If $0.15 \ m$ aqueous solution of $KCl$ freezes at $-0.51^{\circ} C$,calculate the van't Hoff factor of $KCl$ (cryoscopic constant of water is $1.86 \ K \ kg \ mol^{-1}$).

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 experimental depression in freezing point of a dilute solution is $0.025 \ K$. If the van't Hoff factor $(i)$ is $2.0$, the calculated depression in freezing point (in $K$) is

Dimerisation of solute molecules in low dielectric constant solvent is due to

$A$ solution of $1.25 \ g$ of '$P$' in $50 \ g$ of water lowers the freezing point by $0.3^{\circ}C$. The molar mass of '$P$' is $94 \ g \ mol^{-1}$. Given $K_{f(\text{water})} = 1.86 \ K \ kg \ mol^{-1}$,the degree of association of '$P$' in water is:

For a $0.1 \ M$ $Ba(NO_3)_2$ solution,the van't Hoff factor is $2.74$. The degree of dissociation is ....... $\%$.