$A$ solution of urea contains $8.6 \ g/L$ (mol. wt. $60.0$). It is isotonic with a $5\%$ solution of a non-volatile solute. The molecular weight of the solute will be:

Solution $A$ is prepared by dissolving $1 \text{ g}$ of a protein (molar mass = $50000 \text{ g mol}^{-1}$) in $0.5 \text{ L}$ of water at $300 \text{ K}$. Its osmotic pressure is $x \text{ bar}$. Solution $B$ is made by dissolving $2 \text{ g}$ of the same protein in $1 \text{ L}$ of water at $300 \text{ K}$. The osmotic pressure of solution $B$ is $y \text{ bar}$. The entire solution of $A$ is mixed with the entire solution of $B$ at the same temperature. The osmotic pressure of the resultant solution is $z \text{ bar}$. $x, y$ and $z$ respectively are: $(R = 0.083 \text{ L bar mol}^{-1} \text{ K}^{-1})$

$A$ $5 \%$ solution of cane sugar (mol. wt. $= 342$) is isotonic with $1 \%$ solution of a substance $X$. The molecular weight of $X$ is

Which of the following pairs of aqueous solutions exhibits the same osmotic pressure at the same temperature? $\left[ \text{Molar mass of urea} = 60 \ g \ mol^{-1}, \text{sucrose} = 342 \ g \ mol^{-1} \right]$

When $10 \ g$ of glucose $(P_1)$,$10 \ g$ of urea $(P_2)$,and $10 \ g$ of sucrose $(P_3)$ are dissolved in $250 \ mL$ of water,what is the relationship between their osmotic pressures at $273 \ K$?

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