The Van't Hoff factor of $BaCl_2$ at a concentration of $0.01 \ M$ is $1.98$. The percentage dissociation of $BaCl_2$ at this concentration will be: (in $\%$)

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 $=$ $1.86 \ K \ kg \ mol^{-1}$.

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,$K_b = 2.65 \ K \ m^{-1}$,$K_f = 5.12 \ K \ m^{-1}$,$T_b^o = 80 \ ^\circ C$,$T_f^o = 5.5 \ ^\circ C$)

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.

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 $K_{f} = 1.86 \ K \ kg \ mol^{-1}$)

Benzoic acid undergoes dimerisation in benzene solution. The van't Hoff factor $(i)$ is related to the degree of association '$x$' of the acid as