Calculate the van't Hoff factor $(i)$ for an aqueous solution of $0.02 \text{ m}$ formic acid if it freezes at $-0.045^{\circ}\text{C}$. Given: $K_f = 1.86 \text{ K kg mol}^{-1}$ and the freezing point of pure water $= 0^{\circ}\text{C}$.

The difference between the boiling point and the freezing point of a $0.2 \ m$ solution of acetic acid in benzene is $75.7 \ ^\circ C$. Calculate the value of the van't Hoff factor $i$. (For benzene,$K_b = 2.65 \ K \ m^{-1}$,$K_f = 5.12 \ K \ m^{-1}$,$T_b^o = 80 \ ^\circ C$,$T_f^o = 5.5 \ ^\circ C$)

The values of observed and calculated molecular weight of silver nitrate are $90$ and $170$ respectively. The degree of dissociation of silver nitrate is ......... $\%$.

The molecular weight of $NaCl$ determined by osmotic pressure method will be

$HA_{(aq)} \rightleftharpoons H^{+}_{(aq)} + A^{-}_{(aq)}$
The freezing point depression of a $0.1 \ m$ aqueous solution of a monobasic weak acid $HA$ is $0.20^{\circ} C$. The dissociation constant for the acid is. Given: $K_{f}(H_2O) = 1.8 \ K \ kg \ mol^{-1}$,molality $\equiv$ molarity.

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: $K_f = 4 \ K \ kg \ mol^{-1}$.