---
title: "Stereochemistry: Chirality and Isomers"
book: "School Chemistry — Grades 1 to 12"
subject: chemistry
language: en
chapter: 39
exercises: 15
source: https://one-course.com/books/chemistry/1/en/chapter/39-stereochemistry-chirality-and-isomers
license: CC-BY-NC-SA-4.0
credit: "One Chemistry Book, One Course (one-course.com)"
---

# Chapter 39 — Stereochemistry: Chirality and Isomers

Spearmint leaves and caraway seeds smell nothing alike: one is the fresh smell of chewing gum, the other the warm smell of rye bread. Yet the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) responsible for each smell is the same carvone, made of the same [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) bonded in the same order. The two carvones differ only as a left hand differs from a right hand: each is the mirror image of the other. Our nose, built of [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) that are themselves “handed”, tells them apart. This chapter learns to see [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) in three dimensions.

**You already know.**

The shape of [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule), and the wedges and dashes that draw them in space ([Chapter 24](https://one-course.com/books/chemistry/1/en/chapter/24-lewis-structures-and-the-shape-of-molecules#ch-g10-lewis-and-shape)). [Constitutional isomers](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-isomer) ([Chapter 32](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#ch-g11-organic-skeletons)). [Functional groups](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-functional-group) ([Chapter 33](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#ch-g11-functional-groups)).

![Spearmint and caraway: two mirror-image molecules, two smells.](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/img-f6d99421ef6c.jpg)

*Spearmint and caraway: two mirror-image [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule), two smells.*

## 39.1 Molecules in space

**Definition 39.1 (Stereoisomers).**

*Stereoisomers* are [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) with the same formula and the same sequence of bonded [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), which differ only by the arrangement of their [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) in space.

**Definition 39.2 (Cram representation).**

In the *Cram representation* of a carbon [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) with four single bonds, two bonds are drawn in the plane of the paper as plain lines, at an angle, the bond pointing towards the reader as a solid wedge and the bond pointing away as a dashed wedge.

## 39.2 Chirality

**Definition 39.3 (Chiral, asymmetric carbon).**

An object or a [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) is *chiral* if it cannot be superimposed on its mirror image, like a hand. A carbon [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) bonded to four different [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) or groups is an *asymmetric carbon*; it is often marked with a star.

**Proposition 39.4 (One asymmetric carbon makes a molecule chiral).**

A [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) with exactly one [asymmetric carbon](#def-g12-stereochemistry-chiral) is [chiral](#def-g12-stereochemistry-chiral).

**Proof.** Admitted: exchanging two of the four different groups around the [asymmetric carbon](#def-g12-stereochemistry-chiral) gives the mirror image, and no rotation of the whole [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) can bring it back, since the four groups are all different. ∎

**Definition 39.5 (Enantiomers, racemic mixture).**

Two [stereoisomers](#def-g12-stereochemistry-stereoisomer) that are mirror images of each other and not superimposable are *enantiomers*. A [mixture](https://one-course.com/books/chemistry/1/en/chapter/8-pure-substances-and-mixtures#def-g6-pure-substances-and-mixtures-mixture) of equal amounts of two enantiomers is a *racemic mixture*.

![The two enantiomers of lactic acid, CH3-CH(OH)-COOH, in Cram representation. The central carbon is asymmetric (H, OH, CH3, COOH). No rotation turns A into B: they are as different as a left and a right hand.](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/fig-fe42c38315b7.svg)

*The two [enantiomers](#def-g12-stereochemistry-enantiomer) of lactic acid, $\ce{CH3-CH(OH)-COOH}$, in [Cram representation](#def-g12-stereochemistry-cram). The central carbon is asymmetric ($\ce{H}$, $\ce{OH}$, $\ce{CH3}$, $\ce{COOH}$). No rotation turns A into B: they are as different as a left and a right hand.*

**Method 39.6 (Is a molecule chiral?).**

1. Look for [asymmetric carbons](#def-g12-stereochemistry-chiral) : a carbon with four different groups. None: the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) is (in this book) not [chiral](#def-g12-stereochemistry-chiral) .
2. Exactly one: the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) is [chiral](#def-g12-stereochemistry-chiral) .
3. Two or more: look for a plane that cuts the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) into two mirror halves, in one of its shapes; if there is one, the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) is not [chiral](#def-g12-stereochemistry-chiral) , otherwise it is.

