$A$ solution has a $1:4$ mole ratio of pentane to hexane. The vapour pressure of the pure hydrocarbons at $20 \ ^oC$ are $440 \ mm \ Hg$ for pentane and $120 \ mm \ Hg$ for hexane. The mole fraction of pentane in the vapour phase would be

$A$ solution of urea (molar mass $60 \ g \ mol^{-1}$) boils at $100.20^{\circ}C$ at atmospheric pressure. If $K_{f}$ and $K_{b}$ for water are $1.86$ and $0.512 \ K \ kg \ mol^{-1}$ respectively,the freezing point of the solution will be:

An aqueous solution of a non-electrolyte boils at $100.52 \, ^\circ C$. The freezing point of the solution will be ............ $^\circ C$.

The freezing point of an aqueous solution is $-0.186 \ ^oC$. The boiling point of the same solution is ........ $^oC$. (Given: $K_f = 1.86 \ K \ kg \ mol^{-1}$ and $K_b = 0.512 \ K \ kg \ mol^{-1}$)

Solid Lead nitrate is dissolved in $1 \, L$ 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: $K_b = 0.5 \, K \, kg \, mol^{-1}$ and $K_f = 1.8 \, K \, kg \, mol^{-1}$. Assume molality to be equal to molarity in all cases.

The freezing point depression of $0.001 \ M$ of $A_x B_y[Fe(CN)_6]$ is $5.58 \times 10^{-3} \ K$. If the oxidation state of $Fe$ is $+2$ and $K_f = 1.86 \ K \ kg \ mol^{-1}$,then the total number of possibilities for different types of $A$ and $B$ cations are