Which one of the following aqueous solutions will exhibit highest elivation in boiling point?

Options

A. 0.05 m glucose (non ionisable)
B. 0.01 m `KNO_3` (50 % ioisable )
C. 0.015 m Urea (non ionisable)
D. 0.01 m `Na_2SO_4` (75% ionizable)

Answer

To determine which aqueous solution exhibits the highest elevation in boiling point, we can use the formula for boiling point elevation:

\[ \Delta T_b = i \cdot K_b \cdot m \]

Where:
- \(\Delta T_b\) = elevation in boiling point
- \(i\) = van't Hoff factor (number of particles the solute breaks into)
- \(K_b\) = ebullioscopic constant of the solvent (for water, it is constant)
- \(m\) = molality of the solution

Since \(K_b\) is constant for all solutions in water, the elevation in boiling point will depend on the product of \(i\) (the van't Hoff factor) and \(m\) (the molality).

### Step-by-Step Solution:

1. **Identify the Solutions and Their Properties**:
- **Glucose**: Non-electrolyte, \(i = 1\), \(m = 0.05\)
- **KNO3**: Electrolyte, dissociates into \(K^+\) and \(NO_3^-\), \(i = 1 + 1 = 2\) (assuming 50% ionization), \(m = 0.01\)
- **Urea**: Non-electrolyte, \(i = 1\), \(m = 0.015\)
- **Na2SO4**: Electrolyte, dissociates into \(2Na^+\) and \(SO_4^{2-}\), \(i = 3\) (assuming 75% ionization), \(m = 0.01\)

2. **Calculate \(\Delta T_b\) for Each Solution**:
- **For Glucose**:
\[ \Delta T_b = i \cdot K_b \cdot m = 1 \cdot K_b \cdot 0.05 = 0.05 K_b \]
- **For KNO3**:
\[ \Delta T_b = i \cdot K_b \cdot m = 1.5 \cdot K_b \cdot 0.01 = 0.015 K_b \]
- **For Urea**:
\[ \Delta T_b = i \cdot K_b \cdot m = 1 \cdot K_b \cdot 0.015 = 0.015 K_b \]
- **For Na2SO4**:
\[ \Delta T_b = i \cdot K_b \cdot m = 2.25 \cdot K_b \cdot 0.01 = 0.0225 K_b \]

3. **Compare the Values of \(\Delta T_b\)**:
- Glucose: \(0.05 K_b\)
- KNO3: \(0.015 K_b\)
- Urea: \(0.015 K_b\)
- Na2SO4: \(0.0225 K_b\)

4. **Determine the Highest Elevation**:
The highest elevation in boiling point is from the glucose solution, which has the highest \(\Delta T_b\) value of \(0.05 K_b\).

### Conclusion:
The aqueous solution that exhibits the highest elevation in boiling point is the solution of **Glucose**.

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