**Remark 39.7 (Same properties, different smells).**

Two [enantiomers](#def-g12-stereochemistry-enantiomer) have the same melting and boiling temperatures, the same [solubility](https://one-course.com/books/chemistry/1/en/chapter/9-solutions-and-solubility#def-g6-solutions-and-solubility-solubility), the same spectra: every measurement made with something that is not itself [chiral](#def-g12-stereochemistry-chiral) gives the same result for both. They differ only when they meet something [chiral](#def-g12-stereochemistry-chiral), such as polarised light, which they turn in opposite directions, or the receptors of the nose: one carvone smells of spearmint, its enantiomer of caraway.

## 39.3 Diastereomers

**Definition 39.8 (Diastereomers).**

[Stereoisomers](#def-g12-stereochemistry-stereoisomer) that are not mirror images of each other are *diastereomers*. Unlike [enantiomers](#def-g12-stereochemistry-enantiomer), diastereomers have different physical properties.

**Proposition 39.9 (Counting stereoisomers).**

A [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) with $n$ [asymmetric carbons](#def-g12-stereochemistry-chiral) has at most $2^n$ [stereoisomers](#def-g12-stereochemistry-stereoisomer). There are fewer when the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) has two alike halves: then one of the combinations has a mirror plane and is not [chiral](#def-g12-stereochemistry-chiral) (a *meso* form).

**Proof.** Each [asymmetric carbon](#def-g12-stereochemistry-chiral) can take two arrangements, independently of the others: $2 \times 2 \times \dots \times 2 = 2^n$ combinations. When two combinations are the same [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule), the count drops. ∎

![The three stereoisomers of tartaric acid. L and D are enantiomers; each is a diastereomer of the meso form, which has a mirror plane in one of its shapes: three stereoisomers, not 22 = 4.](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/fig-7e60f00eab21.svg)

*The three [stereoisomers](#def-g12-stereochemistry-stereoisomer) of tartaric acid. L and D are [enantiomers](#def-g12-stereochemistry-enantiomer); each is a diastereomer of the meso form, which has a mirror plane in one of its shapes: three [stereoisomers](#def-g12-stereochemistry-stereoisomer), not $2^2 = 4$.*

**History — Pasteur sorts crystals by hand, 1848.**

In 1848 the young chemist Louis Pasteur looked with a magnifying glass at crystals of a salt of “racemic acid”, a form of tartaric acid that turned polarised light neither way. He noticed that the crystals came in two shapes, mirror images of each other, and sorted them one by one with tweezers. Dissolved, one pile turned polarised light to the right, the other, by the same amount, to the left: racemic acid was a [mixture](https://one-course.com/books/chemistry/1/en/chapter/8-pure-substances-and-mixtures#def-g6-pure-substances-and-mixtures-mixture) of two mirror-image [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule). [Molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule), he concluded, can be handed.

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/img-84b8a6bd387f.jpg)

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/img-a602a95824c2.jpg)

*Louis Pasteur (1822–1895), photographed by Paul Nadar.*

*Ammonium tartrate crystals from Pasteur’s collection. Photo Marie-Lan Taÿ Pamart, CC BY 4.0.*

## 39.4 Z and E isomers

**Definition 39.10 (Z and E isomers).**

When each carbon of a $\ce{C=C}$ [double bond](https://one-course.com/books/chemistry/1/en/chapter/24-lewis-structures-and-the-shape-of-molecules#def-g10-lewis-and-shape-multiple-bond) carries two different [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) or groups, two [stereoisomers](#def-g12-stereochemistry-stereoisomer) exist, because the [double bond](https://one-course.com/books/chemistry/1/en/chapter/24-lewis-structures-and-the-shape-of-molecules#def-g10-lewis-and-shape-multiple-bond) does not rotate. On each carbon, the group whose [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) bonded to it has the larger [atomic number](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-atomic-number) has priority. If the two priority groups are on the same side of the [double bond](https://one-course.com/books/chemistry/1/en/chapter/24-lewis-structures-and-the-shape-of-molecules#def-g10-lewis-and-shape-multiple-bond), the isomer is *Z*; if they are on opposite sides, it is *E*.

