Molal depression constant for a solvent is 4.0 K kg `mol^(-1)`. The depression in the freezing point of the solvent for 0.5 mol `kg^(-1)` solution of KI (Assume complete dissociation of the electrolyte) is _______ .

Explanation

To solve the problem, we need to calculate the depression in freezing point (ΔTf) of a solvent when a 0.5 mol/kg solution of KI is prepared, assuming complete dissociation of the electrolyte. Here’s a step-by-step solution:

### Step 1: Identify the formula for depression in freezing point
The depression in freezing point can be calculated using the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- \( \Delta T_f \) = depression in freezing point
- \( i \) = Van't Hoff factor (number of particles the solute dissociates into)
- \( K_f \) = molal depression constant of the solvent
- \( m \) = molality of the solution

### Step 2: Determine the values given in the problem
From the problem, we have:
- \( K_f = 4.0 \, \text{K kg mol}^{-1} \)
- \( m = 0.5 \, \text{mol kg}^{-1} \)

### Step 3: Calculate the Van't Hoff factor (i)
Since KI dissociates completely in solution:
\[ \text{KI} \rightarrow \text{K}^+ + \text{I}^- \]
This means that one formula unit of KI produces two ions (K⁺ and I⁻). Therefore, the number of dissociated ions \( n = 2 \).

For complete dissociation, the Van't Hoff factor \( i \) can be calculated as:
\[ i = n = 2 \]

### Step 4: Substitute the values into the depression formula
Now, substituting the values into the depression in freezing point formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
\[ \Delta T_f = 2 \cdot 4.0 \, \text{K kg mol}^{-1} \cdot 0.5 \, \text{mol kg}^{-1} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \Delta T_f = 2 \cdot 4.0 \cdot 0.5 = 4.0 \, \text{K} \]

### Conclusion
The depression in the freezing point of the solvent for the 0.5 mol/kg solution of KI is:
\[ \Delta T_f = 4.0 \, \text{K} \]

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