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

$1.2 \ mL$ of acetic acid having density $1.06 \ g \ cm^{-3}$ is dissolved in $1 \ L$ of water. The depression in freezing point observed for this concentration of acid was $0.041^{\circ} C$. The van't Hoff factor of the acid is $(K_f \text{ of water } = 1.86 \ K \ kg \ mol^{-1})$

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?

One molal solution of a carboxylic acid in benzene shows the elevation of boiling point of $1.518 \ K$. The degree of association for dimerization of the acid in benzene is $........ \%$. ($K_b$ for benzene $= 2.53 \ K \ kg \ mol^{-1}$)

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

If $m$ is the normal molecular weight and $x$ is the degree of dissociation of $K_4[Fe(CN)_6]$,then the abnormal molecular weight in the solution of the salt will be $:-$