RULE 1 -

Having ranked the four groups attached to a chiral carbon, we describe the stereochemical configuration around the carbon by orienting the molecule so that the group with the lowest ranking (4) points directly away from us. We then look at the three remaining substituents, which now appear to radiate toward us like the spokes on a steering wheel (FIGURE 5.8). If a curved arrow drawn from the highest to second-highest to thirdhighest ranked substituent $(1 \rightarrow 2 \rightarrow 3)$ is clockwise, we say that the chirality center has the $\boldsymbol{R}$ configuration ( $S$ for the Latin rectus, meaning "right"). If an arrow from $1 \rightarrow 2 \rightarrow 3$ is counterclockwise, the chirality center has the $\boldsymbol{S}$ configuration (Latin sinister, meaning "left"). To remember these assignments, think of a car's steering wheel when making a Right (clockwise) turn.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0137.jpg?height=741&width=1353&top_left_y=1478&top_left_x=386)

FIGURE 5.8 Assigning $\boldsymbol{R}$ and $\boldsymbol{S}$ configurations to chirality centers. When the molecule is oriented so that the lowest-ranked group (4) is toward the rear, the remaining three groups radiate toward the viewer like the spokes of a steering wheel. If the direction of travel $1 \rightarrow 2 \rightarrow 3$ is clockwise (right turn), the center has the $R$ configuration. If the direction of travel $1 \rightarrow 2 \rightarrow 3$ is counterclockwise (left turn), the center is $S$.


RULE 1 -

Look at (-)-lactic acid in FIGURE 5.9 for an example of how to assign configuration. Sequence rule 1 says that -OH is ranked 1 and -H is ranked 4 , but it doesn't allow us to distinguish between $-\mathrm{CH}_{3}$ and $-\mathrm{CO}_{2} \mathrm{H}$ because both groups have carbon as their first atom. Sequence rule 2, however, says that $-\mathrm{CO}_{2} \mathrm{H}$ ranks higher than $-\mathrm{CH}_{3}$ because O (the highest second atom in $-\mathrm{CO}_{2} \mathrm{H}$ ) outranks H (the highest second atom in $-\mathrm{CH}_{3}$ ). Now, turn the
molecule so that the fourth-ranked group ( -H ) is oriented toward the rear, away from the observer. Since a curved arrow from $1(-\mathrm{OH})$ to $2\left(-\mathrm{CO}_{2} \mathrm{H}\right)$ to $3\left(-\mathrm{CH}_{3}\right)$ is clockwise (right turn of the steering wheel), ( - )-lactic acid has the $R$ configuration. Applying the same procedure to (+)-lactic acid leads to the opposite assignment.
(a)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0138.jpg?height=825&width=485&top_left_y=395&top_left_x=451)
$R$ configuration
(-)-Lactic acid
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0138.jpg?height=613&width=234&top_left_y=374&top_left_x=967)
(b)
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0138.jpg?height=327&width=378&top_left_y=514&top_left_x=1199)
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![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0138.jpg?height=220&width=218&top_left_y=996&top_left_x=1195)
$S$ configuration
(+)-Lactic acid
FIGURE 5.9 Assigning configuration to (a)(R)-(-)-lactic acid and (b) (S)-(+)-lactic acid.


RULE 1 -

Further examples are provided by naturally occurring (-)-glyceraldehyde and (+)-alanine, which both have the $S$ configuration as shown in FIGURE 5.10. Note that the sign of optical rotation, $(+)$ or $(-)$, is not related to the $R, S$ designation. (S)-Glyceraldehyde happens to be levorotatory (-), and (S)-alanine happens to be dextrorotatory $(+)$. There is no simple correlation between $R, S$ configuration and direction or magnitude of optical rotation.
(a)
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(S)-Glyceraldehyde
[(S)-(-)-2,3-Dihydroxypropanal]
$[\alpha]_{D}=-8.7$
(b)
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(S)-Alanine
[(S)-(+)-2-Aminopropanoic acid]
$[\alpha]_{D}=+8.5$


RULE 1 -

FIGURE 5.10 Assigning configuration to (a) (-)-glyceraldehyde. (b) (+)-alanine. Both happen to have the Sconfiguration, although one is levorotatory and the other is dextrorotatory.


