$30 \mathrm{mL}$ of methanol (density $=0.7980 \mathrm{g} {\mathrm{mL}}^{-1}$) on mixing with $70 \mathrm{mL}$ of water (density $=0.9984 \mathrm{g} {\mathrm{mL}}^{-1}$) at $298 \mathrm{K}$ gave a solution of density $0.9575 \mathrm{g} {\mathrm{mL}}^{-1}$. Calculate the freezing point of the solution in ${}^{\mathrm{o}}\mathrm{C}$ and report the value by rounding off to two significant figures

${\mathrm{K}}_{\mathrm{f}}\left({\mathrm{H}}_2\mathrm{O}\right)=1.86$

The freezing point of a solution containing $0.2 \mathrm{g}$ of acetic acid in $20.0 \mathrm{g}$ of benzene is lowered by $0.45°\mathrm{C}$. Calculate the degree of association of acetic acid in benzene. ${\mathrm{K}}_{\mathrm{f}}\left({\mathrm{C}}_6{\mathrm{H}}_6\right)=5.12 \mathrm{K} {\mathrm{mol}}^{-1} \mathrm{kg}$.

Given: $\mathrm{Au}-\mathrm{sol},{\mathrm{Sb}}_2{\mathrm{S}}_3-\mathrm{sol}$

Methylene blue, ${\mathrm{TiO}}_2-\mathrm{sol}$, Gelatin, Starch, Congo red, ${\mathrm{Fe}}_2{\mathrm{O}}_3\times {\mathrm{H}}_2\mathrm{O}$ Number of common positive sols $=\mathrm{x}$

Number of common negative sols $=\mathrm{y}$, then $2\mathrm{x}-\mathrm{y}$ value is

The tallest trees known are the redwoods in California. Assuming the height of a redwood tree to be $105 \mathrm{m}$, estimate the osmotic pressure required to push water up from the roots to the treetop. $\left({\mathrm{d}}_{{\mathrm{H}}_2\mathrm{O}}=1 \mathrm{g}/\mathrm{cc}, \mathrm{g}=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

If the answer is of type $\mathrm{y}\times {10}^6 \mathrm{Pa}$, mention the value of $\mathrm{y}$ correct up to nearest integer value.

A solution of crab hemocyanin, a pigmented protein extracted from crabs was prepared by dissolving $0.75 \mathrm{g}$ in $125 \mathrm{cc}$ of an aqueous medium. At $4°\mathrm{C}$, the osmotic pressure rise of $2.6 \mathrm{mm}$ of the solution was observed. The solution had a density of $1 \mathrm{g} {\mathrm{cc}}^{-1}$. Determine the molecular weight (in g mole^-1) of the protein. $\left(\mathrm{R}=0.0821 \mathrm{atm}-\mathrm{L} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}\right)$

Report your answer after dividing it by ${10}^4$ and rounding-off up to nearest integer.

A solution of cane sugar at $27°\mathrm{C}$ develops an osmotic pressure of$4.93$$\mathrm{atm}$. Calculate the magnitude of freezing point of this solution (${\mathrm{K}}_{\mathrm{f}} =1.86 \mathrm{K} {\mathrm{molal}}^{-1}$).

Give answer after multiplying with 100 and rounding off to the nearest integer value.