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NEET CHEMISTRYEasy

A solution of sucrose (molar mass = 342 g mol1342 \text{ g mol}^{-1}) has been prepared by dissolving 68.5 g68.5 \text{ g} of sucrose in 1000 g1000 \text{ g} of water. The freezing point of the solution obtained will be: (KfK_f for water = 1.86 K kg mol11.86 \text{ K kg mol}^{-1})

A

0.372C-0.372^\circ\text{C}

B

0.372C0.372^\circ\text{C}

C

0.572C0.572^\circ\text{C}

D

0.572C-0.572^\circ\text{C}

Step-by-Step Solution

Given: Mass of solute (sucrose, w2w_2) = 68.5 g68.5 \text{ g} Molar mass of sucrose (M2M_2) = 342 g mol1342 \text{ g mol}^{-1} Mass of solvent (water, w1w_1) = 1000 g=1 kg1000 \text{ g} = 1 \text{ kg} KfK_f for water = 1.86 K kg mol11.86 \text{ K kg mol}^{-1}

First, we calculate the molality (mm) of the solution: m=w2M2×w1 (in kg)=68.5342×10.2 mol kg1m = \frac{w_2}{M_2 \times w_1 \text{ (in kg)}} = \frac{68.5}{342 \times 1} \approx 0.2 \text{ mol kg}^{-1}

Now, calculate the depression in freezing point (ΔTf\Delta T_f): ΔTf=Kf×m=1.86×0.2=0.372C\Delta T_f = K_f \times m = 1.86 \times 0.2 = 0.372^\circ\text{C}

The freezing point of pure water is 0C0^\circ\text{C}. Therefore, the freezing point of the solution (TfT_f) is: Tf=TfΔTf=0C0.372C=0.372CT_f = T_f^\circ - \Delta T_f = 0^\circ\text{C} - 0.372^\circ\text{C} = -0.372^\circ\text{C}.

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