Calculate the molal depression constant of a solvent, which freezes at $15^{\circ}C$. The latent heat of fusion is $180.7 \ Jg^{-1}$.

Calculate the cryoscopic constant $(K_f)$ when $0.8 \ g$ of a non-volatile solute with a molar mass of $64 \ g \ mol^{-1}$ is dissolved in $43 \ g$ of a solvent,lowering the freezing point by $0.34 \ K$.

What is the cryoscopic constant of water if $5 \ g$ of glucose in $100 \ g$ of water causes a depression in freezing point of $2.15 \ K$? (Molar mass of glucose $= 180 \ g \ mol^{-1}$)

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 $\Delta_{\text{mix}} V = 0$)

Arrange the following solutions in order of decreasing freezing points:
$(a) \ 0.075 \ M \ CuSO_4$ $(b) \ 0.060 \ M \ (NH_4)_2SO_4$
$(c) \ 0.14 \ M \ \text{urea}$ $(d) \ 0.04 \ M \ MgCl_2$

The molal depression constant for a liquid is $2.77^{\circ} C \ kg \ mol^{-1}$. What is its value on the Kelvin scale?