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 = $1 \ g/mL$)

Consider the given plots of vapour pressure $(VP)$ vs temperature $(T / K)$. Which amongst the following options is the correct graphical representation showing $\Delta T_f$,the depression in the freezing point of the solvent in a solution?

The freezing point of a $0.05 \ molal$ solution of a non-electrolyte in water is $.......... \ ^oC$. $(K_f = 1.86 \ K \ kg \ mol^{-1})$

Calculate the molar mass of the solute when $1.5 \ g$ of a non-volatile solute is dissolved in $100 \ mL$ of a solvent having a density of $0.8 \ g \ mL^{-1}$,which lowers its freezing point by $0.75 \ K$. (Freezing point depression constant for the solvent is $5 \ K \ kg \ mol^{-1}$).

The molal depression constant for water is $1.86\,^{\circ}C/m$. If $342\,g$ of sugar $(C_{12}H_{22}O_{11})$ is dissolved in $1000\,g$ of water,the freezing point of the solution will be ............. $^{\circ}C$.

What is the unit of cryoscopic constant?