The cryoscopic constant of a solvent is K_f = (M R T_f^2)/(1000 Delta H_fus) (M in g mol^-1). Which of the following statements is/are correct?

For a given solvent, K_f has the same value for every non-volatile solute.

If Delta H_fus of a solvent is smaller (other quantities equal), its K_f is larger.

K_f is directly proportional to Delta H_fus of the solvent.

For a given solvent, K_f has the same value for every non-volatile solute.

If Delta H_fus of a solvent is smaller (other quantities equal), its K_f is larger.

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3so073

The cryoscopic constant of a solvent is $K_{f} = \frac{MR T _{f}^{2}}{1000 Δ H _{f u s}}$ ( $M$ in $g mo l^{- 1}$ ). Which of the following statements is/are correct?

A $K_{f}$ is directly proportional to $Δ H_{f u s}$ of the solvent.
B $K_{f}$ has the unit $K kg mo l^{- 1}$ .
CFor a given solvent, $K_{f}$ has the same value for every non-volatile solute.
DIf $Δ H_{f u s}$ of a solvent is smaller (other quantities equal), its $K_{f}$ is larger.

From the expression,

K_{f}

contains only solvent properties (

M

T_{f}

Δ H_{f u s}

), so it is independent of the solute.

Δ H_{f u s}

is in the denominator, so

K_{f}

is inversely (not directly) proportional to it, and a smaller

Δ H_{f u s}

gives a larger

K_{f}

. Since

K_{f} = Δ T_{f} / m

, its unit is

K kg mo l^{- 1}