**Method 39.11 (Z or E?).**

1. Check that each carbon of the [double bond](https://one-course.com/books/chemistry/1/en/chapter/24-lewis-structures-and-the-shape-of-molecules#def-g10-lewis-and-shape-multiple-bond) carries two different groups; otherwise there is no [Z](#def-g12-stereochemistry-z-e) / [E](#def-g12-stereochemistry-z-e) isomerism.
2. On each carbon, give priority to the group whose first [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) has the larger [atomic number](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-atomic-number) (the full rules for ties are given in the Year 1 volume).
3. Same side: [Z](#def-g12-stereochemistry-z-e) . Opposite sides: [E](#def-g12-stereochemistry-z-e) .

![The two stereoisomers of but-2-ene. On each carbon, CH3 (carbon, Z = 6) has priority over H (Z = 1). They are diastereomers: they boil at different temperatures.](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/fig-3871266973b9.svg)

*The two [stereoisomers](#def-g12-stereochemistry-stereoisomer) of but-2-ene. On each carbon, $\ce{CH3}$ (carbon, $Z = 6$) has priority over $\ce{H}$ ($Z = 1$). They are [diastereomers](#def-g12-stereochemistry-diastereomer): they boil at different temperatures.*

## 39.5 Conformations

**Definition 39.12 (Conformation).**

The [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) of a [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) can rotate about a single bond. Each arrangement reached by such rotations is a *conformation* of the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule). Conformations of one [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) are not [isomers](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-isomer): they turn into one another all the time at room temperature.

![Two conformations of ethane, CH3-CH3, seen along the C-C bond: the front carbon is the centre, the back carbon the circle. The staggered conformation, where the atoms are farthest apart, is the most stable.](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/fig-ca9416f9d56a.svg)

*Two [conformations](#def-g12-stereochemistry-conformation) of ethane, $\ce{CH3-CH3}$, seen along the $\ce{C-C}$ bond: the front carbon is the centre, the back carbon the circle. The staggered [conformation](#def-g12-stereochemistry-conformation), where the [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) are farthest apart, is the most stable.*

**Remark 39.13 (Why it matters).**

Living things are built of [chiral](#def-g12-stereochemistry-chiral) [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) (proteins, sugars), and the receptors and enzymes made of them distinguish [enantiomers](#def-g12-stereochemistry-enantiomer): two [enantiomers](#def-g12-stereochemistry-enantiomer) can smell, taste or act as medicines very differently. That is why chemists who make a drug with an [asymmetric carbon](#def-g12-stereochemistry-chiral) must know which enantiomer they make, and test each one.

## 39.6 Exercises

**Exercise 39.1 ★.**

Which of these [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) have an [asymmetric carbon](#def-g12-stereochemistry-chiral)? Mark it with a star. Butan-2-ol $\ce{CH3-CH(OH)-CH2-CH3}$; propan-2-ol $\ce{CH3-CH(OH)-CH3}$; 2-chlorobutane; lactic acid $\ce{CH3-CH(OH)-COOH}$.

**Solution of Exercise 39.1.**

Butan-2-ol: carbon 2 ($\ce{H}$, $\ce{OH}$, $\ce{CH3}$, $\ce{CH2CH3}$). Propan-2-ol: none (carbon 2 carries two identical $\ce{CH3}$). 2-Chlorobutane: carbon 2. Lactic acid: carbon 2 ($\ce{H}$, $\ce{OH}$, $\ce{CH3}$, $\ce{COOH}$).

**Exercise 39.2 ★.**

Is each isomer [Z](#def-g12-stereochemistry-z-e) or [E](#def-g12-stereochemistry-z-e)?

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/fig-d5a87cedaa5b.svg)

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/fig-97e19125cb1f.svg)

**Solution of Exercise 39.2.**

First: the two $\ce{Cl}$ (priority over $\ce{H}$) on the same side: [Z](#def-g12-stereochemistry-z-e). Second: on the left, $\ce{CH3}$ has priority, upper side; on the right, $\ce{CH2CH3}$ has priority, lower side: [E](#def-g12-stereochemistry-z-e).

**Exercise 39.3 ★.**

Which are [chiral](#def-g12-stereochemistry-chiral): a glove, a spoon, a screw, a cube? Which of the [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) $\ce{CH2Cl2}$ and $\ce{CHFClBr}$ is [chiral](#def-g12-stereochemistry-chiral)?

**Solution of Exercise 39.3.**

[Chiral](#def-g12-stereochemistry-chiral): the glove, the screw. Not [chiral](#def-g12-stereochemistry-chiral): the spoon, the cube (each has a mirror plane). $\ce{CHFClBr}$ is [chiral](#def-g12-stereochemistry-chiral) (four different [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) on carbon); $\ce{CH2Cl2}$ is not.

