The van't Hoff factor for $BaCl_2$ is $2.47$. Calculate the percentage dissociation of $BaCl_2$ in its aqueous solution. (in $\%$)

$2 \ g$ of benzoic acid $(C_6H_5COOH)$ dissolved in $25 \ g$ of benzene shows a depression in freezing point equal to $1.62 \ K$. The molal depression constant for benzene is $4.9 \ K \ kg \ mol^{-1}$. The percentage of benzoic acid in dimeric form is ......... $\%$.

$0.004 \ M \ Na_2SO_4$ is isotonic with $0.01 \ M$ glucose. The degree of dissociation of $Na_2SO_4$ is ........... $\%$.

If the van't Hoff factor of a weak electrolyte $A_xB_y$ is $i$,then the degree of dissociation $(\alpha)$ is represented by which equation?

Assertion : Molecular mass of benzoic acid when determined by colligative properties is found high.
Reason : Dimerisation of benzoic acid.

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