Calculate the molal depression constant of a solvent which has freezing point $16.6\,^oC$ and latent heat of fusion $180.75\,J\,g^{-1}$.

$1.00 \ g$ 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 .......... $K$.

$A$ solution of sucrose (molar mass $= 342 \, g \, mol^{-1}$) has been prepared by dissolving $68.5 \, g$ of sucrose in $1000 \, g$ of water. The freezing point of the solution obtained will be ......... $^oC$. ($K_f$ for water $= 1.86 \, K \, kg \, mol^{-1}$)

If molality of the dilute solution is doubled,the value of molal depression constant $(K_f)$ will be

Ethylene glycol is used as an antifreeze in cold climates. To prevent $4 \ kg$ of water from freezing at $-6^{\circ}C$,how many grams of ethylene glycol must be added? (Given for water: $K_f = 1.86 \ K \ kg \ mol^{-1}$,Molar mass of ethylene glycol $= 62 \ g \ mol^{-1}$)

When $x \times 10^{-2} \ mL$ methanol (molar mass $= 32 \ g \ mol^{-1}$; density $= 0.792 \ g \ cm^{-3}$) is added to $100 \ mL$ water (density $= 1 \ g \ cm^{-3}$),the following diagram is obtained.
$x = $ . . . . . . (nearest integer)
[Given: Molal freezing point depression constant of water at $273.15 \ K$ is $1.86 \ K \ kg \ mol^{-1}$]