The osmotic pressure of a solution is given by the relation

Calculate the mass of a non-volatile solute dissolved in $0.3 \text{ dm}^3$ of water, which has an osmotic pressure of $0.1 \text{ atm}$ at $300 \text{ K}$. [Molar mass of solute = $328 \text{ g mol}^{-1}$, $R = 0.082 \text{ dm}^3 \text{atm K}^{-1} \text{mol}^{-1}$] (in $\text{ g}$)

If osmotic pressure of a solution is $2 \ atm$ at $273 \ K$,then at $546 \ K$,the osmotic pressure is ........... $atm.$

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: $(R = 0.083 \text{ L bar mol}^{-1} \text{ K}^{-1})$

When does the osmotic pressure of a solution increase?

Assuming complete ionisation,arrange the following solutions in order of increasing osmotic pressure.
$(a)$ $0.5 \ m \ Li_2SO_4$
$(b)$ $0.5 \ m \ KCl$
$(c)$ $0.5 \ m \ Al_2(SO_4)_3$
$(d)$ $0.1 \ m \ BaCl_2$