**Exercise 39.4 ★.**

What is a [racemic mixture](#def-g12-stereochemistry-enantiomer)? Does it smell of spearmint, of caraway, or of both, in the case of carvone?

**Solution of Exercise 39.4.**

A [mixture](https://one-course.com/books/chemistry/1/en/chapter/8-pure-substances-and-mixtures#def-g6-pure-substances-and-mixtures-mixture) of equal amounts of two [enantiomers](#def-g12-stereochemistry-enantiomer). Racemic carvone contains both [enantiomers](#def-g12-stereochemistry-enantiomer), so the nose receives both smells at once.

**Exercise 39.5 ★.**

Can but-1-ene $\ce{CH2=CH-CH2-CH3}$ exist as [Z](#def-g12-stereochemistry-z-e) and [E isomers](#def-g12-stereochemistry-z-e)? Why?

**Solution of Exercise 39.5.**

No: carbon 1 carries two identical [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), $\ce{H}$ and $\ce{H}$; exchanging them gives the same [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule).

**Exercise 39.6 ★★.**

Draw the two [enantiomers](#def-g12-stereochemistry-enantiomer) of butan-2-ol in [Cram representation](#def-g12-stereochemistry-cram), with a mirror between them.

**Solution of Exercise 39.6.**

![](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/fig-81bcf9e315e2.svg) mirror ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/fig-856f9d84e304.svg)

**Exercise 39.7 ★★.**

How many [stereoisomers](#def-g12-stereochemistry-stereoisomer) do these have: 2-chlorobutane; 2,3-dichlorobutane $\ce{CH3-CHCl-CHCl-CH3}$; pent-2-ene $\ce{CH3-CH=CH-CH2-CH3}$?

**Solution of Exercise 39.7.**

2-Chlorobutane: 2 (one [asymmetric carbon](#def-g12-stereochemistry-chiral)). 2,3-Dichlorobutane: 3 (two [asymmetric carbons](#def-g12-stereochemistry-chiral) with alike halves: a pair of [enantiomers](#def-g12-stereochemistry-enantiomer) and a meso form). Pent-2-ene: 2 ([Z](#def-g12-stereochemistry-z-e) and [E](#def-g12-stereochemistry-z-e)).

**Exercise 39.8 ★★.**

Say whether these pairs are [enantiomers](#def-g12-stereochemistry-enantiomer), [diastereomers](#def-g12-stereochemistry-diastereomer) or the same [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule): L- and D-tartaric acid; L- and meso-tartaric acid; ([Z](#def-g12-stereochemistry-z-e))- and ([E](#def-g12-stereochemistry-z-e))-but-2-ene; meso-tartaric acid and its own mirror image.

**Solution of Exercise 39.8.**

[Enantiomers](#def-g12-stereochemistry-enantiomer); [diastereomers](#def-g12-stereochemistry-diastereomer); [diastereomers](#def-g12-stereochemistry-diastereomer); the same [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) (meso tartaric acid is superimposable on its mirror image).

**Exercise 39.9 ★★.**

Butane, $\ce{CH3-CH2-CH2-CH3}$, seen along its central bond. Draw the staggered [conformation](#def-g12-stereochemistry-conformation) where the two $\ce{CH3}$ groups are opposite, and an eclipsed one where they face each other. Which is the more stable? Why?

**Solution of Exercise 39.9.**

In the staggered [conformation](#def-g12-stereochemistry-conformation) with opposite $\ce{CH3}$ groups, the large groups are as far apart as possible: it is the most stable. In the eclipsed one, the two $\ce{CH3}$ face each other and crowd one another.

**Exercise 39.10 ★★.**

meso-Tartaric acid has two [asymmetric carbons](#def-g12-stereochemistry-chiral) but is not [chiral](#def-g12-stereochemistry-chiral). Explain, using its mirror plane.

**Solution of Exercise 39.10.**

Its two halves, each $\ce{CH(OH)COOH}$, are mirror images of each other: a plane between the two central carbons cuts the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) into two mirror halves. A [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) with a mirror plane is its own mirror image: not [chiral](#def-g12-stereochemistry-chiral).

**Exercise 39.11 ★★.**

Draw and name the [Z](#def-g12-stereochemistry-z-e) and [E isomers](#def-g12-stereochemistry-z-e) of pent-2-ene.

