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NEET CHEMISTRYMedium

At 100C100^\circ\text{C} the vapour pressure of a solution of 6.5 g6.5 \text{ g} of a solute in 100 g100 \text{ g} water is 732 mm732 \text{ mm}. If Kb=0.52K_b = 0.52, the boiling point of this solution will be

A

100C100^\circ\text{C}

B

102C102^\circ\text{C}

C

103C103^\circ\text{C}

D

101C101^\circ\text{C}

Step-by-Step Solution

At 100C100^\circ\text{C}, pure water boils, so its vapour pressure (pp^\circ) is equal to the atmospheric pressure, which is 760 mm Hg760 \text{ mm Hg}. Given vapour pressure of the solution (psp_s) = 732 mm Hg732 \text{ mm Hg}. Mass of solvent water (w1w_1) = 100 g=0.1 kg100 \text{ g} = 0.1 \text{ kg}. Molar mass of water (M1M_1) = 18 g mol118 \text{ g mol}^{-1}.

According to the relative lowering of vapour pressure: ppsps=n2n1\frac{p^\circ - p_s}{p_s} = \frac{n_2}{n_1} 760732732=n2100/18\frac{760 - 732}{732} = \frac{n_2}{100/18} 28732=n25.555\frac{28}{732} = \frac{n_2}{5.555} n2=28×5.5557320.2125 moln_2 = \frac{28 \times 5.555}{732} \approx 0.2125 \text{ mol}

Now, calculate the molality (mm) of the solution: m=n2w1 (in kg)=0.21250.1=2.125 mol kg1m = \frac{n_2}{w_1 \text{ (in kg)}} = \frac{0.2125}{0.1} = 2.125 \text{ mol kg}^{-1}

Elevation in boiling point (ΔTb\Delta T_b) is given by: ΔTb=Kb×m=0.52×2.1251.105C\Delta T_b = K_b \times m = 0.52 \times 2.125 \approx 1.105^\circ\text{C}

Therefore, the boiling point of the solution is: Tb=100C+1.105C=101.105C101CT_b = 100^\circ\text{C} + 1.105^\circ\text{C} = 101.105^\circ\text{C} \approx 101^\circ\text{C}.

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