GATE 2025 CY – Question 33

Organic Chemistry · Stereochemistry: Chirality and symmetry of organic molecules with or without chiral centres and determination of their absolute configurations and optical purity. Relative stereochemistry in compounds having more than one stereogenic centre. Homotopic, enantiotopic and diastereotopic atoms, groups and faces. Conformational analysis of acyclic and cyclic compounds. Geometrical isomerism and optical isomerism. Configurational and conformational effects, atropisomerism, and neighbouring group participation on reactivity and selectivity/specificity. Stereoselective and stereospecific synthesis. Enantiomeric excess. · 1 mark · Numerical answer

The specific rotation of enantiomerically pure (S)-2-butanol is +14°. The specific rotation of enantiomeric mixture of 2-butanol obtained from an asymmetric reduction of 2-butanone is found to be +7°. The percentage of (R)-2-butanol present in the reaction mixture is _____ (in integer).

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Correct answer: 25

Explanation

**Optical purity.** The specific rotation of the mixture divided by that of the pure enantiomer gives the enantiomeric excess (ee):
$$ee=\frac{[\alpha]_{mix}}{[\alpha]_{pure}}=\frac{+7}{+14}=0.50=50\% .$$

The positive sign shows that the (S) enantiomer is in excess (pure S is +14°).

**Composition.** $ee=x_S-x_R=0.50$ and $x_S+x_R=1$:
$$x_R=\frac{1-0.50}{2}=0.25 .$$

The mixture contains **25%** of the (R)-2-butanol.