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Optical Purity and Enantiomeric Excess

All About Optical Purity and Enantiomeric Excess

What is a racemic mixture? What is “optically active”, “optically inactive”, and “optically pure”. What do the terms, “l” and “d” mean? What is the formula for optical purity? What is the difference between optical purity and enantiomeric excess? [OK, that one’s quick: they’re the same thing].

In this post we answer all these burning questions, and do some worked examples of optical purity and enantiomeric excess besides.

Table of Contents

  1. Louis Pasteur and The Discovery Of “Enantiomers”
  2. A Racemic Mixture Is An Equal Mixture Of Two Enantiomers And Has A Specific Rotation of 0° (Optically Inactive)
  3. An “Optically Pure” Solution Contains Only One Enantiomer
  4. The Terms “l-” And “d-” Refer To The “Levorotatory (–)” And “Dextrorotatory (+)” Forms Of Each Enantiomer
  5. The Formula For Optical Purity
  6. Using “Optical Purity” To Determinine The Molar Composition Of A Mixture
  7. Optical Purity = Enantiomeric Excess
  8. Another Practice Problem For Enantiomeric Excess
  9. An Optical Purity Practice Problem
  10. Notes

This post was co-authored with Matt Pierce of Organic Chemistry Solutions.  Ask Matt about scheduling an online tutoring session here.

1. Louis Pasteur And The Discovery Of  “Enantiomers”

In our last post on optical rotation, we saw that when Louis Pasteur crystallized a salt of a compound then known as “racemic acid” he discovered that it formed two different types of crystals.

When redissolved in water, one set of crystals rotated plane-polarized light clockwise (dextrorotatory, “to the right”).

The other set of crystals rotated plane-polarized light to exactly the same extent, but counterclockwise (levorotatory, “to the left”).

This was surprising for two reasons.

  • First, racemic acid was thought at the time to be a single compound. It turned out to be a 50:50 mixture of two compounds!
  • Second, racemic acid did not rotate plane-polarized light: in other words, it was optically inactive. However, each of the two components were themselves optically active: they rotated plane polarized light to equal and opposite extents.

This immediately explained why racemic acid is optically inactive: just like two equal and opposite vectors cancel to give zero, the equal and opposite rotations due to each component cancel each other out.

Pasteur also noticed that the crystal forms were mirror images of each other. Then, in a leap of insight made without knowing the precise structure of the molecule, he then proposed that the molecules themselves were mirror images of each other.  [note 1]

We now know this to be true. We call two molecules that are non-superimposable mirror images of each other, “enantiomers”.

(Molecules that are superimposable mirror images, we just call, “the same molecule”. In chemistry, “∀” is just “A” that’s been rotated)

2. A Racemic Mixture Is An Equal Mixture Of Two Enantiomers And Has A Specific Rotation of 0° (Optically Inactive)

The two components of “racemic acid” are (2S,3S)-tartaric acid, which is levorotatory, or (–); and (2R, 3R) tartaric acid, which is dextrotoratory, or (+). They are enantiomers of each other: stereoisomers which are non-superimposable mirror images.

We now use the term “racemic mixture” to refer to a 50:50 mixture of two enantiomers. (“Racemic” comes from the Latin racemus, or “a bunch of grapes”, a nod to the fact that tartaric acid crystals are also known as “wine diamonds”)

So Pasteur’s achievement was the first resolution of a racemic mixture.


3. An “Optically Pure” Solution Contains Only One Enantiomer

As we said, the two enantiomers of tartaric acid rotate plane-polarized light to equal and opposite extents. In the last post we introduced a more precise way of saying this, in that the two enantiomers of tartaric acid have equal and opposite specific rotations. 


These “specific rotations” have to be measured experimentally: there’s no simple correlation between the configuration of a chiral centre (R or S) and the optical rotation.

This term “specific rotation” means that for the given concentration, temperature, wavelength, and solvent

  • An “optically pure” (or “enantiomerically pure”) solution of 100% (S,S) tartaric acid and 0% (R,R) tartaric acid will have an optical rotation of –12°.
  • An “optically pure” solution of 100% (R,R) tartaric acid and 0% (S,S) tartaric acid will have an optical rotation of +12° .

