Question

Which of the following is/are correct?
Here,
$K_f\text{is cryoscopic constant}$
$T_f\text{is Freezing point of pure solvent}$
$M\text{is the molar mass of solvent}$
$\Delta H_{\text{fus}}\text{is the molar enthalpy of fusion of the solvent}$
All quantities are in SI units

• A. $K_f=\frac{R\times T_f^2\times M}{1000\times \Delta H_{fus}}$
• B. $K_f$ value is dependent on the nature of the solvent
• C. Cryoscopic constant is the elevation in freezing point when the molality of solution is equal to that of depression in freezing point
  
• D. $K_f$ value is dependent on the nature of the solute

Answer 1

Answer: (A), (B)

$K_f$ value is dependent on the nature of the solvent

Depression in Freezing Point is a colligative property. It is dependent on solute concentration and not its nature.

Cryoscopic constant is the depression in freezing point when the molality of solution is unity.
Option (b) is incorrect.

$K_f=\frac{R\times T_f^2\times M}{1000\times \Delta H_{fus}}=\frac{R\times T_f^2}{1000\times L_{fus}}$

$L_{fus}\text{is the latent heat of fusion of the solvent per g}$
Option (a) is correct.

$K_f=\frac{{\text{J K}}^{-1}{\text{mol}}^{-1}\times {\text{K}}^2}{{\text{J kg}}^{-1}}$
$\Rightarrow \text{Unit of Cryoscopic constant is}{\text{K kg mol}}^{-1}$

Cryoscopic constant varies with type of solvent. Thus, option (c) is correct.