MHTCET 11 May 2024 Shift 2 Paper

Concept:Boiling point elevation is a colligative property.It depends only on the number of solute particles, not their identity.Equal boiling points mean equal molality for both solutions.Explanation:For glucose, concentration is $18\ \mathrm{g\,dm^{-3}}$ and molar mass is $180\ \mathrm{g\,mol^{-1}}$.Moles of glucose per $\mathrm{dm^3}$ are:$$\frac{18}{180} = 0.1\ \mathrm{mol\,dm^{-3}}$$For solute A, concentration is $6\ \mathrm{g\,dm^{-3}}$.Let the molar mass of A be $M\ \mathrm{g\,mol^{-1}}$.Moles of A per $\mathrm{dm^3}$ are:$$\frac{6}{M}$$Since both solutions boil at the same temperature, their molalities are equal.For dilute aqueous solutions, the volume basis is directly proportional to solvent mass.Therefore, we can equate the molar concentrations:$$0.1 = \frac{6}{M}$$Solving for $M$:$$M = \frac{6}{0.1} = 60\ \mathrm{g\,mol^{-1}}$$Thus, the molar mass of solute A is $60\ \mathrm{g\,mol^{-1}}$.Answer:The molar mass of A is $60\ \mathrm{g\,mol^{-1}}$, which corresponds to option D.