$A$ solution of $5 \ g$ nonvolatile solute in $50 \ g$ water decreases its freezing point by $0.2 \ K$. Calculate the molar mass of solute if $K_{f}$ of water is $1.86 \ K \ kg \ mol^{-1}$.

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 $B$.

Under identical conditions,which aqueous solutions have the same freezing point? (Molecular mass of urea $= 60 \ u$ and glucose $= 180 \ u$)

$40 \ g$ of glucose (Molar mass $= 180 \ g \ mol^{-1}$) is mixed with $200 \ mL$ of water. The freezing point of the solution is $..... \ K$. (Nearest integer)
[Given : $K_{f} = 1.86 \ K \ kg \ mol^{-1};$ Density of water $= 1.00 \ g \ cm^{-3};$ Freezing point of water $= 273.15 \ K$]

Which of the following $0.10 \ m$ aqueous solutions will have the lowest freezing point?

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 $\text{ g}$)