We’ve also seen that a “racemic mixture” of 50% (S,S) tartaric acid and 50% (R,R) tartaric acid will have an optical rotation of 0°.

4. The Terms “l-” And “d-” Refer To The “Levorotatory (–)” And “Dextrorotatory (+)” Forms Of Each Enantiomer

If we call the “levorotatory” (–) form of tartaric acid  “l-”  and the “dextrorotatory” (+) form of tartaric acid “d-“, then we can make the following three points on a graph. [note: in the real world, this graph is not always so linear, but it will do for our purposes]


100% optically pure l-tartaric acid has a specific rotation of –12°, which gradually rises to 0° as the proportion of the d enantiomer is raised to 50%. As the the molar composition of the d form increases, so does the optical rotation, going up to +12° again for the optically pure d-enantiomer.

5. The Formula For Optical Purity

This suggests an idea. Let’s say you had a non-racemic but optically impure mixture of l and d enantiomers, a situation that arises quite frequently in modern organic chemistry [2].

By measuring the optical rotation of the mixture for a compound whose specific rotation is known,  you can figure out its optical purity and could work backwards to determine the ratio of enantiomers. [3]

For example, let’s say you had a mixture of enantiomers of tartaric acid that has an observed rotation of +6° .

We can define the optical purity as the observed rotation of a mixture divided by the specific rotation of the pure enantiomer (obtained under identical conditions).


For our solution of tartaric acid with an observed rotation of +6°, our optical purity would be 50%


6. Going From “Optical Purity” To Determining The Molar Composition Of The Mixture

Now comes the part which sometimes trips people up. What’s the molar composition of the mixture?

Your first answer might be 50:50.  50% d- and 50% l- . 

But when you think about it, that can’t be right: a 50-50 mixture would be racemic, which would have no optical rotation at all!

An “optical purity” of 50% actually means that the major enantiomer (d- in this case, since the solution is dextrorotatory) is present in 50% excess over the minor enantiomer. (l-)

The molar composition of the l-  and d- forms must add up to 100%:


So using some basic algebra, we can use these two equations to calculate the ratio of enantiomers.

For instance, in equation #2,  we can isolate the % of d- as being (50% + % l- ). We can then plug that value into equation #1 and we obtain the value for % l-  as 25%. The value for % d- must then be 75%.


So, far from being 50-50,  a mixture with 50% optical purity is actually a 75% : 25% mixture of enantiomers.

One way of looking at a 50% value for “optical purity” is that it’s 50% the dominant enantiomer, and 50% a racemic mixture.

7. Optical Purity = Enantiomeric Excess

If you do the math in the above example,  you’ll note that the percentage of the d– enantiomer (75%) exceeds the percentage of the l- enantiomer (25%) by 50%. This also happens to be the value we calculated for optical purity.

Thus, the optical purity is thus equal to the percentage excess of the major enantiomer over the minor enantiomer. 

This term, the “enantiomeric excess”, or “e.e.” for short,  is equivalent to the optical purity and is actually used far more often for expressing the enantiomeric purity of a mixture.

So an “optically pure” solution containing 100% of the d – enantiomer and 0% of the l- enantiomer would have an enantiomeric excess of:

100% – 0% = 100%

The same would be true for an optically pure solution of the l- enantiomer: 100% e.e.

A racemic mixture, as we saw, has an optical purity of 0%. And so, too,  the enantiomeric excess is also 0%.

50%d  – 50% = 0%

8. Another Practice Problem For Enantiomeric Excess

Let’s do another problem!

A sample of 2-bromobutane has an enantiomeric excess (e.e.) of 75% favouring the d– enantiomer. What is the percentage of each enantiomer?

First, identify the relevant equations:

e.e. = %d – %l  = 75%

%d- + %l-  = 100%

Next, solve one equation for either variable so you can plug that into the other equation. In this case we arbitrarily solve for the % of the d– enantiomer using the second equation.


Now, plug in what we found to the first equation, solving in this case for the percent of the d- enantiomer.


