The decreases in the freezing point of an aqueoues solution of a substance is `1.395K` and that in the freezing point of benzene solution of the same substance is `1.280K`. Explain the difference in `DeltaT`. The substance:

Options

A. dissociates in the aqueous solution as well as in the benzene solution
B. forms complexes in solution
C. associates in the benzene solution
D. dissociates in the aqueous solution and not in the benzene solution

Answer

To explain the difference in the decrease in freezing point (ΔT) of an aqueous solution and a benzene solution of the same substance, we can follow these steps:

### Step 1: Understand the Concept of Freezing Point Depression
The freezing point depression is a colligative property, which means it depends on the number of solute particles in a solution rather than the identity of the solute. The formula for freezing point depression is given by:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- \(\Delta T_f\) = freezing point depression
- \(i\) = Van't Hoff factor (number of particles the solute dissociates into)
- \(K_f\) = freezing point depression constant of the solvent
- \(m\) = molality of the solution

### Step 2: Compare the Freezing Point Depression Values
Given:
- For the aqueous solution, \(\Delta T_f = 1.395 \, K\)
- For the benzene solution, \(\Delta T_f = 1.280 \, K\)

From these values, we can see that the freezing point depression is greater in the aqueous solution than in the benzene solution.

### Step 3: Analyze the Van't Hoff Factor (i)
The difference in the freezing point depression can be attributed to the Van't Hoff factor (\(i\)). The Van't Hoff factor indicates how many particles the solute produces in solution:
- A higher \(i\) value means more particles, leading to a greater freezing point depression.
- A lower \(i\) value means fewer particles, resulting in a smaller freezing point depression.

Since the freezing point depression is greater in the aqueous solution, we can conclude that the Van't Hoff factor for the solute in the aqueous solution is greater than that in the benzene solution.

### Step 4: Conclusion
The difference in the freezing point depressions indicates that the solute dissociates or associates differently in the two solvents. Specifically:
- The solute likely dissociates in the aqueous solution, contributing to a higher \(i\).
- In the benzene solution, the solute may not dissociate effectively, leading to a lower \(i\).

Thus, the difference in ΔT can be explained by the varying degrees of dissociation or association of the solute in the two solvents.