When $12.2 \ g$ of benzoic acid is dissolved in $100 \ g$ of water,the freezing point of the solution was found to be $-0.93^{\circ} C$ $(K_{f}(H_{2}O) = 1.86 \ K \ kg \ mol^{-1})$. The number $(n)$ of benzoic acid molecules associated (assuming $100 \ \%$ association) is ........ .

Molecules of benzoic acid $(C_6H_5COOH)$ dimerise in benzene. '$w$' $g$ of the acid dissolved in $30 \ g$ of benzene shows a depression in freezing point equal to $2 \ K.$ If the percentage association of the acid to form dimer in the solution is $80,$ then $w$ is : ............. $g$
(Given that $K_f = 5 \ K \ kg \ mol^{-1},$ Molar mass of benzoic acid $= 122 \ g \ mol^{-1}$ )

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.$)$

When acetic acid is dissolved in benzene,its molecular mass:

Phenol associates in benzene to a certain extent to form a dimer. $A$ solution containing $20 \times 10^{-3} \ kg$ of phenol in $1 \ kg$ of benzene has its freezing point decreased by $0.69 \ K$. Calculate the percentage degree of association of phenol. ($K_f$ for benzene $= 5.12 \ K \ kg \ mol^{-1}$)

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 ...........