When $20 \ g$ of naphthoic acid $(C_{11}H_8O_2)$ is dissolved in $50 \ g$ of benzene, a freezing point depression of $2 \ K$ is observed. The van't Hoff factor $(i)$ is [$K_f = 1.72 \ K \ kg \ mol^{-1}$].

When $0.0106 \text{ mole}$ of acetic acid is dissolved in $1 \text{ kg}$ of water, the observed freezing point depression is $0.0205 \text{ K}$. If the calculated freezing point depression is $0.0197 \text{ K}$, the Van't Hoff factor $(i)$ and the degree of dissociation $(\alpha)$ of acetic acid are respectively:

The molecular weight of benzoic acid in benzene as determined by the depression in freezing point method corresponds to:

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

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 for $BaCl_2$ is $2.47$. Calculate the percentage dissociation of $BaCl_2$ in its aqueous solution. (in $\%$)