$180 \ g$ of glucose,$C_6H_{12}O_6$,is dissolved in $1 \ kg$ of water in a vessel. The temperature at which water boils at $1.013 \ bar$ is $ . . . . . . $ (given,$K_b$ for water is $0.52 \ K \ kg \ mol^{-1}$. Boiling point for pure water is $373.15 \ K$) (in $K$)

$5 \text{ g}$ 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 $\text{ g}$)

When $174.5 \ mg$ of octatomic sulfur $(S_8)$ is added to $78 \ g$ of bromine $(Br_2)$,the boiling point of bromine becomes ............. $K$. Given: $K_b$ for $Br_2 = 5.2 \ K \ kg \ mol^{-1}$ and the boiling point of pure $Br_2 = 332.15 \ K$.

When $0.5143 \ g$ of anthracene is dissolved in $35 \ g$ of $CHCl_3$,the boiling point of $CHCl_3$ increases by $0.323 \ K$. Calculate the molar mass of anthracene. ($K_b$ for $CHCl_3 = 3.9 \ K \ kg \ mol^{-1}$)

Vessel-$1$ contains $w_2 \ g$ of a non-volatile solute $X$ dissolved in $w_1 \ g$ of water. Vessel-$2$ contains $w_2 \ g$ of another non-volatile solute $Y$ dissolved in $w_1 \ g$ of water. Both the vessels are at the same temperature and pressure. The molar mass of $X$ is $80 \%$ of that of $Y$. The van't Hoff factor for $X$ is $1.2$ times that of $Y$ for their respective concentrations. The elevation of boiling point for the solution in Vessel-$1$ is . . . . . . $\%$ of the solution in Vessel-$2$.

If the enthalpy of vaporization is approximately the same,for which of the following will the value of the ebullioscopic constant $(K_b)$ be maximum?