Which of the following aqueous solution of same concentration has highest depression in freezing point?

Options

A. Glycine
B. Glycerol
C. `KHSO_4`
D. Glucose

Answer

To determine which of the given aqueous solutions has the highest depression in freezing point, we will use the formula for depression in freezing point:

\[ \Delta T_f = i \cdot K_f \cdot m \]

Where:
- \(\Delta T_f\) = depression in freezing point
- \(i\) = van 't Hoff factor (number of particles the solute breaks into)
- \(K_f\) = molal freezing point depression constant (same for all solutions in this case)
- \(m\) = molality (same for all solutions in this case)

Since \(K_f\) and \(m\) are constant for all solutions, the depression in freezing point will depend solely on the van 't Hoff factor \(i\).

Now, let's analyze each of the given options:

1. **Glycine (NH2CH2COOH)**:
- Glycine is an amino acid and does not dissociate into ions in solution. Therefore, \(i \approx 1\).

2. **Glycerol (C3H8O3)**:
- Glycerol is a polyol and also does not dissociate into ions in solution. Therefore, \(i \approx 1\).

3. **KHSO4 (Potassium hydrogen sulfate)**:
- KHSO4 dissociates into K⁺ and HSO4⁻ ions in solution. Therefore, \(i = 2\) (1 K⁺ and 1 HSO4⁻).

4. **Glucose (C6H12O6)**:
- Glucose is a simple sugar and does not dissociate into ions in solution. Therefore, \(i \approx 1\).

Now, we can summarize the van 't Hoff factors for each solution:
- Glycine: \(i \approx 1\)
- Glycerol: \(i \approx 1\)
- KHSO4: \(i = 2\)
- Glucose: \(i \approx 1\)

Since KHSO4 has the highest van 't Hoff factor \(i\), it will result in the highest depression in freezing point.

**Conclusion**: The aqueous solution with the highest depression in freezing point is KHSO4.