If the freezing point of an aqueous urea solution is $271.14 \ K$ at $1 \ \text{atm}$ pressure (given $K_f$ of water = $1.86 \ K \ kg/mol$),then what is the mole fraction of urea in this solution? (Freezing point of pure water is $273 \ K$)

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 $K_f = 3.5 \ K \ kg \ mol^{-1}$.

How much glucose $(molecular \ weight = 180 \ g/mol)$ should be added to $200 \ g \ H_2O$ so that when the solution is cooled to $-0.5^{\circ}C$,$14 \ g$ of ice separates out of the solution: [$K_f = 1.86 \ K \ kg/mol$ and melting point of $H_2O = 0^{\circ}C$] (in $g$)

Calculate the mass of ascorbic acid $(\text{C}_6\text{H}_8\text{O}_6)$ to be dissolved in $75 \text{ g}$ of acetic acid to lower its melting point by $1.5^\circ\text{C}$. $[K_f = 3.9 \text{ K kg mol}^{-1}, \text{H} = 1, \text{C} = 12, \text{O} = 16 \text{ amu}]$ (in $\text{ g}$)

If the $K_f$ value of $H_2O$ is $1.86$,what is the value of $\Delta T_f$ for a $0.1 \ m$ solution of a non-volatile solute?

The freezing point of a solution containing $10 \ mL$ of non-volatile and non-electrolyte liquid $A$ in $500 \ g$ of water is $-0.413^{\circ} C$. If $K_f$ of water is $1.86 \ K \ kg \ mol^{-1}$ and the molecular weight of $A = 60 \ g \ mol^{-1}$, what is the density of the solution in $g \ mL^{-1}$? (Assume $\Delta_{\text{mix}} V = 0$)