RULE 1 -

One additional point needs to be mentioned-the matter of absolute configuration. How do we know that the assignments of $R$ and $S$ configuration are correct in an absolute sense, rather than a relative, sense? Since
there is no correlation between the $R, S$ configuration and the direction or magnitude of optical rotation, how do we know that the $R$ configuration belongs to the levorotatory enantiomer of lactic acid? This difficult question was finally solved in 1951, when an X-ray diffraction method was found for determining the absolute spatial arrangement of atoms in a molecule. Based on those results, we can say with certainty that the $R, S$ conventions are correct.


WORKED EXAMPLE 5.3 -


Assigning Configuration to Chirality Centers -


Strategy -

It takes practice to be able to visualize and orient a chirality center in three dimensions. You might start by indicating where the observer must be located $-180^{\circ}$ opposite the lowest-ranked group. Then imagine yourself in the position of the observer, and redraw what you would see.


Solution -

In (a), you would be located in front of the page toward the top right of the molecule, and you would see group 2 to your left, group 3 to your right, and group 1 below you. This corresponds to an $R$ configuration.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0139.jpg?height=303&width=1040&top_left_y=1366&top_left_x=540)

In (b), you would be located behind the page toward the top left of the molecule from your point of view, and you would see group 3 to your left, group 1 to your right, and group 2 below you. This also corresponds to an $R$ configuration.
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0139.jpg?height=329&width=1039&top_left_y=1820&top_left_x=543)


WORKED EXAMPLE 5.4 -


Drawing the Three-Dimensional Structure of a Specific Enantiomer -

Draw a tetrahedral representation of ( $R$ )-2-chlorobutane.


Strategy -

Begin by ranking the four substituents bonded to the chirality center: (1) -Cl , (2) $-\mathrm{CH}_{2} \mathrm{CH}_{3}$, (3) $-\mathrm{CH}_{3}$, (4) -H . To draw a tetrahedral representation of the molecule, orient the lowest-ranked group ( -H ) away from you and imagine that the other three groups are coming out of the page toward you. Then, place the remaining three substituents such that the direction of travel $1 \rightarrow 2 \rightarrow 3$ is clockwise (right turn), and tilt the molecule toward you to bring the rear hydrogen into view. Using molecular models is a real help in working problems of this sort.


Solution -

![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0140.jpg?height=163&width=594&top_left_y=561&top_left_x=603)
(R)-2-Chlorobutane


Solution -

PROBLEM Which member in each of the following sets ranks higher?
5-7 (a) -H or -Br
(b) -Cl or -Br
(c) $-\mathrm{CH}_{3}$ or $-\mathrm{CH}_{2} \mathrm{CH}_{3}$
(d) $-\mathrm{NH}_{2}$ or -OH
(e) $-\mathrm{CH}_{2} \mathrm{OH}$ or $-\mathrm{CH}_{3}$
(f) $-\mathrm{CH}_{2} \mathrm{OH}$ or $-\mathrm{CH}=\mathrm{O}$

PROBLEM Rank each of the following sets of substituents:
5-8 (a) $-\mathrm{H},-\mathrm{OH},-\mathrm{CH}_{2} \mathrm{CH}_{3},-\mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}$
(b) $-\mathrm{CO}_{2} \mathrm{H},-\mathrm{CO}_{2} \mathrm{CH}_{3},-\mathrm{CH}_{2} \mathrm{OH},-\mathrm{OH}$
(c) $-\mathrm{CN},-\mathrm{CH}_{2} \mathrm{NH}_{2},-\mathrm{CH}_{2} \mathrm{NHCH}_{3},-\mathrm{NH}_{2}$ (d) $-\mathrm{SH},-\mathrm{CH}_{2} \mathrm{SCH}_{3},-\mathrm{CH}_{3},-\mathrm{SSCH}_{3}$


