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

When $12.2 \ g$ of benzoic acid is dissolved in $100 \ g$ of water,the freezing point of the solution was found to be $-0.93^{\circ} C$ $(K_{f}(H_{2}O) = 1.86 \ K \ kg \ mol^{-1})$. The number $(n)$ of benzoic acid molecules associated (assuming $100 \ \%$ association) is ........ .

Three particles of a solute $A$ associate in benzene to form a trimer $A_3$. Calculate the freezing point of a $0.25 \ m$ solution if the degree of association of solute $A$ is $0.80$. The freezing point of benzene is $5.5 \ ^oC$ and $K_f$ is $5.12 \ K \ kg \ mol^{-1}$. (Answer in $K$)

When $2.44 \ g$ of benzoic acid $(C_6H_5COOH)$ is dissolved in $25 \ g$ of benzene,it shows a depression of freezing point equal to $2.2 \ K$. The molal depression constant of benzene is $5.0 \ K \ kg \ mol^{-1}$. What is the percentage association of the acid,if it forms a dimer in the solution (in $\%$)?

$A$ compound $MX_2$ has observed and normal molecular masses $65.6$ and $164$ respectively. Calculate the percentage of ionization of $MX_2$ ............ $\%$

The van't Hoff factor $(i)$ is .....