Question

Which of the following aqueous non-electrolyte solution will produce the highest freezing point if 20g of the solute is dissolved in 1000g of water?

• A. Sucrose
• B. Glycerol
• C. Ethanol
• D. Glucose
• E. Methanol

Hint:

Higher Molar Mass \(\to\) Fewer Particles \(\to\) Less Effect on Colligative Properties (like Freezing Point Depression).
Therefore, for a fixed mass of solute, the "bulkiest" molecule causes the least freezing point drop.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The freezing point of a solution is lower than that of the pure solvent. This is "depression in freezing point" (\(\Delta T_f\)).
Highest freezing point means lowest depression (\(\Delta T_f\)).

Step 2: Key Formula or Approach:
For non-electrolytes (where \(i = 1\)):
\[ \Delta T_f = K_f \times m \]
where \(m = \text{molality} = \frac{\text{mass of solute}}{\text{molar mass} \times \text{mass of solvent (kg)}}\).
Since the mass of solute (20g) and solvent (1000g) are constant for all options, \(\Delta T_f \propto \frac{1}{\text{Molar Mass}}\).

Step 3: Detailed Explanation:
To have the lowest \(\Delta T_f\) (highest freezing point), we need the highest Molar Mass.
Let's check the molar masses of the solutes:
- (A) Sucrose (\(C_{12}H_{22}O_{11}\)): \(\approx 342 \text{ g/mol}\)
- (B) Glycerol (\(C_3H_8O_3\)): \(\approx 92 \text{ g/mol}\)
- (C) Ethanol (\(C_2H_5OH\)): \(\approx 46 \text{ g/mol}\)
- (D) Glucose (\(C_6H_{12}O_6\)): \(\approx 180 \text{ g/mol}\)
- (E) Methanol (\(CH_3OH\)): \(\approx 32 \text{ g/mol}\)

Since Sucrose has the highest molar mass, it will produce the lowest number of moles, the lowest molality, and thus the smallest depression in freezing point.

Step 4: Final Answer:
The sucrose solution will have the highest freezing point.