Solution -


Solution -

PROBLEM Draw a tetrahedral representation of ( $S$ )-2-pentanol (2-hydroxypentane).
5-11
PROBLEM Assign $R$ or $S$ configuration to the chirality center in the following molecular model of the amino 5-12 acid methionine (blue $=\mathrm{N}$, yellow $=\mathrm{S}$ ):
![](https://cdn.mathpix.com/cropped/2025_02_06_5556f7656cbdcaa0f9a7g-0140.jpg?height=297&width=530&top_left_y=2020&top_left_x=429)


Solution - 5.6 Diastereomers

Molecules like lactic acid, alanine, and glyceraldehyde are relatively simple because each has only one chirality center and thus only two stereoisomers. The situation becomes more complex, however, with molecules that have more than one chirality center. As a general rule, a molecule with $n$ chirality centers can have up to
$2^{n}$ stereoisomers (although it may have fewer, as we'll see below). Take the amino acid threonine (2-amino-3-hydroxybutanoic acid), for example. Since threonine has two chirality centers (C2 and C3), there are four possible stereoisomers, as shown in FIGURE 5.11. Check for yourself that the $R, S$ configurations of all stereoisomers are correct.
Enantiomers
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Enantiomers


Solution - 5.6 Diastereomers

FIGURE 5.11 The four stereoisomers of 2-amino-3-hydroxybutanoic acid.
The four stereoisomers of 2-amino-3-hydroxybutanoic acid can be grouped into two pairs of enantiomers. The $2 R, 3 R$ stereoisomer is the mirror image of $2 S, 3 S$, and the $2 R, 3 S$ stereoisomer is the mirror image of $2 S, 3 R$. But what is the relationship between any two molecules that are not mirror images? What, for instance, is the relationship between the $2 R, 3 R$ isomer and the $2 R, 3 S$ isomer? They are stereoisomers, yet they aren't enantiomers. To describe such a relationship, we need a new term-diastereomer.


Solution - 5.6 Diastereomers

Diastereomers (dia-stair-e-oh-mers) are stereoisomers that are not mirror images. Since we used the right-hand/left-hand analogy to describe the relationship between two enantiomers, we might extend the analogy by saying that the relationship between diastereomers is like that of hands from different people. Your hand and your friend's hand look similar, but they aren't identical and they aren't mirror images. The same is true of diastereomers: they're similar, but they aren't identical and they aren't mirror images.


Solution - 5.6 Diastereomers

Note carefully the difference between enantiomers and diastereomers: enantiomers have opposite configurations at all chirality centers, whereas diastereomers have opposite configurations at some (one or more) chirality centers but the same configuration at others. A full description of the four stereoisomers of threonine is given in TABLE 5.2. Of the four, only the $2 S, 3 R$ isomer, $[\alpha]_{\mathrm{D}}=-28.3$, occurs naturally in plants and animals and is an essential nutrient for humans. This result is typical: most biological molecules are chiral, and usually only one stereoisomer is found in nature.

| TABLE 5.2 Relationships among the Four Stereoisomers of
 Threonine |
| :--- | :--- |
| Stereoisomer Enantiomer Diastereomer
 $2 R, 3 R$ $2 S, 3 S$ $2 R, 3 S$ and $2 S, 3 R$
 $2 S, 3 S$ $2 R, 3 R$ $2 R, 3 S$ and $2 S, 3 R$ |

TABLE 5.2 Relationships among the Four Stereoisomers of
Threonine


Solution - 5.6 Diastereomers

| Stereoisomer | Enantiomer | Diastereomer |
| :--- | :--- | :--- |
| $2 R, 3 S$ | $2 S, 3 R$ | $2 R, 3 R$ and $2 S, 3 S$ |
| $2 S, 3 R$ | $2 R, 3 S$ | $2 R, 3 R$ and $2 S, 3 S$ |