In an experiment to estimate the molecular weight of benzoic acid by the elevation in boiling point method, the experimental value of the molecular weight was double the actual value. Calculate the degree of association of the dimer.

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

$1.2 \ mL$ of acetic acid having density $1.06 \ g \ cm^{-3}$ is dissolved in $1 \ L$ of water. The depression in freezing point observed for this concentration of acid was $0.041^{\circ} C$. The van't Hoff factor of the acid is $(K_f \text{ of water } = 1.86 \ K \ kg \ mol^{-1})$

The freezing point of benzene decreases by $0.45 ^\circ C$ when $0.2 \ g$ of acetic acid is added to $20 \ g$ of benzene. If acetic acid associates to form a dimer in benzene,the percentage association of acetic acid in benzene will be .......... $\%$
$(K_f \text{ for benzene} = 5.12 \ K \ kg \ mol^{-1})$

The Van't Hoff factor $i$ for a $0.2 \ m$ aqueous solution of urea is

$75.2 \ g$ of phenol is added to $1 \ kg$ of solvent. The depression in freezing point is $7 \ K$. If phenol undergoes dimerization,calculate the percentage of association. $(K_f = 14 \ K \ kg \ mol^{-1})$