$x$ moles of $CO(NH_2)_2$ are present in $1200 \ g$ of water. If the freezing point of the solution is $-4.02 \ ^oC$,calculate the value of $x$. Given $k_f \ (H_2O) = 1.86 \ K \ kg \ mol^{-1}$.

Given that $\Delta T_f$ is the depression in freezing point of the solvent in a solution of a non-volatile solute of molality $m$,the quantity $\lim_{m \to 0} \left( \frac{\Delta T_f}{m} \right)$ is equal to:

What is the mass of solute having molar mass $60 \ g \ mol^{-1}$ when dissolved in $98 \ g$ of solvent decreases its freezing point by $0.2 \ K$ (in $g$)? (The numerical value of cryoscopic constant of solvent is $1.71 \ K \ kg \ mol^{-1}$)

What is the molality of a solution that has a freezing point depression of $3 \ K$ and a freezing point depression constant of $5 \ K \ kg \ mol^{-1}$ (in $m$)?

Calculate $\Delta T_f$ of $0.15 \ m$ solution of nonvolatile solute $\left[K_f = 1.5 \ K \ kg \ mol^{-1}\right]$ (in $K$)

Which of the following aqueous solutions has the highest freezing point?