$1.00 \ g$ of a non-electrolyte solute (molar mass $250 \ g \ mol^{-1}$) was dissolved in $51.2 \ g$ of benzene. If the freezing point depression constant,$K_f$ of benzene is $5.12 \ K \ kg \ mol^{-1},$ the freezing point of benzene will be lowered by .......... $K$.

Calculate the cryoscopic constant $(K_f)$ when $0.8 \ g$ of a non-volatile solute with a molar mass of $64 \ g \ mol^{-1}$ is dissolved in $43 \ g$ of a solvent,lowering the freezing point by $0.34 \ K$.

$1 \ kg$ 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: $K_{f}(H_{2}O) = 1.86 \ K \ kg \ mol^{-1}$

$1.80 \ g$ of solute $A$ was dissolved in $62.5 \ cm^{3}$ of ethanol and the freezing point of the solution was found to be $155.1 \ K$. The molar mass of solute $A$ is $.......... \ g \ mol^{-1}$.
[Given: Freezing point of ethanol is $156.0 \ K$,Density of ethanol is $0.80 \ g \ cm^{-3}$,Freezing point depression constant of ethanol is $2.00 \ K \ kg \ mol^{-1}$]

$5 \ g$ sucrose (molar mass $= 342 \ g \ mol^{-1}$) is dissolved in $100 \ g$ of solvent,decreasing the freezing point by $2.15 \ K$. What is the cryoscopic constant $(K_{f})$ of the solvent?

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?