The osmotic pressure of a urea solution at $10\,^oC$ is $500\, mm\, of\, Hg$. The solution is diluted such that the temperature increases to $25\,^oC$ and the osmotic pressure becomes $131.6\, mm\, of\, Hg$. By what factor has the solution been diluted?

$20 \text{ g}$ hemoglobin in a $1 \text{ L}$ aqueous solution $(A)$ at $300 \text{ K}$ is separated from pure water by a semi-permeable membrane. At equilibrium, the height of the solution in a tube dipped in solution $(A)$ is found to be $80.0 \text{ mm}$ higher than the tube dipped in water. The molar mass of hemoglobin is . . . . . . $\text{kg mol}^{-1}$. (Nearest integer) (Given: $g = 10 \text{ m s}^{-2}$, $R = 8.3 \text{ kPa dm}^3 \text{ K}^{-1} \text{mol}^{-1}$, density of solution = $1000 \text{ kg m}^{-3}$)

Assertion $(A)$: Blood cells collapse when suspended in saline water.
Reason $(R)$: Cell membrane dissolves in saline water.

Assume a living cell with $0.9 \% (\omega / \omega)$ of glucose solution (aqueous). This cell is immersed in another solution having equal mole fraction of glucose and water. (Consider the data up to the first decimal place only). The cell will :

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

Which method is most suitable to determine the molecular mass of a polymer?