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CBSE Class 12 Chemistry 2017 Delhi Set 1 Solved Paper

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Question : 11 of 26
Marks: +1, -0
A 10%10\% solution (by mass) of sucrose in water has freezing point of 269.15K269.15 \mathrm{K}. Calculate the freezing point of 10%10\% glucose in water, if freezing point of pure water is 273.15K273.15 \mathrm{K}.
Given : (Molar mass of sucrose =342gmol−1=342 \mathrm{g} \mathrm{mol}^{-1} )
(Molar mass of glucose =180gmol−1=180 \mathrm{g} \mathrm{mol}^{-1} )
Solution:  
ΔTt=(273.15−269.15)K=4K\Delta T_t = (273.15-269.15) \mathrm{K} = 4 \mathrm{K}
Molar mass of sucrose (C12H22O11)(\mathrm{C}_{12}\mathrm{H}_{22}\mathrm{O}_{11})
  =(12×12)+(22×1)+(11×16)\; = (12 \times 12) + (22 \times 1) + (11 \times 16)
  =342gmol−1\; = 342 \mathrm{g} \mathrm{mol}^{-1}
10%10\% solution of sucrose in water means 10g10 \mathrm{g} of sucrose is present in (100−10)g(100-10) \mathrm{g} of water.
  Number of moles of sucrose  =  10342\; \text{Number of moles of sucrose} \; = \; \frac{10}{342}
  =0.0292mol\; = 0.0292 \mathrm{mol}
Therefore, molality of the solution
=0.0292×100090=0.3244molkg−1= \frac{0.0292 \times 1000}{90} = 0.3244 \mathrm{mol} \mathrm{kg}^{-1}
We know that ΔTt=Kf×m\Delta T_t = K_f \times m
⇒Kf=ΔTtm=40.3244\Rightarrow K_f = \frac{\Delta T_t}{m} = \frac{4}{0.3244} =12.33KKgmol−1= 12.33 \mathrm{K} \mathrm{Kg} \mathrm{mol}^{-1}
Molar mass of glucose (C6H12O6)(\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6)
=(6×12)+(12×1)+(6×16)= (6 \times 12) + (12 \times 1) + (6 \times 16) =180gmol−1= 180 \mathrm{g} \mathrm{mol}^{-1}
10%10\% solution of glucose in water means 10g10 \mathrm{g} of glucose is present in (100−10)g(100-10) \mathrm{g} of water.
  Number of moles of glucose  \; \text{Number of moles of glucose} \; =10180=0.0555mol= \frac{10}{180} = 0.0555 \mathrm{mol}
Therefore,molality of the solution
  =0.0555×100090\; = \frac{0.0555 \times 1000}{90}
  =0.6166molkg−1\; = 0.6166 \mathrm{mol} \mathrm{kg}^{-1}
  We know that  ΔTt=Kf×m\; \text{We know that} \; \Delta T_t = K_f \times m
⇒  ΔTt=12.33×0.6166=7.60K\Rightarrow \; \Delta T_t = 12.33 \times 0.6166 = 7.60 \mathrm{K}
So, the freezing point of 10%10\% glucose solution in water is (273.15−7.60)K=265.55K(273.15-7.60) \mathrm{K} = 265.55 \mathrm{K}
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