Question

Calculate the depression in freezing point for a given solution using the cryoscopic constant (\(K_f\)).

Hint:

Always ensure molality is calculated correctly before applying the formula.

Answer 1

Concept: Depression in freezing point is a colligative property and is calculated using the formula: \[ \Delta T_f = K_f \times m \] where \( \Delta T_f \) is the depression in freezing point, \( K_f \) is the cryoscopic constant, and \( m \) is the molality of the solution.
Answer:
To calculate the depression in freezing point:

• First, calculate molality (\(m\)): \[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]
• Then apply the formula: \[ \Delta T_f = K_f \times m \]

Example:
If \(K_f = 1.86 \, K\,kg\,mol^{-1}\) and \(m = 0.5 \, mol/kg\), then: \[ \Delta T_f = 1.86 \times 0.5 = 0.93\,K \] Thus, the freezing point decreases by \(0.93\,K\).