$1.7920 \ g$ 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.

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

The measured freezing point depression for a $0.1 \ m$ aqueous $CH_{3}COOH$ solution is $0.19^{\circ} C$. The acid dissociation constant $K_{a}$ at this concentration will be (Given, $K_{f}$ the molal cryoscopic constant $= 1.86 \ K \ kg \ mol^{-1}$)

When $0.0106 \text{ mole}$ of acetic acid is dissolved in $1 \text{ kg}$ of water, the observed freezing point depression is $0.0205 \text{ K}$. If the calculated freezing point depression is $0.0197 \text{ K}$, the Van't Hoff factor $(i)$ and the degree of dissociation $(\alpha)$ of acetic acid are respectively:

When substance $A$ is dissolved in solvent $B$,it associates to form $A_3$. The van't Hoff factor $i$ is:

$A$ molecule $M$ associates in a given solvent according to the equation $M \rightleftharpoons (M)_n$. For a certain concentration of $M,$ the van't Hoff factor was found to be $0.9$ and the fraction of associated molecules was $0.2.$ The value of $n$ is