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JEE Main 2024 · Chemistry · Biomolecules and Polymers · medium

42 g of sucrose is completely hydrolysed and the solution is made up to 100 mL. Specific rotations: glucose +52.5^°, fructose -92.4^° (in deg mL g^-1…

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3.42 g3.42\ \mathrm{g} of sucrose is completely hydrolysed and the solution is made up to 100 mL100\ \mathrm{mL}. Specific rotations: glucose +52.5∘+52.5^\circ, fructose −92.4∘-92.4^\circ (in deg mL g−1 dm−1\mathrm{deg\,mL\,g^{-1}\,dm^{-1}}). The observed rotation in a 10 cm10\ \mathrm{cm} tube is nearly (molar mass of sucrose =342=342)
  1. A. −0.72∘-0.72^\circ
  2. B. +0.72∘+0.72^\circ
  3. C. −0.36∘-0.36^\circ
  4. D. −1.44∘-1.44^\circ
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Answer: (A) −0.72∘-0.72^\circ

3.42 g=0.01003.42\ \mathrm{g}=0.0100 mol sucrose gives 0.01000.0100 mol each of glucose and fructose (180 g mol−1180\ \mathrm{g\,mol^{-1}}), i.e. 1.80 g1.80\ \mathrm{g} of each in 100 mL100\ \mathrm{mL}: c=0.018 g mL−1c=0.018\ \mathrm{g\,mL^{-1}}. Path length l=1 dml=1\ \mathrm{dm}. α=∑[α]cl=(52.5−92.4)(0.018)(1)=−0.718∘\alpha=\sum[\alpha]cl=(52.5-92.4)(0.018)(1)=-0.718^\circ. The negative sign (inversion of sugar) is because fructose rotates more strongly than glucose.
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