Then, solve for %d with our knowledge that the total equals 100%.


The previous two steps contain the answer, but we can also double check by plugging these numbers into the equation for e.e.  

So a mixture with 75% ee is actually composed of 87.5% of the major enantiomer, and 12.5% of the minor enantiomer.

As we said above, another way of looking at it is that it’s 75% composed of the major enantiomer, and 25% of a racemic mixture.

9. An Optical Purity Practice Problem

Let’s do a slightly different problem, this time using optical purity.

A mixture contains 3g of (+)-2-bromobutane and 2g of (–)-2-bromobutane. What is the rotation of the mixture, given that (+)-2-bromobutane has a specific rotation of +23.1°.

First, let’s calculate enantiomeric excess/optical purity as a decimal number. Note that the units here (grams) will cancel.


Now, we’ll solve for the rotation of the mixture using the equation for optical purity. Again, we’ll use the decimal form, which is 0.2 , for optical purity (or enantiomeric excess).


This gives us a rotation of 4.62° for the mixture.

That’s it! By the way, this is about as intense as math will ever get in introductory organic chemistry. You’re welcome.

This ends our two part discussion of optical activity, polarimetry, specific rotation, and optical purity.

Questions or comments about this post? Leave one below!

Thanks again to Matt for helping with this post.Hire Matt as your tutor! 


[Note 1] This was proposed in 1848, about 25 years before Van’t Hoff proposed tetrahedral carbon. Pasteur’s work was one of the foundations on which Van’t Hoff made his proposal; a carbon with 4 different groups can only exist as two different enantiomers if the carbon is tetrahedral. It’s impossible if carbon is square planar.

[Note 2] These situations frequently come about when using an enantioselective reaction on an achiral compound, such as the epoxidation reaction that won Barry Sharpless the 2001 Nobel Prize (fittingly, this reaction employs the enantiomers of tartaric acid to impart  “handedness” to the produc!divAbstractts).  Enzymes are likely a more familiar category of enantioselective catalysts: Baker’s yeast has been used for the enantioselective reduction of ketones, for instance.

[Note 3] Optical rotation measurements (i.e. polarimetry) are actually an unreliable way to determine enantiomeric excess. There are three reasons.

  • The optical rotation of the pure enantiomers may not be known
  • Small amount of optically active impurities may cause the experiment to give drastically incorrect results [UPDATE: Like in the real-life example of Frondisin B].
  • Optical rotation doesn’t always have a linear relationship to enantiomeric excess like we’re claiming it does here. This is because of the Horeau Effect.

A more common way to measure enantiomeric excess is through HPLC or GC with a chiral stationary phase, or through the Mosher method.


System Suitability And Validation For Chiral Purity Assays Of Drug Substances


Validation of chiral purity methods should generally follow the compendial/regulatory guidelines (7). The desired component as the major peak would require evaluation of specificity, precision, linearity, accuracy, range, and analyte stability. The undesired component as the minor peak would require evaluation of these same parameters plus sensitivity. Robustness may be demonstrated during method development though it can be part of validation. System suitability is implicit during method validation and routine analyses. Each of these parameters is briefly discussed below and summarized in Table 1.

System Suitability

It is best to begin with system suitability since it demonstrates acceptable method performance in every run, and acts as a mini-validation in itself. The critical pieces of information to evaluate for performance on chiral assays are resolution, sensitivity, and injector precision.

Peaks of interest must exhibit adequate resolution to quantitate each component separately. Equally important is the need to demonstrate quantitation of a low-level limit for the undesired enantiomer. Imagine a situation with an aging detector lamp and getting deceived into believing a test sample has 100% of the desired component because the undesired one cannot be seen. This principle should be applied to any area percent assay. Finally, monitoring of injection precision is appropriate to assure that column loading is under control throughout the analysis.

The simplest and most efficient way to address system suitability is if key parameters can be assessed with minimal sample preparations and injections. This can be accomplished by preparing a single reference sample containing the desired and undesired components at a ratio corresponding to the specification. The sample can be used to monitor injector precision by injecting it twice during the analysis and calculating percent difference to determine variability. Resolution can be interpreted from these injections as well. The criterion or target value should be appropriate to the method but one should aim for a minimum of 1.7 to represent baseline resolution. As for sensitivity, the criterion may be the target area percent of each species plus a tolerance range. An alternate sensitivity criterion is to verify an acceptable signal/noise ratio typically not less than 10 for the minor component peak.

