$A$ molecule $M$ associates in a given solvent according to the equation $M \rightleftharpoons (M)_n$. For a certain concentration of $M,$ the van't Hoff factor was found to be $0.9$ and the fraction of associated molecules was $0.2.$ The value of $n$ is

The values of observed and calculated molecular mass of silver nitrate are $92.64$ and $170$ respectively. The degree of dissociation of silver nitrate is ........ $\%$.

$A$ solute $A$ undergoes association in a medium as $nA \rightleftharpoons A_n$. If the degree of association is $\alpha$,then the van't Hoff factor $i$ is given by:

$A$ solute $A$ dimerizes in water. The boiling point of a $2 \, M$ solution of $A$ is $100.52^{\circ} C$. The percentage association of $A$ is ..... $\%$.
(Round off to the Nearest integer)
[Use : $K_{b}$ for water $= 0.52 \, K \, kg \, mol^{-1}$,Boiling point of water $= 100^{\circ} C$]

If a solution prepared by adding $6.1 \ g$ of benzoic acid $(C_6H_5COOH)$ in $500 \ g$ of benzene freezes at $-0.290 \ ^oC$,find the percentage of association. (Given: $K_f$ of benzene $= 5.12 \ K \ kg/mol$,freezing point of pure benzene $= 5.50 \ ^oC$,molar mass of benzoic acid $= 122 \ g/mol$) (in $\%$)

If a $0.01 \ m$ aqueous solution of an electrolyte freezes at $-0.056 \ ^{\circ}C$,calculate the van't Hoff factor $(i)$ for the electrolyte. (Cryoscopic constant of water $K_{f} = 1.86 \ K \ kg \ mol^{-1}$)