The freezing point of a $5\%$ (by mass) aqueous solution of sucrose is $271 \, K$ and the freezing point of pure water is $273.15 \, K$. The freezing point of a $5\%$ (by mass) aqueous solution of glucose is .......... $K$.

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 $B$.

Lead storage battery contains $38\%$ by weight solution of $H_2SO_4$. The van't Hoff factor is $2.67$ at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is $..........$ (Nearest integer). Given $K_f = 1.8 \, K \, kg \, mol^{-1}$.

Calculate the freezing point of a $0.05 \ m$ aqueous solution of a non-electrolyte. (in $K$)

$3 \times 10^{-3} \ kg$ acetic acid is added into $500 \ cm^{3}$ water. If dissociation of acetic acid is $23\%$ then find out depression in freezing point? $K_f$ of water $= 1.86 \ K \ kg \ mol^{-1}$ and density $= 0.997 \ g \ cm^{-3}$.

What should be the freezing point of an aqueous solution containing $17 \ g$ of $C_2H_5OH$ in $1000 \ g$ of water? (Given: $K_f$ of water = $1.86 \ K \ kg \ mol^{-1}$)