The fundamental cause of `DeltaT` (depression is):

Options

A. higher entropy of the solution relative to that of pure solvent
B. lower entropy of the solution relative to that of pure solvent
C. higher enthalpy of the solution relative to that of pure solvent
D. lower enthalpy of the relative to that of pure solvent

Explanation

To solve the question regarding the fundamental cause of the depression of the freezing point (ΔT), we can follow these steps:

### Step 1: Understand the Concept of Freezing Point Depression
Freezing point depression occurs when a solute is added to a solvent, resulting in a lower freezing point of the solution compared to the pure solvent. This phenomenon is a colligative property, which depends on the number of solute particles in the solution rather than the identity of the solute.

**Hint:** Recall that colligative properties are properties that depend on the number of solute particles in a solution.

### Step 2: Relate Entropy to Freezing Point
Entropy (S) is a measure of disorder in a system. When a solute is added to a solvent, the overall entropy of the solution increases. The entropy of the solution is greater than that of the pure solvent because the solute particles disrupt the orderly arrangement of solvent molecules.

**Hint:** Consider how the addition of solute affects the arrangement of solvent molecules and the overall disorder.

### Step 3: Use the Relationship Between Entropy and Freezing Point
The relationship between entropy and the freezing point can be expressed as:
\[ \Delta S = \frac{\Delta H_{fusion}}{T_{f}} \]
where ΔS is the change in entropy, ΔH_fusion is the enthalpy of fusion, and T_f is the freezing point. For a solution, the entropy change is greater than that for the pure solvent, leading to the conclusion that the freezing point of the solution is lower.

**Hint:** Think about how an increase in entropy corresponds to a decrease in the freezing point.

### Step 4: Conclude the Cause of Freezing Point Depression
Since the entropy of the solution is greater than that of the pure solvent, we can conclude that the freezing point of the solution is lower than that of the pure solvent. Therefore, the fundamental cause of ΔT (depression) is the higher entropy of the solution relative to that of the pure solvent.

**Hint:** Summarize the relationship: Higher entropy in the solution leads to a lower freezing point.

### Final Answer
The fundamental cause of ΔT (depression) is the higher entropy of the solution relative to that of the pure solvent.