$A$ solution containing $7.5 \ g$ of urea (molar mass $= 60 \ g \ mol^{-1}$) in $1 \ kg$ of water freezes at the same temperature as another solution containing $15 \ g$ of solute $X$,in the same amount of water. The molar mass of $X \ (g \ mol^{-1})$ is

Identify the correct relation between depression in freezing point and the freezing point of a pure solvent.

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 $B$.

The aqueous solution of urea has a freezing point of $-0.6\,^\circ C$. To prepare such a solution,how many grams of urea are needed to dissolve in $3\,kg$ of water? $(M = 60\,g\,mol^{-1}, K_{f} = 1.5\,^\circ C\,kg\,mol^{-1})$

The freezing point of a $0.01 \ m$ aqueous glucose solution is $-0.18^\circ C$. If an equal volume of $0.002 \ m$ glucose solution is added to it,the freezing point of the resulting solution will be ...... $^\circ C$.

An aqueous solution of a weak monobasic acid containing $0.1 \text{ g}$ of the acid in $21.7 \text{ g}$ of water freezes at $272.813 \text{ K}$. If the value of $K_f$ for water is $1.86 \text{ K kg/mol}$, what is the molecular mass of the monobasic acid in $\text{g/mol}$? (Assume the freezing point of pure water is $273 \text{ K}$)