Which of the following aqueous solutions will have maximum vapour pressure?

Options

A. `0.05 M K_(4)[Fe(CN)_(6)]`
B. `0.02 M BaCI_(2)`
C. `20%w//w "glucose solution"`
D. An aqueous solution of `i_(2)(s)` in water having mole fraction of iodine equal to 0.01

Answer

To determine which aqueous solution has the maximum vapor pressure, we can use the concept of relative lowering of vapor pressure, which is given by the formula:

\[ \text{Relative lowering in vapor pressure} = \frac{P_0 - P_s}{P_0} = i \cdot C \]

Where:
- \( P_0 \) is the vapor pressure of the pure solvent (water in this case).
- \( P_s \) is the vapor pressure of the solution.
- \( i \) is the van 't Hoff factor (the number of particles the solute dissociates into).
- \( C \) is the concentration of the solute.

### Step-by-Step Solution:

1. **Identify the Solutions**: We have four solutions to analyze:
- A: \( K_4[Fe(CN)_6] \) at 0.05 M
- B: \( BaCl_2 \) at 0.02 M
- C: 20% w/w glucose
- D: 0.01 M \( I_2 \)

2. **Calculate the van 't Hoff Factor (i)**:
- For \( K_4[Fe(CN)_6] \):
- It dissociates into 4 \( K^+ \) ions and 1 \( Fe(CN)_6^{4-} \) ion.
- Thus, \( i = 4 + 1 = 5 \).
- Effective concentration \( C = 0.05 \) M.
- Contribution to lowering vapor pressure: \( i \cdot C = 5 \cdot 0.05 = 0.25 \).

- For \( BaCl_2 \):
- It dissociates into 1 \( Ba^{2+} \) ion and 2 \( Cl^- \) ions.
- Thus, \( i = 1 + 2 = 3 \).
- Effective concentration \( C = 0.02 \) M.
- Contribution to lowering vapor pressure: \( i \cdot C = 3 \cdot 0.02 = 0.06 \).

- For glucose (non-electrolyte):
- \( i = 1 \) (does not dissociate).
- 20% w/w means 20 g of glucose in 80 g of water.
- Molar mass of glucose = 180 g/mol.
- Moles of glucose = \( \frac{20}{180} \approx 0.111 \) moles.
- Volume of water = \( \frac{80}{18} \approx 4.44 \) moles.
- Concentration \( C \approx \frac{0.111}{4.44} \approx 0.025 \) M.
- Contribution to lowering vapor pressure: \( i \cdot C = 1 \cdot 0.025 = 0.025 \).

- For \( I_2 \):
- It does not dissociate, so \( i = 1 \).
- Concentration \( C = 0.01 \) M.
- Contribution to lowering vapor pressure: \( i \cdot C = 1 \cdot 0.01 = 0.01 \).

3. **Compare the Contributions**:
- \( K_4[Fe(CN)_6] \): 0.25
- \( BaCl_2 \): 0.06
- Glucose: 0.025
- \( I_2 \): 0.01

4. **Determine the Maximum Vapor Pressure**:
- The solution with the lowest contribution to lowering vapor pressure will have the highest vapor pressure.
- Therefore, the order of vapor pressures from highest to lowest is:
- Glucose (0.025) > \( I_2 \) (0.01) > \( BaCl_2 \) (0.06) > \( K_4[Fe(CN)_6] \) (0.25).

### Conclusion:
The aqueous solution with the maximum vapor pressure is the glucose solution.