Amygdalin & Mandelic Acid — Stereocentres, Enantiomers, Optical Rotation: 04-BS-12, May 2017, Q4

Question 4: Amygdalin & Mandelic Acid — Stereocentres, Enantiomers, Optical Rotation

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

amygdalin — mandelonitrile β-gentiobioside (two glucopyranose rings + the benzylic nitrile carbon)

(a) Eleven stereocentres. Tracing the structure: each of amygdalin's two glucopyranose rings contributes five stereocentres (the anomeric carbon plus C2, C3, C4, C5 — the standard count for a cyclic hexopyranose), and the benzylic carbon bearing –OH/–CN/phenyl/the glycosidic oxygen (the mandelonitrile carbon) is an eleventh. 2 rings × 5 + 1 = 11 stereocentres (the count of potential stereocentres does not depend on which configuration is assigned at each centre). The maximum number of stereoisomers is $$2^{11}=2048.$$

(b) Mandelic acid, PhCH(OH)COOH, has a single stereocentre (the benzylic carbon bearing OH, COOH, phenyl and H):

(R)-mandelic acid

(S)-mandelic acid

(c) A 60:40 mixture of R and S is a partially resolved sample; its observed rotation scales with the enantiomeric excess, not with the raw 60% alone, because the 40% S-fraction cancels an equal 40% of the R-fraction's rotation (racemic pairs contribute nothing):

Given. $[\alpha]_{\text{pure R}}=-154$; sample is 60% R, 40% S.

Find. $[\alpha]_{\text{obs}}$ of the mixture.

Enantiomeric excess. $$\mathrm{ee}=0.60-0.40=0.20\ (20\%)$$
Observed rotation scales linearly with ee. $$[\alpha]_{\text{obs}}=\mathrm{ee}\times[\alpha]_{\text{pure R}}=0.20\times(-154)=\boxed{-30.8^{\circ}}$$ The mixture is R-enriched, so it rotates plane-polarised light in the same (negative) sense as pure R, just scaled down to 20% of the pure compound's magnitude.

Quantity	Value
Stereocentres in amygdalin	11
Max. stereoisomers	2048
ee of the mandelic acid sample	20%
[α]_obs	−30.8°

Concept & Theory

Topic. Counting stereocentres in a polysaccharide/glycoside; enantiomeric excess and observed specific rotation.

Key relations. Max stereoisomers $=2^{n}$ for $n$ independent stereocentres (before accounting for any meso reduction). $[\alpha]_{\text{obs}}=\mathrm{ee}\times[\alpha]_{\text{pure}}$, where $\mathrm{ee}=|\%R-\%S|$.

Why this works. Optical rotation is additive and the two enantiomers rotate light equally and oppositely; a racemic 50:50 pair exactly cancels, so only the excess of one enantiomer over the other contributes net rotation.

Common pitfall. Using the raw major-isomer fraction (60%) instead of the excess (20%) when scaling the pure rotation — a 60:40 mixture is optically far weaker than a naive "60% of pure" calculation would suggest.

Source. McMurry, Organic Chemistry, 9th ed., Ch.5 (stereochemistry, optical rotation, enantiomeric excess); Ch.25 (carbohydrate stereochemistry).

Question 4 of 13: Amygdalin & Mandelic Acid — Stereocentres, Enantiomers, Optical Rotation

Question 4: Amygdalin & Mandelic Acid — Stereocentres, Enantiomers, Optical Rotation