The freezing point of a $0.262 \ mol \ kg^{-1}$ solution of acetic acid in benzene is $277.4 \ K$. If the $K_f$ value for benzene is $5.0 \ K \ kg \ mol^{-1}$ and the freezing point of pure benzene is $278.4 \ K$,then the van't Hoff factor is ...........

Solute $A$ associates in water. When $0.7 \ g$ of solute $A$ is dissolved in $42.0 \ g$ of water,it depresses the freezing point by $0.2^{\circ} C$. The percentage association of solute $A$ in water is $..... \ \%$.
[Given: Molar mass of $A = 93 \ g \ mol^{-1}$. Molal depression constant of water is $1.86 \ K \ kg \ mol^{-1}$]

The molecular mass of acetic acid $(CH_3COOH)$ dissolved in water is $60$,whereas when dissolved in benzene,it is $120$. This difference in behavior is because:

When $1.5 \ g$ of phenol $(C_6H_5OH)$ is dissolved in $100 \ g$ of toluene,a decrease in freezing point of $0.56 \ K$ is observed. If the association is dimeric in nature,find the percentage of association. Given: $K_f = 4 \ K \ kg \ mol^{-1}$.

$A$ solution of $1.25 \ g$ of '$P$' in $50 \ g$ of water lowers the freezing point by $0.3^{\circ}C$. The molar mass of '$P$' is $94 \ g \ mol^{-1}$. Given $K_{f(\text{water})} = 1.86 \ K \ kg \ mol^{-1}$,the degree of association of '$P$' in water is:

If $0.1 \ M$ solution of $NaCl$ is isotonic with $1.1 \ w \%$ urea solution, the degree of ionisation of $NaCl$ is $($Molar masses of urea and $NaCl$ are $60 \ g \ mol^{-1}$ and $58.5 \ g \ mol^{-1}$, respectively.$)$