2 g of a non-volatile non-electrolyte solute is dissolved in 200 g of two different solvents A and B whose ebullioscopic constants are in the ratio of 1 : 8. The elevation in boiling points of A and B are in the ratio x \over y (x : y). The value of y is \underline\hspace2cm . (Nearest integer)

Solutions PYQ — JEE Main 2022 · 27 Jun · Shift 1 · Q12 with Solution

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Correct answer: 8

For a non-volatile, non-electrolyte solute:

$\Delta T_b = K_b \, m$

where $K_b$ is the ebullioscopic constant and $m$ is the molality.

We are told:

Molality is

$m = \frac{\text{moles of solute}}{\text{kg of solvent}}$

Since both the solute mass and solvent mass are same in the two solvents, the molality is the same for both solutions.

So,

$\Delta T_b \propto K_b$

Given:

$K_{b,A} : K_{b,B} = 1:8$

Therefore,

$\Delta T_{b,A} : \Delta T_{b,B} = 1:8$

Hence,

$x:y = 1:8$

So,

$y = 8$

The required nearest integer is:

$\boxed{8}$