Q.Derive the relation between elevation of boiling point and molar mass of solute.

Elevation in boiling point is proportional to molality; rearranging the defining relation gives the solute's molar mass.

When a non-volatile solute is dissolved in a volatile solvent, the vapour pressure of the solution is lowered, which raises its boiling point (the solution must be heated to a higher temperature before its vapour pressure equals atmospheric pressure). Experimentally, for dilute solutions, the elevation in boiling point $\Delta T_b = T_b(\text{solution}) - T_b(\text{pure solvent})$ is directly proportional to the molal concentration ($m$, moles of solute per kg of solvent) of the solution:

$\Delta T_b \propto m \ \Rightarrow\ \Delta T_b = K_b\,m$

where $K_b$ is the molal elevation constant (ebullioscopic constant) of the solvent, a solvent-specific constant.

Molality $m = \dfrac{n_2 \times 1000}{w_1} = \dfrac{(w_2/M_2)\times 1000}{w_1}$, where $w_2$ = mass of solute, $M_2$ = molar mass of solute (unknown), $w_1$ = mass of solvent in grams.

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