At $$27^{\circ} \mathrm{C}$$, a solution containing $$2.5 \mathrm{~g}$$ of solute in $$250.0 \mathrm{~mL}$$ of solution exerts an osmotic pressure of $$400 \mathrm{~Pa}$$. The molar mass of the solute is ___________ $$\mathrm{g} \mathrm{~mol}^{-1}$$ (Nearest integer)

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

Lead storage battery contains $38 \%$ by weight solution of $\mathrm{H}_{2} \mathrm{SO}_{4}$. The van't Hoff factor is $2.67$ at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is ________. (Nearest integer).

Given $\mathrm{K}_{f}=1.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$

A solution containing $$2 \mathrm{~g}$$ of a non-volatile solute in $$20 \mathrm{~g}$$ of water boils at $$373.52 \mathrm{~K}$$. The molecular mass of the solute is ___________ $$\mathrm{g} ~\mathrm{mol}^{-1}$$. (Nearest integer)

Given, water boils at $$373 \mathrm{~K}, \mathrm{~K}_{\mathrm{b}}$$ for water $$=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$$

Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at 100.15$$^\circ$$C. When 0.2 mol of NaCl is added to the resulting solution, it was observed that the solution froze at $$-0.8^\circ$$ C. The solubility product of PbCl$$_2$$ formed is __________ $$\times$$ 10$$^{-6}$$ at 298 K. (Nearest integer)

Given : $$\mathrm{K_b=0.5}$$ K kg mol$$^{-1}$$ and $$\mathrm{K_f=1.8}$$ K kg mol$$^{-1}$$. Assume molality to the equal to molarity in all cases.