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JIPMER 2007
Exam
JIPMER
Year
2007
Subject
Chemistry
Chapter
Solutions

JIPMER 2007 · Chemistry · Solutions

A solution of urea (mol. mass 56 ~g ~mol^ -1 ) boils at 100.18^ C...

A solution of urea (mol. mass 56 g mol−156 \mathrm{~g} \mathrm{~mol}^{-1} ) boils at 100.18∘C100.18^{\circ} \mathrm{C} at the atmospheric pressure. If kfk_f and kbk_b for water are 1.86 and 0.512 K kg mol−10.512 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1} respectively, the above solution will freeze at

Options

  1. A−6.54∘C-6.54^{\circ} \mathrm{C}
  2. B6.54∘C6.54^{\circ} \mathrm{C}
  3. C0.654∘C0.654^{\circ} \mathrm{C}
  4. D−0.654∘C-0.654^{\circ} \mathrm{C}

Correct answer

D. −0.654∘C-0.654^{\circ} \mathrm{C}

Step-by-step solution

∵ΔTf=kf× Molality of  solution ΔTb=kb× Molality of solution \begin{aligned} \because \Delta T_f & =k_f \times \text{ Molality\text{ of } solution } \\ \Delta T_b & =k_b \times \text{ Molality of solution }\end{aligned}or \frac{\Delta T_f}{\Delta T_b}=\frac{k_f}{k_b}GiventhatGiven that\Delta T_b=T_2-T_1=100.18-100=0.18 kf for  water =1.86Kkgmol−1kb for water =0.512Kkgmol−1\begin{aligned} & k_f \text{\text{ for } water }=1.86 \mathrm{ K} \mathrm{ kg} \mathrm{ mol}^{-1} \\ & k_b \text{ for water }=0.512 \mathrm{ K} \mathrm{ kg} \mathrm{ mol}^{-1}\end{aligned} \therefore \frac{\Delta T_f}{0.18}=\frac{1.86}{0.512} ΔTf=1.86×0.180.512=0.6539∼0.654ΔTf=T1−T20.654=0∘C−T2\begin{aligned} \Delta T_f & =\frac{1.86 \times 0.18}{0.512} \\ & =0.6539 \sim 0.654 \\ \Delta T_f & =T_1-T_2 \\ 0.654 & =0^{\circ} \mathrm{C}-T_2\end{aligned} \therefore T_2=-0.654^{\circ} \mathrm{C} (T2→T_2 \rightarrow Freezing point of aqueous urea solution)$
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