$75.2 \ g$ of $C_6H_5OH$ (phenol) is dissolved in a solvent of $K_f = 14 \ K \ kg \ mol^{-1}$. If the depression in freezing point is $7 \ K$,then find the percentage of phenol that dimerises. (in $\%$)

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

$2$ molal solution of a weak acid $HA$ has a freezing point of $-3.885^{\circ} C$. The degree of dissociation of this acid is ........ $\times 10^{-3}$. (Round off to the Nearest Integer).
[Given: Molal depression constant of water = $1.85 \ K \ kg \ mol^{-1}$,Freezing point of pure water = $0^{\circ} C$]

The degree of dissociation $(\alpha)$ of a weak electrolyte,$A_xB_y$ is related to van't Hoff factor $(i)$ by the expression

When $20 \ g$ of naphthoic acid $(C_{11}H_8O_2)$ is dissolved in $50 \ g$ of benzene, a freezing point depression of $2 \ K$ is observed. The van't Hoff factor $(i)$ is [$K_f = 1.72 \ K \ kg \ mol^{-1}$].

$A$ non-volatile solute '$A$' tetramerizes in water to the extent of $80\%$. $2.5 \text{ g}$ of '$A$' in $100 \text{ g}$ of water lowers the freezing point by $0.3^\circ \text{C}$. The molar mass of $A$ in $\text{g mol}^{-1}$ is ($K_f$ for water $= 1.86 \text{ K kg mol}^{-1}$)