Step 1: Understanding the Concept:
Freezing point depression (\( \Delta T_f \)) is a colligative property, meaning it depends on the total number of solute particles (ions or molecules) present in the solution. Step 2: Key Formula or Approach:
We use the van't Hoff factor (\( i \)) to account for dissociation:
\[ \Delta T_f = i \cdot K_f \cdot m \]
Since the concentration (\( 0.10 \, \text{M} \)) is the same for all, we compare the value of \( i \) for each solute. Step 3: Detailed Explanation:
1. Glycine: An amino acid that exists mainly as a zwitterion in water but does not dissociate into multiple ions. \( i \approx 1 \).
2. Glucose: A non-electrolyte sugar that does not dissociate. \( i = 1 \).
3. \( \text{KHSO}_4 \): A strong electrolyte. In water, it dissociates completely into potassium ions and bisulfate ions:
\[ \text{KHSO}_4 \to \text{K}^+ + \text{HSO}_4^- \]
Additionally, \( \text{HSO}_4^- \) is a moderately strong acid and can further dissociate:
\[ \text{HSO}_4^- \rightleftharpoons \text{H}^+ + \text{SO}_4^{2-} \]
Thus, \( i \) is at least 2 and likely higher due to partial second dissociation.
4. Hydrazine (\( \text{N}_2\text{H}_4 \)): A weak base that barely dissociates in water. \( i \approx 1 \). Step 4: Final Answer:
\( \text{KHSO}_4 \) provides the highest number of particles in solution, leading to the largest freezing point depression.
