Difficulty: Intermediate | Prerequisites: Stereochemistry fundamentals (R/S, enantiomers, chirality)
Chiral molecules rotate plane-polarised light. The direction and magnitude of that rotation depend on the molecule's identity, its concentration and the path length of the sample cell. Enantiomeric excess (ee) tells you how much of one enantiomer you have over the other, and it links the observed rotation of a mixture to the specific rotation of the pure compound. Most exam problems in this area are just algebra once you know the three formulas.
Specific rotation [α]
The intrinsic optical rotation of a pure compound, measured under standard conditions (typically at 25 °C using the sodium D line, 589 nm). It is a physical constant for a given compound, like a melting point. In simple terms, it is the compound's "signature" rotation.
Observed rotation (α)
The actual rotation measured by a polarimeter for a particular sample. It depends on three things: the specific rotation of the compound, the concentration of the sample, and the path length of the sample cell.
Optically active
A substance that rotates plane-polarised light. All pure chiral compounds are optically active.
Optically inactive
A substance that does not rotate plane-polarised light. This can mean the compound is achiral, or it can mean you have a racemic mixture (equal amounts of both enantiomers, whose rotations cancel out).
Racemic mixture (racemate)
A 50:50 mixture of two enantiomers. The rotations cancel, so the observed rotation is zero. In simple terms, equal parts of left-handed and right-handed molecules, so the net twist on light is nil.
Enantiomeric excess (ee)
The percentage by which one enantiomer exceeds the other in a mixture. An ee of 100% means the sample is enantiopure. An ee of 0% means it is racemic. Think of it as a measure of optical purity.
Polarimeter
The instrument used to measure optical rotation. It passes plane-polarised light through a sample and measures how many degrees the light has been rotated.
Plane-polarised light
Light whose electric field oscillates in a single plane. When it passes through a chiral sample, the plane rotates by a measurable angle.
The relationship between observed and specific rotation is:
α = [α] × c × l
Where:
α = observed rotation (in degrees), the number the polarimeter reads.
[α] = specific rotation (in degrees), the compound's intrinsic property.
c = concentration (in g/mL).
l = path length of the sample cell (in dm, where 1 dm = 10 cm).
Key points:
Enantiomers have specific rotations of equal magnitude but opposite sign. If (2S,5E)-mysteriol has [α] = –30°, then its enantiomer (2R,5E)-mysteriol has [α] = +30°.
Diastereomers have specific rotations that are unrelated in magnitude or sign. You cannot predict the specific rotation of (2R,5Z)-mysteriol from the specific rotation of (2S,5E)-mysteriol because they are diastereomers, not enantiomers.
Observed rotation is directly proportional to concentration: if you halve the concentration, you halve the observed rotation.
A racemic mixture has [α]_mixture = 0 because the contributions cancel.
Three equivalent formulas for ee:
ee = % major enantiomer – % minor enantiomer
ee = 100% × [α]_mixture / [α]_pure
From the ratio: if the mixture is A:B (where A > B), then ee = (A – B) / (A + B) × 100%
Given: [α] of (2S,5E)-mysteriol = –30°.
Example (a): Specific rotation of a 5:1 mixture of (2S,5E)-mysteriol and its enantiomer.
The enantiomer has [α] = +30°.
ee = (5 – 1) / (5 + 1) × 100% = 4/6 × 100% = 66.7%
[α]_mixture = ee × [α]_pure / 100% = 66.7% × (–30°) / 100% = –20°
The specific rotation of the mixture is –20°.
Example (b): A mixture of (2S,5E)-mysteriol and its enantiomer has [α] = –6°. What is the ratio of enantiomers?
ee = 100% × |–6| / |–30| = 20%
This means: % major – % minor = 20%, and % major + % minor = 100%.
Solving: % major = 60%, % minor = 40%.
Ratio = 60:40 = 3:2, or equivalently 1.5:1.
The major enantiomer is (2S,5E)-mysteriol (negative rotation), present at 60%.
Example (c): What is the specific rotation of pure (2R,5Z)-mysteriol?
You cannot know. (2R,5Z)-mysteriol is a diastereomer of (2S,5E)-mysteriol (both the stereocentre and the alkene geometry differ). Diastereomers have unrelated specific rotations. There is no way to calculate it from the information given.
Example (d): A sample of mysteriol has an observed rotation of +22°. You dilute it to half its original concentration. What is the new observed rotation?
α = [α] × c × l. If c is halved and everything else stays the same, α is halved.
New observed rotation = +22° / 2 = +11°.
α = [α] × c × l (observed rotation = specific rotation × concentration × path length)
ee = % major enantiomer – % minor enantiomer
ee = 100% × [α]_mixture / [α]_pure
[α]_mixture = [α]_A × fraction_A + [α]_B × fraction_B (for a two-component enantiomeric mixture)
Students often assume that R configuration always corresponds to (+) rotation (dextrorotatory) and S to (–) rotation (levorotatory). There is no such correlation. R/S is a naming convention based on spatial arrangement; the sign of rotation is an experimental measurement.
Diluting a solution does not change the specific rotation. It changes the observed rotation. Specific rotation is an intrinsic property of the compound, like density.
Students sometimes try to predict the specific rotation of a diastereomer from the specific rotation of another diastereomer. This cannot be done. Only enantiomers have predictable relationships (± same magnitude).
A common error is forgetting that ee relates percentages, not absolute amounts. If you have 60% of one enantiomer and 40% of the other, ee = 20%, not 60%.
⚠️ ee calculation problems are almost guaranteed on a stereochemistry exam. Practise converting between ratio, ee and [α]_mixture until it is automatic.
⚠️ The "can you know this?" question (like example c above) tests whether you understand the difference between enantiomers and diastereomers. If the question asks about a diastereomer's specific rotation, the answer is "cannot be determined."
⚠️ Dilution problems test whether you know that observed rotation depends on concentration. Specific rotation does not change with dilution.
⚠️ A racemic mixture is optically inactive (always true). This is a classic true/false question.
Q: A pure chiral compound has [α] = +50°. You measure a mixture of this compound and its enantiomer and find [α]_mixture = +30°. What is the ee, and what is the ratio of enantiomers?
A: ee = 100% × 30/50 = 60%. This means % major – % minor = 60 and % major + % minor = 100. So % major = 80%, % minor = 20%. Ratio = 80:20 = 4:1.
Q: You know the specific rotation of (S)-alanine. Can you predict the specific rotation of (S)-leucine?
A: No. They are different compounds entirely (different structures), so their specific rotations are unrelated. You can only predict the rotation of the enantiomer of a given compound.
Q: A sample of a chiral compound in a 1 dm cell at concentration 0.5 g/mL gives α = +15°. What is the specific rotation?
A: [α] = α / (c × l) = 15 / (0.5 × 1) = +30°.
Q: You have a sample with observed rotation +22°. You double the path length. What is the new observed rotation?
A: +44°. Observed rotation is directly proportional to path length.
Optical activity ties directly to stereochemistry fundamentals (covered in the companion notes): you need to know whether two compounds are enantiomers or diastereomers before you can say anything about their rotations. It also connects forward to reaction selectivity: when a reaction produces one enantiomer preferentially (an asymmetric synthesis), the ee of the product tells you how selective the reaction was.
Optical activity, optical rotation, specific rotation, observed rotation, enantiomeric excess, ee, racemic mixture, racemate, optically active, optically inactive, polarimeter, plane-polarised light, dextrorotatory, levorotatory, (+) and (–) rotation, chiral, enantiopure, optical purity, stereochemistry calculations, organic chemistry practice problems