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.

The number of pairs of the solutions having the same value of the osmotic pressure from the following is _________.

(Assume 100% ionization)

A. 0.500 $$\mathrm{M~C_2H_5OH~(aq)}$$ and 0.25 $$\mathrm{M~KBr~(aq)}$$

B. 0.100 $$\mathrm{M~K_4[Fe(CN)_6]~(aq)}$$ and 0.100 $$\mathrm{M~FeSO_4(NH_4)_2SO_4~(aq)}$$

C. 0.05 $$\mathrm{M~K_4[Fe(CN)_6]~(aq)}$$ and 0.25 $$\mathrm{M~NaCl~(aq)}$$

D. 0.15 $$\mathrm{M~NaCl~(aq)}$$ and 0.1 $$\mathrm{M~BaCl_2~(aq)}$$

E. 0.02 $$\mathrm{M~KCl.MgCl_2.6H_2O~(aq)}$$ and 0.05 $$\mathrm{M~KCl~(aq)}$$

The osmotic pressure of solutions of PVC in cyclohexanone at 300 K are plotted on the graph.

The molar mass of PVC is ____________ g mol$$^{-1}$$ (Nearest integer)

(Given : R = 0.083 L atm K$$^{-1}$$ mol$$^{-1}$$)

The total pressure observed by mixing two liquids A and B is 350 mm Hg when their mole fractions are 0.7 and 0.3 respectively.

The total pressure becomes 410 mm Hg if the mole fractions are changed to 0.2 and 0.8 respectively for A and B. The vapour pressure of pure A is __________ mm Hg. (Nearest integer)

Consider the liquids and solutions behave ideally.