Osmotic pressure of a urea solution at $10\,^{\circ}C$ is $500\,mm$. The osmotic pressure of the solution becomes $105.3\,mm$ when it is diluted and the temperature is raised to $25\,^{\circ}C$. The extent of dilution is .......... times.

Which of the following pairs of solutions can be isotonic at the same temperature?

$A$ $5\% \text{ (w/v)}$ solution of cane sugar (molar mass = $342 \text{ g/mol}$) is isotonic with a $1\% \text{ (w/v)}$ solution of an unknown solute. What is the molar mass of the unknown solute in $\text{g/mol}$?

$A$ $3\% \, w/v$ aqueous solution of urea is isotonic with a $5\% \, w/v$ aqueous solution of another solute. Assuming the van't Hoff factor for the solute is $1.0$,calculate the molar mass of the solute in $g/mol$.

At $300 \ K$,a one litre solution of sucrose (molecular weight: $342$) was prepared by dissolving $40 \ g$ of sucrose. What is the approximate osmotic pressure (in $kPa$) of the solution at the same temperature? $(R = 8.314 \times 10^6 \ cm^3 \ Pa \ K^{-1} \ mol^{-1})$

What is the osmotic pressure of a semi-molar solution at $27^{\circ} C$ (in $atm$)?
$(R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1})$