A $0.5\%$ aqueous solution of $\mathrm{KCl}$ was found to freeze at $272.76 \mathrm{K}$. Calculate the van't Hoff factor and the degree of dissociation of $\mathrm{KCl}$ at this concentration.

${\mathrm{K}}_{\mathrm{f}}\left({\mathrm{H}}_2\mathrm{O}\right)=1.86°\mathrm{C} {\mathrm{m}}^{-1}$.

When $60.26 \mathrm{g}$ of ${\mathrm{VCl}}_4$ was added to $1000 \mathrm{g}$ of solvent ${\mathrm{CCl}}_4$, the freezing point of ${\mathrm{CCl}}_4$ was depressed by $5.415°\mathrm{C}$. ${\mathrm{K}}_{\mathrm{f}}$ for ${\mathrm{CCl}}_4$ is $29.9$. Compare the number of moles of particles with the number predicted by the formula. Calculate the number of dimers, ${\mathrm{V}}_2{\mathrm{Cl}}_8$ present.

[Hint: $2{\mathrm{VCl}}_4\to {\mathrm{V}}_2{\mathrm{Cl}}_8$]

The vapour pressure of a $0.01 \mathrm{m}$ solution of a weak base $\mathrm{BOH}$ in water at $20°\mathrm{C}$ is $17.536 \mathrm{mm}.$ Calculate ${\mathrm{K}}_{\mathrm{b}}$ for the base. Aqueous tension at $20°\mathrm{C}=17.54 \mathrm{mm}$. (Give answer as ${\mathrm{K}}_{\mathrm{b}} \times {10}^4$ )

[Hint $\mathrm{i}=\frac{\text{ observed lowering in}\mathrm{vapour} \mathrm{pressure}}{\text{ calculated lowering in vapour pressure }}=\frac{\mathrm{p}-{\mathrm{p}}_{\text{obs. }}}{{\mathrm{p}}^0·\frac{\mathrm{n}}{\mathrm{N}}}=\frac{17.540-17.536}{17.54\times \frac{0.01}{1000/18}},$

Then apply $\mathrm{i}=1+\mathrm{x}$ and ${\mathrm{K}}_{\mathrm{b}}=\frac{0.01{\mathrm{x}}^2}{1-\mathrm{x}}$]

In an Ostwald-Walker experiment, dry air was first blown through a solution containing a certain amount of solute $(\mathrm{M}=278)$ in $150 \mathrm{g}$ of water and then also through pure water. The loss in mass of water was found to be $0.0827 \mathrm{g}$, while the mass of water absorbed in sulphuric acid was $3.317 \mathrm{g}$. Calculate the amount of the solute.

Give your answer up to two decimal places without rounding-off.

The vapour pressure of pure water at $25°\mathrm{C}$ is $23.62 \mathrm{mm}$ $\mathrm{Hg}$, What will be the vapour pressure of a solution of $1.5 \mathrm{g}$ of urea in $50 \mathrm{g}$ of water?

Give your answer up to two decimal places.