The amount of urea to be dissolved in $500 \ mL$ of water $(K_f = 18.6 \ K \ kg \ mol^{-1})$ to produce a depression of $0.186 \ ^oC$ in freezing point is $....... \ g$. (Assume density of water = $1 \ g/mL$)

$0.440 \ g$ of a substance dissolved in $22.2 \ g$ of benzene lowered the freezing point of benzene by $0.567 \ ^oC$. Calculate the molecular mass of the substance. (Given: $K_f = 5.12 \ ^oC \ kg \ mol^{-1}$)

The aqueous solution of urea has a freezing point of $-0.6\,^\circ C$. To prepare such a solution,how many grams of urea are needed to dissolve in $3\,kg$ of water? $(M = 60\,g\,mol^{-1}, K_{f} = 1.5\,^\circ C\,kg\,mol^{-1})$

Two elements $A$ and $B$ form compounds with molecular formulas $AB_2$ and $AB_4$. When $1 \ g$ of $AB_2$ is dissolved in $20 \ g$ of $C_6H_6$,the freezing point decreases by $2.3 \ K$. When $1 \ g$ of $AB_4$ is dissolved in $20 \ g$ of $C_6H_6$,the freezing point decreases by $1.3 \ K$. The molal depression constant for benzene is $5.1 \ K \ kg \ mol^{-1}$. Calculate the atomic weights of $A$ and $B$.

The molar freezing point constant for water is $1.86\,^{\circ}C\,kg\,mol^{-1}$. If $342\,g$ of cane sugar $(C_{12}H_{22}O_{11})$ are dissolved in $1000\,g$ of water,the solution will freeze at $............\,^{\circ}C$.

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 $1.86 \ K \ kg \ mol^{-1}$]