MHTCET 15 Apr 2026 Shift 1 Paper

Concept:For the boiling points of two solutions to be equal, their boiling point elevations must be equal.Since both solutes are dissolved in water, the ebullioscopic constant $K_b$ is the same for both solutions.Therefore, the molalities of the two solutions must be equal.Explanation:Elevation in boiling point is given by:$$\Delta T_b = K_b \times m$$So, equal $\Delta T_b$ with the same $K_b$ implies equal molality $m$.For the urea solution:$$\text{Moles of urea} = \frac{5\ \mathrm{g}}{60\ \mathrm{g\ mol^{-1}}} = \frac{1}{12}\ \mathrm{mol}$$$$\text{Mass of water} = 100\ \mathrm{g} = 0.1\ \mathrm{kg}$$$$m = \frac{\frac{1}{12}\ \mathrm{mol}}{0.1\ \mathrm{kg}} = \frac{1}{1.2} = 0.833\ \mathrm{mol\ kg^{-1}}$$Hence, the glucose solution must also have molality $0.833\ \mathrm{mol\ kg^{-1}}$.For glucose, the mass of water is $120\ \mathrm{g} = 0.12\ \mathrm{kg}$.$$\text{Moles of glucose} = 0.833 \times 0.12 = 0.1\ \mathrm{mol}$$$$\text{Mass of glucose} = 0.1\ \mathrm{mol} \times 180\ \mathrm{g\ mol^{-1}} = 18\ \mathrm{g}$$Answer:The amount of glucose required is $18\ \mathrm{g}$.Correct option: C.