Calculate the molal depression constant of a solvent, which freezes at $15^{\circ}C$. The latent heat of fusion is $180.7 \ Jg^{-1}$.

The freezing point of a diluted milk sample is found to be $-0.2\ ^\circ C$,while it should be $-0.5\ ^\circ C$ for pure milk. How much water has been added to pure milk to make the diluted sample?

What is the molar mass of a solute when $5 \ g$ of solute dissolved in $70 \ g$ of solvent lowers its freezing point by $2.5 \ K$? Given $K_f = 3.5 \ K \ kg \ mol^{-1}$.

$A$ solution of $5 \ g$ nonvolatile solute in $50 \ g$ water decreases its freezing point by $0.2 \ K$. Calculate the molar mass of solute if $K_{f}$ of water is $1.86 \ K \ kg \ mol^{-1}$.

$1 \ kg$ of $0.75 \ m$ aqueous solution of sucrose is cooled to $-4^{\circ} C$. The amount of ice (in $g$) that will be separated out is .... . (Nearest integer)
Given: $K_{f}(H_{2}O) = 1.86 \ K \ kg \ mol^{-1}$

$A$ solution of a nonvolatile solute is obtained by dissolving $1 \ g$ in $100 \ g$ of solvent,which decreases its freezing point by $0.3 \ K$. Calculate the cryoscopic constant of the solvent if the molar mass of the solute is $60 \ g \ mol^{-1}$.