$1 \ g$ of non-volatile non-electrolyte solute is dissolved in $100 \ g$ of two different solvents $A$ and $B$ whose ebullioscopic constants are in the ratio of $1 : 5$. The ratio of the elevation in their boiling points,$\frac{\Delta T_b (A)}{\Delta T_b (B)}$ is

$5 \text{ g}$ of urea is dissolved in $100 \text{ g}$ of water. Find the amount of glucose to be dissolved in $120 \text{ g}$ of water so that the boiling points of both solutions are the same. [Molar mass of urea $= 60 \text{ g mol}^{-1}$, Molar mass of glucose $= 180 \text{ g mol}^{-1}$] (in $\text{ g}$)

$A$ solution of non-volatile solute has a boiling point elevation of $1.75 \ K$. Calculate the molality of the solution $[K_{b} = 3.5 \ K \ kg \ mol^{-1}]$.

Calculate the molar mass of a non-volatile solute when $4 \text{ g}$ of it is dissolved in $100 \text{ g}$ of a solvent that boils at $319.4 \text{ K}$. Given: $K_b = 2.4 \text{ K kg mol}^{-1}$ and the boiling point of the pure solvent is $319 \text{ K}$.

Pure benzene boils at $80\,^oC$. When $1\,g$ of a solute is dissolved in $83.4\,g$ of benzene,the boiling point of the solution becomes $80.175\,^oC$. If the latent heat of vaporization of benzene is $90\,cal/g$,calculate the molar mass of the solute.

$A$ solution containing $2.5 \times 10^{-3} \ kg$ of a solute dissolved in $75 \times 10^{-3} \ kg$ of water boils at $373.535 \ K$. The molar mass of the solute is $..... \ g \ mol^{-1}$. [nearest integer] (Given: $K_b(H_2O) = 0.52 \ K \ kg \ mol^{-1}$,boiling point of water $= 373.15 \ K$)