$0.05$ moles of ${\mathrm{N}}_2$ gas dissolves completely in $900 \mathrm{gm}$ water at $27°\mathrm{C}$, as shown in the following figure.

The available space between piston and liquid solution is $16.42 \mathrm{L}$. Find the number of moles of ${\mathrm{N}}_2$ in gaseous phase.
$\left({\mathrm{K}}_{\mathrm{H}}\right.$ for ${\mathrm{N}}_2$ gas $\left.=7.2\times {10}^4 \mathrm{atm}.\right)(\mathrm{R}=0.0821 \mathrm{atm}-\mathrm{L}/\mathrm{mole}-\mathrm{K})$, Round off the value to the nearest integer.

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.

To $500 {\mathrm{cm}}^3$ of water, $3\times {10}^{-3} \mathrm{kg}$ of acetic acid is added. If $23\%$ of acetic acid is dissociated, what will be the depression in freezing point? ${\mathrm{K}}_{\mathrm{f}}$ and density of water are $1.86 \mathrm{K} {\mathrm{kg}}^{-1} {\mathrm{mol}}^{-1}$ and $0.997 \mathrm{g} {\mathrm{cm}}^{-3}$ respectively.

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

A solution of a nonvolatile solute in water freezes at $-0.30°\mathrm{C}$. The vapour pressure of pure water at $298 \mathrm{K}$ is $23.51 \mathrm{mm} \mathrm{Hg}$ and ${\mathrm{K}}_{\mathrm{f}}$ for water is $1.86 \mathrm{degree}/\mathrm{molal}$. Calculate the magnitude of change in vapour pressure of this solution $\left(\mathrm{in} \mathrm{mmHg}\right)$ at $298 \mathrm{K}$.

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

A $0.1 \mathrm{M}$ solution of an acid (density$=1.01 \mathrm{g}/\mathrm{cc}$ ) is $4.5\%$ ionised. Calculate the depression in fp of the solution. The molecular weight of the acid is $300. {\mathrm{K}}_{\mathrm{f}}=1.86$.

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

An aqueous solution of mannitol in water has a vapour pressure of $17.504 \mathrm{mm}$ at $20°\mathrm{C}$, at which temperature the vapour pressure of pure water is $17.535 \mathrm{mm}$. What is the f.p. depression for this solution?

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

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

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. ${\mathrm{K}}_{\mathrm{f}}\left({\mathrm{C}}_6{\mathrm{H}}_6\right)=5.12 \mathrm{K} {\mathrm{mol}}^{-1} \mathrm{kg}$.

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.