One may track the capacity factor, theoretical plates, and peak tailing as well for system suitability. Sensitivity and resolution are consequences of retention and peak shape quality. If acceptable sensitivity and resolution are demonstrated in the face of a reasonably small retention time shift and/or peak shape deterioration such as from column wear, the method can still be considered suitable for intended use. Chromatographers often recognize the delicate nature of most chiral stationary phases and balance that with the relatively high cost of column replacement.


The method should have no significant interferences with quantitation of the relevant peaks. It is recognized that some methods will include resolution and retention time in this category while others will place these parameters under system suitability. Either way is acceptable as long as they get covered.

Linearity and Sensitivity

Linearity should be demonstrated at an appropriate range, typically 80-120%, centered about the target levels for the desired and undesired components. Linearity dovetails with sensitivity for the undesired component, and the span may be expanded to include the Quantitation Limit. One assumes that the response factor is identical for enantiomers.

Sensitivity is critical only for the undesired component. One should target 50-100% of the specification or target value as the Quantitation Limit. The typical acceptance criterion for the Quantitation Limit may be expressed as a signal/noise ratio of not less than 10, which is consistent with industry practice guidelines. It may be appropriate to determine a Detection Limit as well because this really helps to establish the boundaries of the assay. Similarly, the typical acceptance criterion for the Detection Limit may be expressed as a signal/noise ratio of not less than 3. Sensitivity should be confirmed in every analysis as part of system suitability.

Precision, Accuracy, and Range

Precision is evaluated as variability in the responses for the relevant components at the target assay/specification levels. The extent of validation can be limited to repeatibility or can include intermediate precision, depending on the stage of development and intended use. Considering that chiral columns have relatively poor lot-to-lot reproducibility and that chiral assays are typically performed in an area percent quantitation mode, having a very tight criterion may not be appropriate. A reasonable precision target for the major component is

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19.4: Enantiomeric Purity

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The term enantiomeric purity (or optical purity) is defined as the fractional excess of one enantiomer over the other. This is expressed in Equation 19-4 in terms of the moles (or weights) of the two enantiomers, \(n_1\), and \(n_2\), and is equal to the ratio of the observed optical rotation, \(\alpha_\text{obs}\), and to the optical rotation of either pure enantiomer, \(\alpha_0\):

\[\text{enantiomeric purity of } n_1 = \dfrac{n_1-n_2}{n_1+n_2} = \dfrac{\alpha_\text{obs}}{\alpha_0} \tag{19-4}\]

Thus a racemic mixture (\(n_1 = n_2\)) has an enantiomeric purity of zero. Any other enantiomeric composition in principle can be determined provided the mixture has a measurable rotation and the rotation of the pure enantiomer, \(\alpha_0\), is known. Unfortunately, there is no simple method of calculating \(\alpha_0\), in advance. In fact, specific rotations of optically pure compounds are determined most reliably from Equation 19-4 after measurement of enantiomeric purity by independent methods.

Virtually all of the methods for determining enantiomeric purity rely on the differences in chemical, physical, or spectroscopic properties of diastereomers derived from enantiomeric mixtures. We will mention here two of the most straightforward methods, based on gas-liquid chromatography and nuclear magnetic resonance.

Determination of Enantiomeric Purity by Gas Chromatography

This method amounts to a complete resolution of the type described in Section 19-3D, but on an analytical scale. For example, assume that you have a partially resolved compound, \(A\), consisting of unequal amounts of the enantiomers \(A_+\) and \(A_-\). By reaction with a second chiral enantiomerically pure substance, \(B_+\), A is converted to a mixture of diastereomers \(A_+B_+\) and \(A_-B_+\). Because these diastereomers are chemically and physically different, the mixture usually can be analyzed by gas-liquid chromatography (Section 9-2A). If the reaction of \(B_+\) with \(A_+\) and \(A_-\) was quantitative, the relative areas of the two peaks eluting from the column correspond to the ratio of the diastereomers \(A_+B_+/A_-B_+\), and thus to the ratio of enantiomers \(A_+/A_-\), from which the enantiomeric purity of the partially resolved mixture can be calculated.

