To solve this problem, we need to understand the concept of molal depression constant $(K_f). \\$The molal depression constant $(K_f)$ is a property of the solvent and is defined as the depression in freezing point per unit molality.$\\$The formula for freezing point depression is:$\\ \Delta T_f = K_f \cdot m \\$where $\Delta T_f$ is the depression in freezing point, $K_f$ is the molal depression constant, and $m$ is the molality of the solution.$\\$From the formula, it is clear that $K_f$ is independent of the molality of the solution.$\\$Therefore, if the molality of the dilute solution is doubled, the value of the molal depression constant $(K_f)$ will remain unchanged.$\\$Thus, the correct option is Option 3: unchanged.