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 $K_b = 0.512 \ K \ kg \ mol^{-1}$)

$100 \ mL$ of $1.5\%(w/v)$ solution of urea has an osmotic pressure of $6.0 \ atm$ and $100 \ mL$ of $3.42\%(w/v)$ solution of cane sugar has an osmotic pressure of $2.4 \ atm$. If the two solutions are mixed,the osmotic pressure of the resulting solution in $atm$ is (Assume that there is no reaction between urea and cane sugar).

$1$ 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 $= 1.0\, g\, cm^{-3}$]

For $0.1 \ M$ solutions of urea and $Al_2(SO_4)_3$,which of the following statements is correct? $(a)$ $i$ for urea is $1$ and $i$ for $Al_2(SO_4)_3$ is $5$. $(b)$ $Al_2(SO_4)_3$ has a higher elevation in boiling point. $(c)$ $Al_2(SO_4)_3$ has a higher depression in freezing point. $(d)$ Urea has a higher vapor pressure.

On mixing urea, the boiling point of $H_{2}O$ changed to $100.5^{\circ}C$. Calculate the freezing point of the solution, if $K_{f}$ of water is $1.87 \ K \cdot kg \cdot mol^{-1}$ and $K_{b}$ of water is $0.52 \ K \cdot kg \cdot mol^{-1}$. (in $^{\circ}C$)

Elevation in the boiling point for $1 \ m$ solution of glucose is $2 \ K$. The depression in the freezing point for $2 \ m$ solution of glucose in the same solvent is $2 \ K$. The relation between $K_b$ and $K_f$ is