Source: Dr Uyeda, Purdue University, Lectures 10–11 | Textbook Ch. 3 (7th/8th Ed.)
Difficulty: Intermediate | Prerequisites: Parts 1 and 2 of these notes (R/S configuration, enantiomers/diastereomers, meso compounds)
Tags: optical activity, optically active, plane-polarised light, polarimeter, specific rotation, enantiomeric excess, ee, percent optical purity, racemic mixture, racemate, racemise, dextrorotatory, levorotatory, thalidomide, carvone, CHEM 25500, organic chemistry, Purdue
So far, the discussion of stereoisomers has been about geometry: how atoms are arranged, how to label configurations. This section connects that geometry to something measurable in the lab, namely the way chiral molecules interact with plane-polarised light. It also introduces the quantitative tools (percent optical purity, enantiomeric excess) that let you work out the composition of a mixture of enantiomers from a single measurement. This is where stereochemistry meets experimental reality, and the calculations come up regularly on exams.
Chiral molecules that are not present as a 50:50 mixture rotate plane-polarised light. A polarimeter measures how much. The ratio of observed rotation to the rotation of the pure enantiomer gives you the optical purity, which equals the enantiomeric excess. From the ee you can work out the exact percentages of each enantiomer in the sample.
Plane-polarised light
Light that oscillates in a single plane, produced by passing ordinary light through a polarising filter. In simple terms, ordinary light vibrates in every direction; a polariser lets through only one "slice."
Optically active
Describes a substance that rotates the plane of plane-polarised light. A pure enantiomer or any non-racemic mixture of enantiomers is optically active.
Dextrorotatory (+)
Rotates plane-polarised light clockwise (to the right) when viewed facing the light source. Labelled with a (+) or the older prefix "d."
Levorotatory (−)
Rotates plane-polarised light counter-clockwise (to the left). Labelled with a (−) or the older prefix "l."
Specific rotation [α]
The standardised measure of optical rotation for a pure substance, defined at a given temperature, wavelength, solvent, and concentration. This is the value you look up or are given in a problem.
Polarimeter
The instrument used to measure optical rotation. Light passes through a polariser, then through a sample tube, then through an analyser that detects how far the plane has been rotated.
Racemic mixture (racemate)
An equal (1:1) mixture of two enantiomers. A racemate is optically inactive because the rotations cancel exactly.
Racemise
To convert from a pure or enriched enantiomer into a racemic mixture. Some compounds racemise spontaneously under biological conditions.
Enantiomeric excess (ee) / percent optical purity
The numerical measure of how far a mixture deviates from racemic. Defined as the absolute difference in the percentages of the two enantiomers, or equivalently as the observed rotation divided by the pure-enantiomer rotation, multiplied by 100.
Enantiomers share identical physical properties in an achiral environment: same melting point, boiling point, density, solubility, refractive index, and colour.
The two things that distinguish enantiomers are:
Their interaction with plane-polarised light (one rotates it clockwise, the other counter-clockwise, by the same magnitude).
Their interaction with other chiral molecules (different binding to chiral receptors, enzymes, etc.).
Diastereomers are different compounds in every respect. They have different melting points, boiling points, solubilities, and reactivities.
Ordinary light oscillates in all planes perpendicular to the direction of travel.
A polarising filter produces plane-polarised light, which oscillates in only one plane.
When plane-polarised light passes through a solution of a chiral, non-racemic substance, the plane of polarisation rotates.
A polarimeter measures this rotation (α) in degrees.
The direction of rotation is unrelated to the R/S label. You cannot predict the sign of rotation from the configuration; it must be measured experimentally.
Percent optical purity:
Percent optical purity = ([α]_sample / [α]_pure enantiomer) × 100
Enantiomeric excess:
ee = |%R − %S| (or equivalently |%S − %R|)
Percent optical purity and enantiomeric excess give the same number. They are two names for the same quantity.
0% ee = racemic (50% R, 50% S). No net optical rotation.
100% ee = enantiopure (100% of one enantiomer). Maximum optical rotation.
Given: A sample of mandelic acid shows an observed rotation of −134°. Pure (R)-mandelic acid has a specific rotation of +158°.
Step 1: Calculate percent optical purity.
Optical purity = (−134 / 158) × 100 = 84.8%
The negative sign tells you the sample is enriched in the S enantiomer.
Step 2: Determine composition.
84.8% of the mixture contributes net S rotation, so 84.8% is excess S enantiomer.
The remaining 15.2% is a racemic portion (equal parts R and S): 7.6% R + 7.6% S.
