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

For a $1.5 \, m$ aqueous solution of $Ca(NO_3)_2$,the observed molar mass is $65.4 \, g \, mol^{-1}$ and the theoretical molar mass is $164 \, g \, mol^{-1}$. The degree of dissociation is .............

$2 \ g$ 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 ......... $\%$.

Benzoic acid undergoes dimerisation in benzene solution. The van't Hoff factor $(i)$ is related to the degree of association '$x$' of the acid as

If a $0.02 \, M \, Pb(NO_3)_2$ solution is isotonic with a $0.05 \, M$ aqueous glucose solution,the degree of dissociation of $Pb(NO_3)_2$ will be ..........

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 [$K_f = 1.72 \ K \ kg \ mol^{-1}$].