Calculate the osmotic pressure of a $0.2 \ M$ aqueous solution of an electrolyte at $300 \ K$. If the van't Hoff factor is $1.6$,find the osmotic pressure. $\left[R=0.0821 \ atm \ dm^3 \ K^{-1} \ mol^{-1}\right]$ (in $atm$)

At which temperature does a $0.006\% \ w/V$ urea solution have an osmotic pressure of $0.0246 \ atm$ (in $K$)?

$A$ solution containing $10 \, g \, dm^{-3}$ of urea $(M.wt = 60)$ is isotonic with a $5 \%$ solution of a non-volatile solute. The molecular mass of this non-volatile solute is ......... $g \, mol^{-1}$.

The solution containing $4.0 \ g$ of a polyvinyl chloride polymer in $1 \ L$ of dioxane was found to have an osmotic pressure of $6.0 \times 10^{-4} \ atm$ at $300 \ K$. Given $R = 0.082 \ L \ atm \ mol^{-1} \ K^{-1}$,the molecular mass of the polymer is:

Given below are two statements:
Statement $I$: $H_2O$ molecules move from the chamber $1$ to chamber $2$.
Statement $II$: The osmotic pressure of a solution prepared by dissolving $50 \text{ mg}$ of potassium sulphate (molar mass = $174 \text{ g/mol}$) in $2 \text{ L}$ of water (at $27^{\circ}C$) is $0.0107 \text{ bar}$. (Given: $R = 0.083 \text{ dm}^3 \text{ bar K}^{-1} \text{ mol}^{-1}$ and assume complete dissociation of electrolyte).
In the light of the above statements, choose the correct answer from the options given below:

What does a semi-permeable membrane allow to pass through?