Total: 84.8% + 7.6% = 92.4% S, and 7.6% R.
(R)-Carvone smells like caraway; (S)-carvone smells like spearmint. Same molecule, opposite configuration, completely different sensory response, because olfactory receptors are chiral.
Thalidomide was marketed in 1957 as a racemic mixture for treating morning sickness. The (R) enantiomer is a sedative. The (S) enantiomer is teratogenic (causes birth defects). Even when a single enantiomer is administered, racemisation occurs in the body, so separating them before dosing does not solve the problem.
Percent optical purity = ([α]_observed / [α]_pure) × 100
ee = |%R − %S|
If ee = X% and the major enantiomer is S:
%S = 50 + (X / 2)
%R = 50 − (X / 2)
Pharmaceutical companies routinely measure enantiomeric excess during drug production to verify that their synthesis produces enough of the desired enantiomer. The thalidomide disaster led directly to stricter regulatory requirements around stereochemical purity of drugs, and the concept of racemisation in vivo remains a consideration in modern drug design.
Students frequently assume that R = (+) and S = (−). There is no such rule. The sign of rotation is an experimental property that must be measured; the R/S label is a geometric assignment from the CIP rules.
A racemic mixture is optically inactive, but "optically inactive" does not always mean racemic. A meso compound is also optically inactive, and it is a single compound, not a mixture.
When calculating composition from ee, students sometimes forget that the "remaining" percentage is split equally between the two enantiomers (the racemic portion). The ee is the excess, not the total amount of the major enantiomer.
Thalidomide is sometimes cited as a case where separating enantiomers would have prevented harm. The complication is that thalidomide racemises in the body, so administering only (R)-thalidomide still produces the (S) form in vivo.
⚠️ Optical purity / ee calculations are a near-guaranteed exam question. Practise converting between ee, percent composition, and observed rotation in both directions.
⚠️ Know the distinction: R/S = geometric label; (+)/(−) = experimental measurement of light rotation. They are independent.
⚠️ Expect a conceptual question asking you to compare the physical properties of enantiomers vs. diastereomers. Enantiomers: identical except for light rotation and chiral interactions. Diastereomers: different in every measurable property.
⚠️ The thalidomide and carvone examples are commonly tested as illustrations of why chirality matters biologically.
True or false: A racemic mixture rotates plane-polarised light.
Fill in the blank: A compound with an ee of 60% that is enriched in the R enantiomer contains ________% R and ________% S.
True or false: Diastereomers have the same boiling point.
Fill in the blank: (R)-carvone smells like ________; (S)-carvone smells like ________.
True or false: You can predict the sign of optical rotation from the R or S configuration.
Answers: 1. False (the rotations of the two enantiomers cancel). 2. 80% R and 20% S. 3. False. 4. Caraway; spearmint. 5. False.
Q: A sample has an enantiomeric excess of 72% and is enriched in the S enantiomer. What is its composition?
A: The excess portion is 72% S. The remaining 28% is racemic: 14% R + 14% S. Total: 86% S, 14% R.
Q: Pure (S)-2-bromobutane has a specific rotation of −23.1°. A sample shows a rotation of +11.5°. What is the ee, and which enantiomer predominates?
A: Optical purity = (11.5 / 23.1) × 100 = 49.8%. The positive sign means the sample is enriched in the R enantiomer (since pure S is negative). ee ≈ 50%.
Q: Why are enantiomers indistinguishable by melting point but distinguishable by a polarimeter?
A: Melting point depends on the strength of intermolecular forces, which are identical for enantiomers because the atomic composition and connectivity are the same. Optical rotation depends on the interaction of light with a chiral environment, which differs for opposite configurations.
Q: A meso compound is optically inactive. Is it a racemic mixture?
A: No. A meso compound is a single, achiral molecule with an internal plane of symmetry. A racemic mixture is a 50:50 blend of two different enantiomeric molecules. Both are optically inactive, but for different reasons.
Q: Why did separating thalidomide enantiomers before administration not solve the teratogenicity problem?
A: Thalidomide racemises in the body. Even if only the safe (R) enantiomer is given, it converts to a 50:50 mixture of (R) and (S) in vivo, regenerating the harmful form.
Optical activity ties back to the discussion of molecular symmetry from earlier in the course and will return when you study reaction mechanisms: whether a reaction produces a racemic mixture or a single enantiomer tells you something fundamental about the mechanism (SN1 gives racemisation; SN2 gives inversion). The ee calculation is also used in lab courses whenever you run an asymmetric synthesis and need to evaluate how selective it was.
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