If a $0.01 \ m$ aqueous solution of an electrolyte freezes at $-0.056 \ ^{\circ}C$,calculate the van't Hoff factor $(i)$ for the electrolyte. (Cryoscopic constant of water $K_{f} = 1.86 \ K \ kg \ mol^{-1}$)

$A$ $0.004 \ M$ solution of $Na_2SO_4$ is isotonic with a $0.010 \ M$ solution of glucose at the same temperature. The apparent degree of dissociation of $Na_2SO_4$ is $..... \ \%$.

Determine the degree of association (polymerization) for the reaction in aqueous solution $6 HCHO \rightleftharpoons C_6H_{12}O_6$. If the observed (mean) molar mass of the mixture is $150 \ g/mol$. (Given: Molar mass of $HCHO = 30 \ g/mol$)

Calculate the van't Hoff factor $(i)$ for an aqueous solution of $0.02 \text{ m}$ formic acid if it freezes at $-0.045^{\circ}\text{C}$. Given: $K_f = 1.86 \text{ K kg mol}^{-1}$ and the freezing point of pure water $= 0^{\circ}\text{C}$.

$0.004 \ M \ Na_2SO_4$ is isotonic with $0.01 \ M$ glucose. The degree of dissociation of $Na_2SO_4$ is ........... $\%$.

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