**Solution of Exercise 39.11.**

([Z](#def-g12-stereochemistry-z-e))-pent-2-ene ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/fig-6f568f6efb04.svg) and ([E](#def-g12-stereochemistry-z-e))-pent-2-ene ![](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-stereochemistry/fig-3ff1798728a0.svg).

**Exercise 39.12 ★★★.**

2,3-Dibromobutane $\ce{CH3-CHBr-CHBr-CH3}$ has two [asymmetric carbons](#def-g12-stereochemistry-chiral). Draw its [stereoisomers](#def-g12-stereochemistry-stereoisomer) in the zigzag representation used for tartaric acid, and show that one of them is a meso form.

**Solution of Exercise 39.12.**

As for tartaric acid, with $\ce{Br}$ instead of $\ce{OH}$ and $\ce{CH3}$ instead of $\ce{COOH}$: both $\ce{Br}$ solid, both dashed (a pair of [enantiomers](#def-g12-stereochemistry-enantiomer)), and one solid one dashed, which has a mirror plane: the meso form. Three [stereoisomers](#def-g12-stereochemistry-stereoisomer).

**Exercise 39.13 ★★★.**

A drug [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) has one [asymmetric carbon](#def-g12-stereochemistry-chiral). Its [synthesis](https://one-course.com/books/chemistry/1/en/chapter/28-synthesis-yield-and-purity#def-g10-synthesis-yield-synthesis) gives a [racemic mixture](#def-g12-stereochemistry-enantiomer), but only one enantiomer fits the [chiral](#def-g12-stereochemistry-chiral) receptor it must act on. What fraction of the racemic medicine is active? Give two ways a chemist could do better.

**Solution of Exercise 39.13.**

Half. The chemist can separate the two [enantiomers](#def-g12-stereochemistry-enantiomer) (as Pasteur did, by other means), or make only the useful enantiomer, with a reaction that is itself [chiral](#def-g12-stereochemistry-chiral) (a [chiral](#def-g12-stereochemistry-chiral) catalyst, an enzyme, a [chiral](#def-g12-stereochemistry-chiral) starting material).

**Exercise 39.14 ★★★.**

Hexa-2,4-diene, $\ce{CH3-CH=CH-CH=CH-CH3}$, has two [double bonds](https://one-course.com/books/chemistry/1/en/chapter/24-lewis-structures-and-the-shape-of-molecules#def-g10-lewis-and-shape-multiple-bond), each able to be [Z](#def-g12-stereochemistry-z-e) or [E](#def-g12-stereochemistry-z-e). How many [stereoisomers](#def-g12-stereochemistry-stereoisomer) does it have? (Beware of the symmetry of the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule).)

**Solution of Exercise 39.14.**

Three: (2E,4E), (2Z,4Z) and (2E,4Z), the last being the same [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) as (2Z,4E) read from the other end.

**Exercise 39.15 ★★★.**

A sugar [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) has three [asymmetric carbons](#def-g12-stereochemistry-chiral) and no symmetry. How many [stereoisomers](#def-g12-stereochemistry-stereoisomer) can it have at most? How many pairs of [enantiomers](#def-g12-stereochemistry-enantiomer) is that? How many [diastereomers](#def-g12-stereochemistry-diastereomer) does each stereoisomer have?

**Solution of Exercise 39.15.**

$2^3 = 8$ [stereoisomers](#def-g12-stereochemistry-stereoisomer), that is 4 pairs of [enantiomers](#def-g12-stereochemistry-enantiomer). Each stereoisomer has one enantiomer and $8 - 2 = 6$ [diastereomers](#def-g12-stereochemistry-diastereomer).

## 39.7 Problem: Pasteur’s Crystals

**Problem 39.1.**

Weekend problem — tartaric acid has two asymmetric carbons: how many stereoisomers does it really have?

The forms of tartaric acid, $\ce{HOOC-CH(OH)-CH(OH)-COOH}$, played a decisive part in the discovery that [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) can be handed. L-Tartaric acid melts at about $169\,{}^{\circ}\mathrm{C}$.

**Part I — The [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule).**

1. Give the [molecular formula](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-formulas) of tartaric acid and its [molar mass](https://one-course.com/books/chemistry/1/en/chapter/25-the-mole-and-molar-mass#def-g10-the-mole-molar-mass) .
2. Name its [functional groups](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-functional-group) , and say how many of each.
3. Which carbon [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) are asymmetric? List the four groups of each.
4. According to the rule of this chapter, how many [stereoisomers](#def-g12-stereochemistry-stereoisomer) could it have at most?

