Liquids A and B form ideal solution over the entire range of composition. At temperature $$T,$$ equimolar binary solution of liquids $$A$$ and $$B$$ has vapor pressure $$45$$ $$Torr.$$ At the same temperature, a new solution of $$A$$ and $$B$$ having mole fractions $${X_A}$$ and $${X_B}$$, respectively, has vapour pressure of $$22.5$$ $$Torr.$$ The value of $${x_A}/{x_B}$$ in the new solution is ___________.

(given that the vapor pressure of pure liquid $$A$$ is $$20$$ $$Torr$$ at temperature $$T$$)

The solubility of a salt of weak acid $$(AB)$$ at $$pH\,$$ $$3$$ is $$Y \times {10^{ - 3}}$$ $$mol\,{L^{ - 1}}.$$ The value of $$Y$$ is ________________.

(Given that the value of solubility product of $$AB$$ $$\left( {{K_{sp}}} \right) = 2 \times {10^{ - 10}}$$ and the value of ionization constant of $$HB$$ $$\left( {{K_a}} \right) = 1 \times {10^{ - 8}}$$)

A closed tank has two compartments $$A$$ and $$B,$$ both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure $$1.$$). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure $$2$$), the volume (in $${m^3}$$) of the compartment A after the system attains equilibrium is ______________.

The plot given below shows $$P-T$$ curves (where $$P$$ is the pressure and $$T$$ is the temperature) for two solvents $$X$$ and $$Y$$ and isomolal solutions of $$NaCl$$ in these solvents. $$NaCl$$ completely dissociates in both the solvents.



On addition of equal number of moles of a non-volatile solute $$S$$ in equal amount (in $$kg$$) of these solvents, the elevation of boiling point of solvent $$X$$ is three times that of solvent $$Y$$. Solute $$S$$ is known to undergo dimerization in these solvents. If the degree of dimerization is $$0.7$$ in solvent $$Y$$, the degree of dimerization in solvent $$X$$ is ___________.