An alternative and very direct approach is to separate the enantiomers on a column in which the stationary liquid phase is a chiral compound. The diastereomeric interaction is between \(A_+\) or \(A_-\) and the chiral liquid phase, and may be sufficiently different to permit separation of \(A_+\) from \(A_-\). The ratio of the amounts of \(A_+\) and \(A_-\) corresponds to the enantiomeric purity.

Determination of Enantiomeric Purity by NMR Spectroscopy

The nmr chemical shifts of nuclei of enantiomeric compounds \(A_+\) and \(A_-\) are identical in achiral solvents. However, in a chiral solvent (enantiomerically pure) \(A_+\) and \(A_-\) will be effectively converted to diastereomers as the result of chiral solvation and, accordingly, their nuclei will have nonidentical chemical shifts. Provided that the shift differences are large enough to permit the resonances of one chirally solvated enantiomer to be resolved from those of the other, the ratio of enantiomers \(A_+/A_-\) can be determined from the ratio of their corresponding nmr signal intensities.

Alternatively, with a pure chiral reagent the enantiomeric mixture may be converted (quantitatively) to diastereomers. The nuclei of the diastereomeric compounds are expected to have small differences in chemical shifts, even in achiral solvents, and integration of their respective signal intensities should correspond to the ratio of diastereomers, and hence to the ratio of enantiomers in the original mixture.

Application of the above-described nmr methods for the determination of enantiomeric composition is difficult, if not impossible, if the chemical-shift differences are too small \(\left( 0.02 \: \text{ppm} \right)\) or if the resonances overlap extensively. This problem often can be solved by utilizing the ability of certain chelates of rare earth metals (the lanthanidemetals) to complex with organic compounds, particularly with alcohols, ketones, amines, and other Lewis bases. Chemical shifts in the presence of even small amounts of lanthanide chelates usually are spread over a much wider range of field strengths than for the pure compounds. As discussed previously in Sections 9-10D and 9-10K, increasing chemical shifts can greatly simplify otherwise complex nmr spectra. The shifts are produced by these lanthanide compounds because the electrons on the metal atoms are not all paired, so that the metal atoms are paramagnetic (possess a net electron spin). In an applied magnetic field the unpaired electrons circulate around the metal atoms and produce an induced field (Figure 9-26) which, depending on the nature of the metal, can act either to increase or reduce the applied magnetic field, \(H_0\).

In the complex formed between the lanthanide reagent and the organic substrate, the chemical shifts most strongly affected are those of nuclei close to the paramagnetic metal atom. The resonances of these nuclei also are broadened by the paramagnetic metal (Section 27-1), and this is undesirable. The lanthanide complexes that produce these large shift changes are called shift reagents. Most of them are chelate salts of substituted 2,4-pentanediones, especially of 2,2,6,6-tetramethyl-3,5-heptanedione (Section 17-8).

There are several useful shift reagents, usually of europium, in which the organic ligands are chiral. An example is \(1\):

Stereochemistry - R S Configuration \u0026 Fischer Projections

Enantiomeric excess

Enantiomeric excess (ee) is a measurement of purity used for chiral substances. It reflects the degree to which a sample contains one enantiomer in greater amounts than the other. A racemic mixture has an ee of 0%, while a single completely pure enantiomer has an ee of 100%. A sample with 70% of one enantiomer and 30% of the other has an ee of 40% (70% − 30%).


Enantiomeric excess is defined as the absolute difference between the mole fraction of each enantiomer:[1]

{\displaystyle \ ee=|F_{R}-F_{S}|}


{\displaystyle \ F_{R}+F_{S}=1}

In practice, it is most often expressed as a percent enantiomeric excess.

