In a solvent,$50\,\%$ of an acid $HA$ dimerizes and the rest dissociates. The van't Hoff factor of the acid is $.....\times 10^{-2}$. (Round off to the nearest integer)

$1.7920 \ g$ of $K_2SO_4$ is present in $1000 \ mL$ of solution. If such solution has an osmotic pressure of $0.680 \ bar$ at $26 \ ^\circ C$,then find out the van't Hoff factor value.

Molecules of benzoic acid $(C_6H_5COOH)$ dimerise in benzene. '$w$' $g$ of the acid dissolved in $30 \ g$ of benzene shows a depression in freezing point equal to $2 \ K.$ If the percentage association of the acid to form dimer in the solution is $80,$ then $w$ is : ............. $g$
(Given that $K_f = 5 \ K \ kg \ mol^{-1},$ Molar mass of benzoic acid $= 122 \ g \ mol^{-1}$ )

The experimentally determined molar mass of a non-volatile solute, $BaCl_2$, in water by Cottrell's method, is

$HA_{(aq)} \rightleftharpoons H^{+}_{(aq)} + A^{-}_{(aq)}$
The freezing point depression of a $0.1 \ m$ aqueous solution of a monobasic weak acid $HA$ is $0.20^{\circ} C$. The dissociation constant for the acid is. Given: $K_{f}(H_2O) = 1.8 \ K \ kg \ mol^{-1}$,molality $\equiv$ molarity.

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 $:-$