following solutions:
- 0.1 M NaCl
- 0.1 M Sucrose
- 0.1 M NaCl2
- 0.1 M Na3PO4

2. **Determine the van 't Hoff Factor (i)**:
- **NaCl**: Dissociates into Na⁺ and Cl⁻.
- i = 2 (1 Na⁺ + 1 Cl⁻)
- **Sucrose**: Does not dissociate in solution.
- i = 1
- **NaCl2**: Dissociates into Na⁺ and 2 Cl⁻.
- i = 3 (1 Na⁺ + 2 Cl⁻)
- **Na3PO4**: Dissociates into 3 Na⁺ and 1 PO4³⁻.
- i = 4 (3 Na⁺ + 1 PO4³⁻)

3. **Compare the Values of i**:
- NaCl: i = 2
- Sucrose: i = 1
- NaCl2: i = 3
- Na3PO4: i = 4

4. **Determine the Solution with the Lowest Vapor Pressure**:
According to colligative properties, the vapor pressure of a solution decreases as the number of solute particles increases. Therefore, the solution with the highest i value will have the lowest vapor pressure.
- The highest i value is for Na3PO4, which is 4.

5. **Conclusion**:
The solution with the lowest vapor pressure is **0.1 M Na3PO4**.