{\displaystyle \ \%ee=({|}F_{R}-F_{S}{|}\times 100)\ }






The enantiomeric excess can be determined in another way if we know the amount of each enantiomer produced. If one knows the moles of each enantiomer produced then:

{\displaystyle \ \%ee=((R-S)/(R+S)\times 100)\ }






Enantiomeric excess is used as one of the indicators of the success of an asymmetric synthesis. For mixtures of diastereomers, there are analogous definitions and uses for diastereomeric excess and percent diastereomeric excess.

As an example, a sample with 70 % of R isomer and 30 % of S will have a percent enantiomeric excess of 40. This can also be thought of as a mixture of 40 % pure R with 60 % of a racemic mixture (which contributes half 30 % R and the other half 30 % S to the overall composition).

If given the enantiomeric excess {\displaystyle \ \%ee} of a mixture, the fraction of the main isomer, say R, can be determined using {\displaystyle \ F_{R}=50+(\%ee/2)} and the lesser isomer {\displaystyle \ F_{S}=50-(\%ee/2)}.

A non-racemic mixture of two enantiomers will have a net optical rotation. It is possible to determine the specific rotation of the mixture and, with knowledge of the specific rotation of the pure enantiomer, the optical purity can be determined.[2]

optical purity (%) = [α]obs/[α]max · 100

Ideally, the contribution of each component of the mixture to the total optical rotation is directly proportional to its mole fraction, and as a result the numerical value of the optical purity is identical to the enantiomeric excess. This has led to informal use the two terms as interchangeable, especially because optical purity was the traditional way of measuring enantiomeric excess. However, other methods such as chiral column chromatography and NMR spectroscopy can now be used for measuring the amount of each enantiomer individually.

The ideal equivalence between enantiomeric excess and optical purity does not always hold. For example,

  • the specific rotation of (S)-2-ethyl-2-methyl succinic acid is found to be dependent on concentration
  • in what is known as the Horeau effect[3] the relationship between mole based ee and optical rotation based ee can be non-linear i.d. in the succinic acid example the optical activity at 50% ee is lower than expected.
  • the specific rotation of enantiopure 1-phenylethanol can be enhanced by the addition of achiral acetophenone as an impurity.[4]

The term enantiomeric excess was introduced in 1971 by Morrison and Mosher in their publication Asymmetric Organic Reactions.[5] The use of enantiomeric excess has established itself because of its historic ties with optical rotation. It has been suggested that the concept of ee should be replaced by that of er which stands for enantiomeric ratio or er (S:R) [6] or q (S/R) because determination of optical purity has been replaced by other techniques which directly measure R and S and because it simplifies mathematical treatments such as the calculation of equilibrium constants and relative reaction rates. The same arguments are valid for changing diastereomeric excess (de) to diastereomeric ratio (dr).


  1. ^IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (1996) "Enantiomer excess". doi:10.1351/goldbook.E02070
  2. ^IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (1996) "Optical purity". doi:10.1351/goldbook.O04310
  3. ^J.P. Vigneron, M. Dhaenens, A. Horeau, Nouvelle methode pour porter au maximum la purete optique d'un produit partiellement dedouble sans l'aide d'aucune substance chirale, Tetrahedron, Volume 29, Issue 7, 1973, Pages 1055-1059, ISSN 0040-4020, doi:10.1016/0040-4020(73)80060-2
  4. ^Yamaguchi, S.; Mosher, H. S. (1973). "Asymmetric reductions with chiral reagents from lithium aluminum hydride and (+)-(2S,3R)-4-dimethylamino-3-methyl-1,2-diphenyl-2-butanol". Journal of Organic Chemistry. 38 (10): 1870–1877. doi:10.1021/jo00950a020.
  5. ^Morrison, James D.; Mosher, Harry S.: Asymmetric Organic Reactions, Prentice-Hall, Englewood Cliff, New Jersey, 1971 (ISBN 0130495514)
  6. ^Do the Terms "% ee" and "% de" Make Sense as Expressions of Stereoisomer Composition or Stereoselectivity? Robert E. Gawley J. Org. Chem.; 2006; 71(6) pp 2411 - 2416; doi:10.1021/jo052554w

Purity chiral


7  Analysis of enantiomers

    1. Enantiomeric purity and the enantiomeric excess (e.e.) scale
    2. Determining the enantiomeric excess (e.e.) of a non-racemic compound
      1. Measuring e.e. by polarimetry
      2. Measuring e.e. via sample derivatisation
      3. Chiral chromatography of enantiomeric mixtures
      4. Chiral additives used in high-field NMR spectroscopy

7.1 Enantiomeric purity and the enantiomeric excess (e.e.) scale

A 50:50 mixture of two enantiomers is called a racemicmixture, and is optically inactive. When there is only one enantiomer present, a substance is described as optically pure or homochiral. Between racemic and optically pure lies a range of unequal mixtures of two enantiomers, with one enantiomer present in excess. Although in this situation there will be a measurable rotation in a polarimeter, it will not be the full value of the specific rotation [α]D but an intermediate value depending on the composition of the mixture. Optical activity is linear, so the situation can be shown graphically as a straight-line, as below for lactic acid.

Chart showing the variation of specific rotation with enantiomeric ratio for lactic acid

For example, a mixture consisting of 75% (+)-lactic acid and 25% (−)-lactic acid is said to contain a 50% enantiomeric excess of the (+)-enantiomer.

To calculate the proportions of each enantiomer from an e.e. value, remember that the difference between the % optical purity and 100% is made up of racemic substance, half of which is one enantiomer and half the other enantiomer.

An e.e. value of 60% means 60% optically pure + 40% racemic mixture. The '40% racemic' fraction consists of 20% of each enantiomer, so the ratio of the two enantiomers is major (60+20)%, minor 20%, i.e.80:20.

7.2 Determining the enantiomeric excess (e.e.) of a non-racemic compound

7.2.1 Measuring e.e. by polarimetry

In the previous section it was shown how the optical purity of non-racemic lactic acid could be calculated by measuring the specific rotation of the sample and comparing the value obtained with that of optically pure lactic acid. However, in practice there are a number of problems associated with the accuracy of polarimetry measurements which limit their usefulness as an indicator of optical purity.

  • It may not be possible to measure a rotation value accurately if the [α]D value is small (it can even be zero) or only a small quantity of sample is available.
  • The [α]D of the pure enantiomer may never have been accurately established.
  • The sample must be completely free of impurities, both chiral and achiral.
  • For some compounds there is a non-linear relationship between e.e. and [α]D.

For the above reasons optical rotation measurements should, at best, only be used to obtain a rough estimate of the e.e. value of a non-racemic mixture of enantiomers. In general, greater accuracy can be obtained by one of the methods described below.

7.2.2 Measuring e.e. via sample derivatisation

The principle of derivatisation for assay purposes is the same as that for the preparative resolution of enantiomers (section 6.2). The enantiomeric mixture in question is reacted with an enantiomerically pure derivatising agent to convert the enantiomeric relationship into a diastereoisomeric one. The mixture can then be analysed by any technique which can be used to analyse diastereoisomers quantitatively (e.g. NMR spectroscopy, HPLC, GLC).

Typical derivatisations:

Examples of derivatisation reactions used to assay enantiomeric purity

Some acids used for forming diastereoisomeric derivatives:

The structures of some carboxylic acids that have been used as homochiral derivatising agents

An example involving the use of Mosher's reagent is shown below. The Mosher acid chloride (R)-1 is prepared from Mosher's acid, and then used to 'derivatise' a mixture of enantiomeric amines 2. This gives a mixture of amides 3 and 4 which are diastereoisomers and so can be analysed by HPLC or NMR spectrocopy. An advantage of Mosher's system is the presence of the CF3 group, which allows both 1H and 19F NMR spectroscopy to be used for the assay.

The underlying sequence for assaying the enantiomeric purity of a chiral amine using Mosher's acid chloride

It is important to ensure that the derivatising agent, in this case (R)-1, is enantiomerically pure, because the two amides 5 and 6 which would be formed from the enantiomer (S)-1 would be enantiomers of the amides 4 and 3 respectively, and would therefore be indistinguishable from them by HPLC or NMR, leading to a false result. Other requirements of this strategy are as follows:

  • All of the starting material must have reacted with the derivatising agent before the analysis, in order to be certain that the diastereoisomer ratio exactly matches that of the enantiomers in the original mixture. This is because the chiral derivatising agent may react faster with one enantiomer than the other (kinetic resolution).
  • The crude derivatised product must be analysed without purification, to avoid the possibility that the ratio of the diastereoisomers is changed during purification (remember that diastereoisomers are separable by chemical purification techniques such as chromatography or crystallisation).
  • Test the derivatisation and analysis on a racemic mixture of enantiomers before attempting to analyse any optically active material. This will verify that the procedure works properly if it indicates a 50:50 ratio of enantiomers.
  • Use accurate analytical techniques (e.g. high field NMR spectroscopy, HPLC or GLC) for measuring the ratios of the derivatised (diastereoisomeric) products.

7.2.3 Chiral chromatography of enantiomeric mixtures

Nowadays enantiomers are routinely analysed by passing them through chromatography columns containing chiral materials. Chromatographic separation relies on a difference in affinity between a stationary phase, usually silica, and a mobile phase – the eluting solvent in high performance liquid chromatography (HPLC) or the carrier gas in gas-liquid chromatography (GLC) – mediated by weak interactions (H-bonding, dipole-dipole or van der Waals). A stationary phase can be made chiral simply by bonding it with an enantiomerically pure compound.

Modification of silica by the inclusion of an enantiomerically pure amide side-chain

As two enantiomers interact with a homochiral stationary phase, the interactions of each enantiomer with the stationary phase have a diastereoisomeric relationship. If the difference in the interactions is sufficient, there will be a separation of the enantiomers (the enantiomer which binds more strongly to the stationary phase will take longer to pass through the column). As the enantiomers emerge (at different times) from the column they enter a UV detector (high sensitivity; recall that the enantiomers have the same UV spectrum), and the signals are integrated to provide theassay.

Chiral gas liquid chromatography (GLC) works on the same principle, and is one of the best methods for analysing enantiomer mixtures. The equipment is expensive, but the method is rapid and sensitive (detection limits of better than 0.01% of a minor enantiomer are not uncommon).

7.2.4 Chiral additives used in high-field NMR spectroscopy

Operationally one of the simplest methods for assaying a pair of enantiomers is to add a chiral shift reagent or a chiral solvating agent to the mixture when recording its NMR spectrum. Chiral shift reagents are lanthanide complexes, and as mild Lewis acids – lone pair acceptors – they readily coordinate to heteroatoms e.g. O (or N) in enantiomeric alcohols (or amines). As they are chiral, there is a diastereoisomeric relationship between the complexing agent and each enantiomer of the compound being analysed, and in principle the two resulting diastereoisomeric complexes will have different NMR spectra. As long as comparable signals from the two diasteroisomeric complexes can be completely distinguished (ideally with 'baseline separation'), they can be accurately integrated and the ratio of enantiomers thereby estimated.

Some europium shift reagents used for the assay of enantiomeric mixtures by NMR spectroscopy

The most widely used chiral solvating agent is 2,2,2-trifluoro-1-(9-anthryl)ethanol (TFAE), which can also coordinate (via dipole-dipole or H-bonding interactions) to lone pairs e.g. those on O or N. Combining a single enantiomer of TFAE with the two enantiomers of a chiral compound will give two coordination complexes, and these will be diastereoisomers. If the spectra from the two complexes are distinguishable they can be assayed to determine the original ratio of enantiomers. In the example shown below, (−)-TFAE is used to establish the enantiomeric purity of a sample of enantiomerically enriched 1,2-diphenylethane-1,2-diol (hydrobenzoin) 16.

The structures of (<em>S</em>,<em>S</em>)-hydrobenzoin <strong>16</strong>, (<em>R</em>)-(−)-TFAE and the corresponding H-bonded solvate
NMR spectra obtained from samples of (±)- and (<em>S</em>,<em>S</em>)-hydrobenzoin <strong>16</strong> containing (−)-TFAE as a chiral solvating agent
Optical activity - Stereochemistry - Organic chemistry - Khan Academy


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