If molality of the dilute solutions is doubled ,the value of molal depression constant`(K_(f))`will be:

Options

A. doubled
B. halved
C. tripled
D. unchanged

Explanation

To solve the question regarding the effect of doubling the molality of a dilute solution on the value of the molal depression constant \( K_f \), we can follow these steps:

### Step 1: Understand the relationship
The depression in freezing point (\( \Delta T_f \)) is given by the formula:
\[ \Delta T_f = K_f \cdot m \]
where:
- \( \Delta T_f \) = depression in freezing point
- \( K_f \) = molal depression constant (cryoscopic constant)
- \( m \) = molality of the solution

### Step 2: Analyze the effect of doubling molality
If the molality (\( m \)) of the solution is doubled, we can express this as:
\[ m' = 2m \]
where \( m' \) is the new molality after doubling.

### Step 3: Substitute the new molality into the equation
Substituting \( m' \) into the depression formula gives:
\[ \Delta T_f' = K_f \cdot m' = K_f \cdot (2m) = 2K_f \cdot m \]
This shows that the depression in freezing point will increase, but it does not change the value of \( K_f \).

### Step 4: Conclusion about \( K_f \)
Since \( K_f \) is a constant that depends on the solvent and does not change with the concentration of the solution, we conclude that:
\[ K_f \text{ remains unchanged.} \]

### Final Answer
The value of the molal depression constant \( K_f \) will remain the same, regardless of the change in molality.