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.

$2$ 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 = $0^{\circ} C$]

One mole of a solute $A$ is dissolved in a given volume of a solvent. The association of the solute takes place according to $nA \rightleftharpoons (A)_n$. The Van't Hoff factor $i$ is expressed as:

The Van't Hoff factor calculated from association data is always ... than calculated from dissociation data.

When $1.0 \ g$ of $KCl$ is dissolved in $200 \ g$ water,the decrease in freezing point of such solution is $0.24 \ K$,calculate Van't Hoff factor $(i)$ for such solution. $K_f$ of water $=$ $1.86 \ K \ kg \ mol^{-1}$.

$A$ 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: