All objects may be classified with respect to a property we call chirality (from the Greek cheir meaning hand). A chiral object is not identical in all respects (i.e. superimposable) with its mirror image. An achiral object is identical with (superimposable on) its mirror image. Chiral objects have a "handedness", for example, golf clubs, scissors, shoes and a corkscrew. Thus, one can buy right or left-handed golf clubs and scissors. Likewise, gloves and shoes come in pairs, a right and a left. Achiral objects do not have a handedness, for example, a baseball bat (no writing or logos on it), a plain round ball, a pencil, a T-shirt and a nail. The chirality of an object is related to its symmetry, and to this end it is useful to recognize certain symmetry elements that may be associated with a given object. A symmetry element is a plane, a line or a point in or through an object, about which a rotation or reflection leaves the object in an orientation indistinguishable from the original. Some examples of symmetry elements are shown below.

The face playing card provides an example of a center or point of symmetry. Starting from such a point, a line drawn in any direction encounters the same structural features as the opposite (180º) line. Four random lines of this kind are shown in green. An example of a molecular configuration having a point of symmetry is (E)-1,2-dichloroethene. Another way of describing a point of symmetry is to note that any point in the object is reproduced by reflection through the center onto the other side. In these two cases the point of symmetry is colored magenta.
The boat conformation of cyclohexane shows an axis of symmetry (labeled C₂ here) and two intersecting planes of symmetry (labeled σ). The notation for a symmetry axis is C_n, where n is an integer chosen so that rotation about the axis by 360/nº returns the object to a position indistinguishable from where it started. In this case the rotation is by 180º, so n=2. A plane of symmetry divides the object in such a way that the points on one side of the plane are equivalent to the points on the other side by reflection through the plane. In addition to the point of symmetry noted earlier, (E)-1,2-dichloroethene also has a plane of symmetry (the plane defined by the six atoms), and a C₂ axis, passing through the center perpendicular to the plane.
The existence of a reflective symmetry element (a point or plane of symmetry) is sufficient to assure that the object having that element is achiral.
Chiral objects, therefore, do not have any reflective symmetry elements, but may have rotational symmetry axes, since these elements do not require reflection to operate. In addition to the chiral vs achiral distinction, there are two other terms often used to refer to the symmetry of an object. These are:

As chemists studied organic compounds isolated from plants and animals, a new and subtle type of configurational stereoisomerism was discovered. For example, lactic acid ( a C₃H₆O₃ carboxylic acid) was found in sour milk as well as in the blood and muscle fluids of animals. The physical properties of this simple compound were identical, regardless of the source (m.p, 53 ºC & pK_a 3.80), but there was evidence that the physiological behavior of the compound from the two sources was not the same. Another natural product, the fragrant C₁₀H₁₄O ketone carvone, was isolated from both spearmint and caraway. Again, all the physical properties of carvone from these two sources seemed to be identical (b.p. 230 ºC), but the odors of the two carvones were different and reflected their source. Other examples of this kind were encountered, and suspicions of a subtle kind of stereoisomerism were confirmed by the different interaction these compounds displayed with plane polarized light. We now know that this configurational stereoisomerism is due to different right and left-handed forms that certain structures may adopt, in much the same way that a screw may have right or left-handed threads but the same overall size and shape. Isomeric pairs of this kind are termed enantiomers (from the Greek enantion meaning opposite).

A consideration of the chirality of molecular configurations explains the curious stereoisomerism observed for lactic acid, carvone and a multitude of other organic compounds. Tetravalent carbons have a tetrahedral configuration. If all four substituent groups are the same, as in methane or tetrachloromethane, the configuration is that of a highly symmetric regular tetrahedron. A regular tetrahedron has six planes of symmetry and seven symmetry axes (four C₃ & three C₂) and is, of course, achiral. Examples of these axes and planes were noted above, and may be examined more fully by clicking on the methane formula drawn below.

If one of the carbon substituents is different from the other three, the degree of symmetry is lowered to a C₃ axis and three planes of symmetry, but the configuration remains achiral. The tetrahedral configuration in such compounds is no longer regular, since bond lengths and bond angles change as the bonded atoms or groups change. Further substitution may reduce the symmetry even more, but as long as two of the four substituents are the same there is always a plane of symmetry that bisects the angle linking those substituents, so these configurations are also achiral.

A carbon atom that is bonded to four different atoms or groups loses all symmetry, and is often referred to as an asymmetric carbon. The configuration of such a tetrahedral unit is chiral, and the structure may exist in either a right-handed configuration or a left-handed configuration (one the mirror image of the other). This type of configurational stereoisomerism is termed enantiomorphism, and the non-identical, mirror-image pair of stereoisomers that result are called enantiomers. The structural formulas of lactic acid and carvone are drawn on the right with the asymmetric carbon colored red. Consequently, we expect, and find, these compounds to exist as pairs of enantiomers. The presence of a single asymmetrically substituted carbon atom in a molecule is sufficient to render the whole configuration chiral, and modern terminology refers to such asymmetric (or dissymmetric) groupings as chiral centers. Most of the chiral centers we shall discuss are asymmetric carbon atoms, but it should be recognized that other tetrahedral or pyramidal atoms may become chiral centers if appropriately substituted. When more than one chiral center is present in a molecular structure, care must be taken to analyze their relationship before concluding that a specific molecular configuration is chiral or achiral. This aspect of stereoisomerism will be treated later.

The identity or non-identity of mirror-image configurations of some substituted carbons may be examined as interactive models by Clicking Here.

A useful first step in examining structural formulas to determine whether stereoisomers may exist is to identify all stereogenic elements. A stereogenic element is a center, axis or plane that is a focus of stereoisomerism, such that an interchange of two groups attached to this feature leads to a stereoisomer. Stereogenic elements may be chiral or achiral. The most common chiral stereogenic center is the asymmetric carbon; interchanging any two substituent groups converts one enantiomer to the other. However, care must be taken when evaluating bridged structures in which bridgehead carbons are asymmetric. This caveat will be illustrated by Clicking Here.
Alkenes having two different groups on each double bond carbon (e.g. abC=Cab) constitute an achiral stereogenic element, since interchanging substituents at one of the carbons changes the cis/trans configuration of the double bond. Chiral stereogenic axes or planes may be also be present in a molecular configuration, as in the case of allenes, but these are less common than chiral centers and will not be discussed here.

Structural formulas for eight organic compounds are displayed in the frame below. Some of these structures are chiral and some are achiral. First, try to identify all chiral stereogenic centers. Formulas having no chiral centers are necessarily achiral. Formulas having one chiral center are always chiral; and if two or more chiral centers are present in a given structure it is likely to be chiral, but in special cases, to be discussed later, may be achiral. Once you have made your selections of chiral centers, check them by pressing the "Show Chiral Centers" button. The chiral centers will be identified by red dots.

Structures F and G are achiral. The former has a plane of symmetry passing through the chlorine atom and bisecting the opposite carbon-carbon bond. The similar structure of compound E does not have such a symmetry plane, and the carbon bonded to the chlorine is a chiral center (the two ring segments connecting this carbon are not identical). Structure G is essentially flat. All the carbons except that of the methyl group are sp² hybridized, and therefore trigonal-planar in configuration. Compounds C, D & H have more than one chiral center, and are also chiral. Remember, all chiral structures may exist as a pair of enantiomers. Other configurational stereoisomers are possible if more than one stereogenic center is present in a structure.

Identifying and distinguishing enantiomers is inherently difficult, since their physical and chemical properties are largely identical. Fortunately, a nearly two hundred year old discovery by the French physicist Jean-Baptiste Biot has made this task much easier. This discovery disclosed that the right- and left-handed enantiomers of a chiral compound perturb plane-polarized light in opposite ways. This perturbation is unique to chiral molecules, and has been termed optical activity.

Plane-polarized light is created by passing ordinary light through a polarizing device, which may be as simple as a lens taken from polarizing sun-glasses. Such devices transmit selectively only that component of a light beam having electrical and magnetic field vectors oscillating in a single plane. The plane of polarization can be determined by an instrument called a polarimeter, shown in the diagram below.

Monochromatic (single wavelength) light, is polarized by a fixed polarizer next to the light source. A sample cell holder is located in line with the light beam, followed by a movable polarizer (the analyzer) and an eyepiece through which the light intensity can be observed. In modern instruments an electronic light detector takes the place of the human eye. In the absence of a sample, the light intensity at the detector is at a maximum when the second (movable) polarizer is set parallel to the first polarizer (α = 0º). If the analyzer is turned 90º to the plane of initial polarization, all the light will be blocked from reaching the detector.
Chemists use polarimeters to investigate the influence of compounds (in the sample cell) on plane polarized light. Samples composed only of achiral molecules (e.g. water or hexane), have no effect on the polarized light beam. However, if a single enantiomer is examined (all sample molecules being right-handed, or all being left-handed), the plane of polarization is rotated in either a clockwise (positive) or counter-clockwise (negative) direction, and the analyzer must be turned an appropriate matching angle, α, if full light intensity is to reach the detector. In the above illustration, the sample has rotated the polarization plane clockwise by +90º, and the analyzer has been turned this amount to permit maximum light transmission.
The observed rotations (α) of enantiomers are opposite in direction. One enantiomer will rotate polarized light in a clockwise direction, termed dextrorotatory or (+), and its mirror-image partner in a counter-clockwise manner, termed levorotatory or (–). The prefixes dextro and levo come from the Latin dexter, meaning right, and laevus, for left, and are abbreviated d and l respectively. If equal quantities of each enantiomer are examined , using the same sample cell, then the magnitude of the rotations will be the same, with one being positive and the other negative. To be absolutely certain whether an observed rotation is positive or negative it is often necessary to make a second measurement using a different amount or concentration of the sample. In the above illustration, for example, α might be –90º or +270º rather than +90º. If the sample concentration is reduced by 10%, then the positive rotation would change to +81º (or +243º) while the negative rotation would change to –81º, and the correct α would be identified unambiguously.
Since it is not always possible to obtain or use samples of exactly the same size, the observed rotation is usually corrected to compensate for variations in sample quantity and cell length. Thus it is common practice to convert the observed rotation, α, to a specific rotation, [α], by the following formula:

Specific Rotation =			where l = cell length in dm, c = concentration in g/ml
			D is the 589 nm light from a sodium lamp

Compounds that rotate the plane of polarized light are termed optically active. Each enantiomer of a stereoisomeric pair is optically active and has an equal but opposite-in-sign specific rotation. Specific rotations are useful in that they are experimentally determined constants that characterize and identify pure enantiomers. For example, the lactic acid and carvone enantiomers discussed earlier have the following specific rotations.

A 50:50 mixture of enantiomers has no observable optical activity. Such mixtures are called racemates or racemic modifications, and are designated (±). When chiral compounds are created from achiral compounds, the products are racemic unless a single enantiomer of a chiral co-reactant or catalyst is involved in the reaction. The addition of HBr to either cis- or trans-2-butene is an example of racemic product formation (the chiral center is colored red in the following equation).

CH3CH=CHCH3 + HBr

(±) CH3CH2CHBrCH3

Chiral organic compounds isolated from living organisms are usually optically active, indicating that one of the enantiomers predominates (often it is the only isomer present). This is a result of the action of chiral catalysts we call enzymes, and reflects the inherently chiral nature of life itself. Chiral synthetic compounds, on the other hand, are commonly racemates, unless they have been prepared from enantiomerically pure starting materials.

There are two ways in which the condition of a chiral substance may be changed:
        1.  A racemate may be separated into its component enantiomers. This process is called resolution.
        2.  A pure enantiomer may be transformed into its racemate. This process is called racemization.

Although enantiomers may be identified by their characteristic specific rotations, the assignment of a unique configuration to each has not yet been discussed. We have referred to the mirror-image configurations of enantiomers as "right-handed" and "left-handed", but deciding which is which is not a trivial task. An early procedure assigned a D prefix to enantiomers chemically related to a right-handed reference compound and a L prefix to a similarly related left-handed group of enantiomers. Although this notation is still applied to carbohydrates and amino acids, it required chemical transformations to establish group relationships, and proved to be ambiguous in its general application. A final solution to the vexing problem of configuration assignment was devised by three European chemists: R. S. Cahn, C. K. Ingold and V. Prelog. The resulting nomenclature system is sometimes called the CIP system or the R-S system.
In the CIP system of nomenclature, each chiral center in a molecule is assigned a prefix (R or S), according to whether its configuration is right- or left-handed. No chemical reactions or interrelationship are required for this assignment. The symbol R comes from the Latin rectus for right, and L from the Latin sinister for left. The assignment of these prefixes depends on the application of two rules:   The Sequence Rule and The Viewing Rule.
The sequence rule is the same as that used for assigning E-Z prefixes to double bond stereoisomers. Since most of the chiral stereogenic centers we shall encounter are asymmetric carbons, all four different substituents must be ordered in this fashion.

Once the relative priorities of the four substituents have been determined, the chiral center must be viewed from the side opposite the lowest priority group. If we number the substituent groups from 1 to 4, with 1 being the highest and 4 the lowest in priority sequence, the two enantiomeric configurations are shown in the following diagram along with a viewers eye on the side opposite substituent #4.

Remembering the geometric implication of wedge and hatched bonds, an observer (the eye) notes whether a curved arrow drawn from the # 1 position to the # 2 location and then to the # 3 position turns in a clockwise or counter-clockwise manner. If the turn is clockwise, as in the example on the right, the configuration is classified R. If it is counter-clockwise, as in the left illustration, the configuration is S. Another way of remembering the viewing rule, is to think of the asymmetric carbon as a steering wheel. The bond to the lowest priority group (# 4) is the steering column, and the other bonds are spokes on the wheel. If the wheel is turned from group # 1 toward group # 2, which in turn moves toward group # 3, this would either negotiate a right turn (R) or a left turn (S). This model is illustrated below for a right-handed turn, and the corresponding (R)-configurations of lactic acid and carvone are shown to its right. The stereogenic carbon atom is colored magenta in each case, and the sequence priorities are shown as light blue numbers. Note that if any two substituent groups on a stereogenic carbon are exchanged or switched, the configuration changes to its mirror image.

The sequence order of the substituent groups in lactic acid should be obvious, but the carvone example requires careful analysis. The hydrogen is clearly the lowest priority substituent, but the other three groups are all attached to the stereogenic carbon by bonds to carbon atoms (colored blue here). Two of the immediate substituent species are methylene groups (CH₂), and the third is a doubly-bonded carbon. Rule # 3 of the sequence rules allows us to order these substituents. The carbon-carbon double bond is broken so as to give imaginary single-bonded carbon atoms (the phantom atoms are colored red in the equivalent structure). In this form the double bond assumes the priority of a 3º-alkyl group, which is greater than that of a methylene group. To establish the sequence priority of the two methylene substituents (both are part of the ring), we must move away from the chiral center until a point of difference is located. This occurs at the next carbon, which on one side is part of a carbonyl double bond (C=O), and on the other, part of a carbon-carbon double bond. Rule # 3 is again used to evaluate the two cases. The carbonyl group places two oxygens (one phantom) on the adjacent carbon atom, so this methylene side is ranked ahead of the other.
An interesting feature of the two examples shown here is that the R-configuration in both cases is levorotatory (-) in its optical activity. The mirror-image S-configurations are, of course, dextrorotatory (+). It is important to remember that there is no simple or obvious relationship between the R or S designation of a molecular configuration and the experimentally measured specific rotation of the compound it represents. In order to determine the true or "absolute" configuration of an enantiomer, as in the cases of lactic acid and carvone reported here, it is necessary either to relate the compound to a known reference structure, or to conduct a rather complex X-ray analysis on a single crystal of the sample.

The configurations of lactic acid and carvone enantiomers may be examined as interactive models by Clicking Here.

The module on the right provides examples of chiral and achiral molecules for analysis. These are displayed as three-dimensional structures which may be moved about and examined from various points of view. By using this resource the reader's understanding of configurational notation may be tested. This visualization makes use of the Jmol applet. With some browsers it may be necessary to click a button twice for action.

Select an Example Click the Show Example Button A three-dimensional molecular structure will be displayed here, and may be moved about with the mouse. Carbon is gray, hydrogen is cyan, oxygen is red, and nitrogen is dark blue. Other atoms are colored differently and are labled. Characterize the configuration of the molecule by selecting one of the three terms listed below. A response to your answer will be presented by clicking the Check Answer button. Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 7 Example 8 Example 9 Example 10 Example 11 Example 12 S     R     Achiral A response to your selection will appear here. A sequence assignment will be shown above.

The Chinese shrub Ma Huang (Ephedra vulgaris) contains two physiologically active compounds ephedrine and pseudoephedrine. Both compounds are stereoisomers of 2-methylamino-1-phenyl-1-propanol, and both are optically active, one being levorotatory and the other dextrorotatory. Since the properties of these compounds (see below) are significantly different, they cannot be enantiomers. How, then, are we to classify these isomers and others like them?

Since these two compounds are optically active, each must have an enantiomer. Although these missing stereoisomers were not present in the natural source, they have been prepared synthetically and have the expected identical physical properties and opposite-sign specific rotations with those listed above. The structural formula of 2-methylamino-1-phenylpropanol has two stereogenic carbons (#1 & #2). Each may assume an R or S configuration, so there are four stereoisomeric combinations possible. These are shown in the following illustration, together with the assignments that have been made on the basis of chemical interconversions.

As a general rule, a structure having n chiral centers will have 2ⁿ possible combinations of these centers. Depending on the overall symmetry of the molecular structure, some of these combinations may be identical, but in the absence of such identity, we would expect to find 2ⁿ stereoisomers. Some of these stereoisomers will have enantiomeric relationships, but enantiomers come in pairs, and non-enantiomeric stereoisomers will therefore be common. We refer to such stereoisomers as diastereomers. In the example above, either of the ephedrine enantiomers has a diastereomeric relationship with either of the pseudoephedrine enantiomers.
For an interesting example illustrating the distinction between a chiral center and an asymmetric carbon Click Here.
The configurations of ephedrine and pseudoephedrine enantiomers may be examined as interactive models by Clicking Here.

A close examination of the ephedrine and pseudoephedrine isomers suggests that another stereogenic center, the nitrogen, is present. As noted earlier, single-bonded nitrogen is pyramidal in shape, with the non-bonding electron pair pointing to the unoccupied corner of a tetrahedral region. Since the nitrogen in these compounds is bonded to three different groups, its configuration is chiral. The non-identical mirror-image configurations are illustrated in the following diagram (the remainder of the molecule is represented by R, and the electron pair is colored yellow). If these configurations were stable, there would be four additional stereoisomers of ephedrine and pseudoephedrine. However, pyramidal nitrogen is normally not configurationally stable. It rapidly inverts its configuration (equilibrium arrows) by passing through a planar, sp²-hybridized transition state, leading to a mixture of interconverting R and S configurations. If the nitrogen atom were the only chiral center in the molecule, a 50:50 (racemic) mixture of R and S configurations would exist at equilibrium. If other chiral centers are present, as in the ephedrin isomers, a mixture of diastereomers will result. In any event, nitrogen groups such as this, if present in a compound, do not contribute to isolable stereoisomers.
The inversion of pyramidal nitrogen in ammonia may be examined by clicking on the following diagram.

The problem of drawing three-dimensional configurations on a two-dimensional surface, such as a piece of paper, has been a long-standing concern of chemists. The wedge and hatched line notations we have been using are effective, but can be troublesome when applied to compounds having many chiral centers. As part of his Nobel Prize-winning research on carbohydrates, the great German chemist Emil Fischer, devised a simple notation that is still widely used. In a Fischer projection drawing, the four bonds to a chiral carbon make a cross with the carbon atom at the intersection of the horizontal and vertical lines. The two horizontal bonds are directed toward the viewer (forward of the stereogenic carbon). The two vertical bonds are directed behind the central carbon (away from the viewer). Since this is not the usual way in which we have viewed such structures, the following diagram shows how a stereogenic carbon positioned in the common two-bonds-in-a-plane orientation ( x–C–y define the reference plane ) is rotated into the Fischer projection orientation (the far right formula). When writing Fischer projection formulas it is important to remember these conventions. Since the vertical bonds extend away from the viewer and the horizontal bonds toward the viewer, a Fischer structure may only be turned by 180º within the plane, thus maintaining this relationship. The structure must not be flipped over or rotated by 90º.

A model showing the above rotation into a Fischer projection may be examined by Clicking Here.

In the above diagram, if x = CO₂H, y = CH₃, a = H & b = OH, the resulting formula describes (R)-(–)-lactic acid. The mirror-image formula, where x = CO₂H, y = CH₃, a = OH & b = H, would, of course, represent (S)-(+)-lactic acid.

Using the Fischer projection notation, the stereoisomers of 2-methylamino-1-phenylpropanol are drawn in the following manner. Note that it is customary to set the longest carbon chain as the vertical bond assembly.

The usefulness of this notation to Fischer, in his carbohydrate studies, is evident in the following diagram. There are eight stereoisomers of 2,3,4,5-tetrahydroxypentanal, a group of compounds referred to as the aldopentoses. Since there are three chiral centers in this constitution, we should expect a maximum of 2³ stereoisomers. These eight stereoisomers consist of four sets of enantiomers. If the configuration at C-4 is kept constant (R in the examples shown here), the four stereoisomers that result will be diastereomers. Fischer formulas for these isomers, which Fischer designated as the "D"-family, are shown in the diagram. Each of these compounds has an enantiomer, which is a member of the "L"-family so, as expected, there are eight stereoisomers in all. Determining whether a chiral carbon is R or S may seem difficult when using Fischer projections, but it is actually quite simple. If the lowest priority group (often a hydrogen) is on a vertical bond, the configuration is given directly from the relative positions of the three higher-ranked substituents. If the lowest priority group is on a horizontal bond, the positions of the remaining groups give the wrong answer (you are in looking at the configuration from the wrong side), so you simply reverse it.

The aldopentose structures drawn above are all diastereomers. A more selective term, epimer, is used to designate diastereomers that differ in configuration at only one chiral center. Thus, ribose and arabinose are epimers at C-2, and arabinose and lyxose are epimers at C-3. However, arabinose and xylose are not epimers, since their configurations differ at both C-2 and C-3.

The chiral centers in the preceding examples have all been different, one from another. In the case of 2,3-dihydroxybutanedioic acid, known as tartaric acid, the two chiral centers have the same four substituents and are equivalent. As a result, two of the four possible stereoisomers of this compound are identical due to a plane of symmetry, so there are only three stereoisomeric tartaric acids. Two of these stereoisomers are enantiomers and the third is an achiral diastereomer, called a meso compound. Meso compounds are achiral (optically inactive) diastereomers of chiral stereoisomers. Investigations of isomeric tartaric acid salts, carried out by Louis Pasteur in the mid 19th century, were instrumental in elucidating some of the subtleties of stereochemistry.
Some physical properties of the isomers of tartaric acid are given in the following table.

Fischer projection formulas provide a helpful view of the configurational relationships within the structures of these isomers. In the following illustration a mirror line is drawn between formulas that have a mirror-image relationship. In demonstrating the identity of the two meso-compound formulas, remember that a Fischer projection formula may be rotated 180º in the plane.

A model of meso-tartaric acid may be examined by Clicking Here.
An additional example, consisting of two meso compounds, may be examined by Clicking Here.
Other methods of designating configuration have been proposed. These will be shown by Clicking Here.

As noted earlier, chiral compounds synthesized from achiral starting materials and reagents are generally racemic (i.e. a 50:50 mixture of enantiomers). Separation of racemates into their component enantiomers is a process called resolution. Since enantiomers have identical physical properties, such as solubility and melting point, resolution is difficult. Diastereomers, on the other hand, have different physical properties, and this fact may be used to achieve resolution of racemates. Reaction of a racemate with an enantiomerically pure chiral reagent gives a mixture of diastereomers, which can be separated. Reversing the first reaction then leads to the separated enantiomers plus the recovered reagent.
Many kinds of chemical and physical reactions, including salt formation, may be used to achieve the diastereomeric intermediates needed for separation. The following diagram illustrates this general principle by showing how a nut having a right-handed thread (R) could serve as a "reagent" to discriminate and separate a mixture of right- and left-handed bolts of identical size and weight. Only the two right-handed partners can interact to give a fully-threaded intermediate, so separation is fairly simple. The resolving moiety, i.e. the nut, is then removed, leaving the bolts separated into their right and left-handed forms. Chemical reactions of enantiomers are normally not so dramatically different, but a practical distinction is nevertheless possible.

The Fischer projection formula of meso-tartaric acid has a plane of symmetry bisecting the C2–C3 bond, as shown on the left in the diagram below, so this structure is clearly achiral. The eclipsed orientation of bonds that is assumed in the Fischer drawing is, however, an unstable conformation, and we should examine the staggered conformers that undoubtedly make up most of the sample molecules. The four structures that are shown to the right of the Fischer projection consist of the achiral Fischer conformation (A) and three staggered conformers, all displayed in both sawhorse and Newman projections. The second and fourth conformations (B & D) are dissymmetric, and are in fact enantiomeric structures. The third conformer (C) has a center of symmetry and is achiral.

Conformations of meso-Tartaric Acid
Fischer Projection	A eclipsed, achiral	B staggered, chiral	C staggered, achiral	D staggered, chiral

Since a significant proportion of the meso-tartaric acid molecules in a sample will have chiral conformations, the achiral properties of the sample (e.g. optical inactivity) should not be attributed to the symmetry of the Fischer formula. Equilibria among the various conformations are rapidly established, and the proportion of each conformer present at equilibrium depends on its relative potential energy (the most stable conformers predominate). Since enantiomers have equal potential energies, they will be present in equal concentration, thus canceling their macroscopic optical activity and other chiral behavior. Simply put, any chiral species that are present are racemic.

It is interesting to note that chiral conformations are present in most conformationally mobile compounds, even in the absence of any chiral centers. The gauche conformers of butane, for example, are chiral and are present in equal concentration in any sample of this hydrocarbon. The following illustration shows the enantiomeric relationship of these conformers, which are an example of a chiral axis rather than a chiral center.

Substituted biphenyls may exist as isolable enantiomers. This will be demonstrated by Clicking Here.

The distinction between configurational stereoisomers and the conformers they may assume is well-illustrated by the disubstituted cyclohexanes. The following discussion uses the various isomers of dichlorocyclohexane as examples. The 1,1-dichloro isomer is omitted because it is an unexceptional constitutional isomer of the others, and has no centers of chirality (asymmetric carbon atoms). The 1,2- and 1,3-dichlorocyclohexanes each have two centers of chirality, bearing the same set of substituents. The cis & trans-1,4-dichlorocyclohexanes do not have any chiral centers, since the two ring groups on the substituted carbons are identical.
There are three configurational isomers of 1,2-dichlorocyclohexane and three configurational isomers of 1,3-dichlorocyclohexane. These are shown in the following table.

The 1,2-Dichlorocyclohexanes	The 1,3-Dichlorocyclohexanes

All the 1,2-dichloro isomers are constitutional isomers of the 1,3-dichloro isomers. In each category (1,2- & 1,3-), the (R,R)-trans isomer and the (S,S)-trans isomer are enantiomers. The cis isomer is a diastereomer of the trans isomers. Finally, all of these isomers may exist as a mixture of two (or more) conformational isomers, as shown in the table.

The chair conformer of the cis 1,2-dichloro isomer is chiral. It exists as a 50:50 mixture of enantiomeric conformations, which interconvert so rapidly they cannot be resolved (ie. separated). Since the cis isomer has two centers of chirality (asymmetric carbons) and is optically inactive, it is a meso-compound. The corresponding trans isomers also exist as rapidly interconverting chiral conformations. The diequatorial conformer predominates in each case, the (R,R) conformations being mirror images of the (S,S) conformations. All these conformations are diastereomeric with the cis conformations.

The diequatorial chair conformer of the cis 1,3-dichloro isomer is achiral. It is the major component of a fast equilibrium with the diaxial conformer, which is also achiral. This isomer is also a meso compound. The corresponding trans isomers also undergo a rapid conformational interconversion. For these isomers, however, this interconversion produces an identical conformer, so each enantiomer (R,R) and (S,S) has predominately a single chiral conformation. These enantiomeric conformations are diastereomeric with the cis conformations.

The 1,4-dichlorocyclohexanes may exist as cis or trans stereoisomers. Both are achiral, since the disubstituted six-membered ring has a plane of symmetry. These isomers are diastereomers of each other, and are constitutional isomers of the 1,2- and 1,3- isomers.

All the chair conformers of these isomers are achiral, and the diequatorial conformer of the trans isomer is the predominate species at equilibrium.

Practice Problems

The first five problems ask you to identify equivalent groups of atoms, symmetry elements, stereogenic centers and the presence or absence of chirality. Part two of the fourth problem also requires the application of R/S nomenclature. The nomenclature terminology and classification of stereoisomers is examined in the next two problems, followed by a question concerning the relationship of isomeric pairs. Designation of CIP names is the subject of the next four problems. Products from stereoselective reactions are examined in the next problem, and a review of cyclohexane conformational terminology is the subject of the last two problems.