$A$ saturated solution of $Ag_2SO_4$ shows a $0.003 \ K$ rise in boiling point. Calculate the $K_{sp}$ of $Ag_2SO_4$. Given: $K_b = 5 \ K \ kg \ mol^{-1}$ and $1 \ m = 1 \ M$.

$1$ molal $K_{4}[Fe(CN)_{6}]$ solution has a degree of dissociation of $0.4$. Its boiling point is equal to that of another solution which contains $18.1$ weight percent of a non-electrolytic solute $A$. The molar mass of $A$ is $.......\, u$. (Round off to the Nearest Integer). [Density of water $= 1.0\, g\, cm^{-3}$]

When $1.685 \ g$ of an alkali metal chloride is dissolved in $200 \ g$ water,the boiling point of the solution is measured to be $100.051 \ ^\circ C$. If the ionic solid has a crystal lattice with cation and anion radius $1.70 \ \mathring{A}$ and $1.80 \ \mathring{A}$ respectively,find the edge length of the solid assuming no defect in the crystal. Given: $K_b(H_2O) = 0.51 \ K \ kg \ mol^{-1}$,$N_A = 6 \times 10^{23}$,atomic masses: $[Li = 7, Na = 23, K = 39, Rb = 85.5, Cs = 133, Cl = 35.5]$.

Calculate the freezing point in $^oC$ of an aqueous solution of urea that boils at $100.18\,^oC$. $(K_f = 1.86\, ^oC\, m^{-1}, K_b = 0.512\,^oC\, m^{-1})$

The ionization constant of a monobasic acid $HA$ is to be determined. If a $0.025 \ m$ aqueous solution of the acid freezes at $-0.060 \ ^{\circ}C$,calculate the ionization constant $K_a$. (Assume molality = molarity and $K_f(H_2O) = 1.86 \ K \ kg \ mol^{-1}$).

At $T \ K$,the vapour pressure of pure benzene $(C_6H_6)$ and toluene $(C_7H_8)$ are $75 \ mm \ Hg$ and $22 \ mm \ Hg$ respectively. $23.4 \ g$ of benzene and $64.4 \ g$ of toluene are mixed to form an ideal solution. If the vapours are in equilibrium with the liquid mixture,the mole fraction of toluene in the vapour phase is (Atomic weight: $C=12, H=1$).