**Part II — The [stereoisomers](#def-g12-stereochemistry-stereoisomer).**

5. In the zigzag drawing of L-tartaric acid, are the $\ce{OH}$ groups drawn with solid or dashed wedges?
6. Draw its mirror image. Can the two be superimposed? Name the mirror image.
7. Draw the form with one solid and one dashed wedge. Rotate it in your mind about the central bond, and find a mirror plane.
8. Is this form [chiral](#def-g12-stereochemistry-chiral) ? What is it called?
9. Explain why tartaric acid has only three [stereoisomers](#def-g12-stereochemistry-stereoisomer) .
10. Say whether L and D, then L and meso, are [enantiomers](#def-g12-stereochemistry-enantiomer) or [diastereomers](#def-g12-stereochemistry-diastereomer) .

**Part III — Properties.**

11. At what temperature does D-tartaric acid melt? Why?
12. Must meso-tartaric acid melt at the same temperature? Why?
13. Carvone shows that two [enantiomers](#def-g12-stereochemistry-enantiomer) can smell different. Why can a nose tell them apart while a thermometer cannot?
14. A [racemic mixture](#def-g12-stereochemistry-enantiomer) of L and D tartaric acid: is it a [pure substance](https://one-course.com/books/chemistry/1/en/chapter/8-pure-substances-and-mixtures#def-g6-pure-substances-and-mixtures-pure-substance) ? Is it optically active as a whole?

**Part IV — Pasteur.**

15. Pasteur’s racemic salt gave crystals of two mirror-image shapes. What did each crystal contain?
16. From $10.0\,\mathrm{g}$ of racemic salt, what mass of each kind of crystal could he expect?
17. Why does the meso form never appear among these crystals?
18. How could he check, after sorting, that the two piles were [enantiomers](#def-g12-stereochemistry-enantiomer) ?
19. 3-Chlorobutan-2-ol, $\ce{CH3-CHCl-CH(OH)-CH3}$ , also has two [asymmetric carbons](#def-g12-stereochemistry-chiral) . How many [stereoisomers](#def-g12-stereochemistry-stereoisomer) does it have? Why does it not lose one like tartaric acid?
20. State the final answer: how many [stereoisomers](#def-g12-stereochemistry-stereoisomer) does tartaric acid have?

**Solution of Problem 39.1.**

**1.** $\ce{C4H6O6}$; $M = 4 \times 12.0 + 6 \times 1.0 + 6 \times 16.0
= 150.0\,\mathrm{g}/\mathrm{mol}$.

**2.** Two carboxyl groups (acid) and two hydroxyl groups ([alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol)).

**3.** The two central carbons, each bonded to $\ce{H}$, $\ce{OH}$, $\ce{COOH}$ and $\ce{CH(OH)COOH}$.

**4.** $2^2 = 4$.

**5.** Both with solid wedges.

**6.** Both $\ce{OH}$ with dashed wedges; it cannot be superimposed on L: it is D-tartaric acid, its enantiomer.

**7.** Turned about the central bond so that the two $\ce{OH}$ face the same way, the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) has a plane between its two central carbons that reflects one half onto the other.

**8.** No: it is meso-tartaric acid.

**9.** Of the four combinations (solid, solid), (dashed, dashed), (solid, dashed), (dashed, solid), the last two are the same [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule), the meso form, because the two halves of the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) are alike.

**10.** L and D: [enantiomers](#def-g12-stereochemistry-enantiomer). L and meso: [diastereomers](#def-g12-stereochemistry-diastereomer).

**11.** At $169\,{}^{\circ}\mathrm{C}$ too: [enantiomers](#def-g12-stereochemistry-enantiomer) have the same physical properties.

**12.** No: it is a diastereomer of L, a different compound with its own properties.

**13.** The receptors of the nose are [chiral](#def-g12-stereochemistry-chiral) and distinguish mirror images; a thermometer, not [chiral](#def-g12-stereochemistry-chiral), cannot.

**14.** No, a [mixture](https://one-course.com/books/chemistry/1/en/chapter/8-pure-substances-and-mixtures#def-g6-pure-substances-and-mixtures-mixture) of two compounds; as a whole it is not optically active, the two [enantiomers](#def-g12-stereochemistry-enantiomer) cancelling each other.

**15.** Only one enantiomer: each crystal was built of L or of D alone.

**16.** $5.0\,\mathrm{g}$ of each.

**17.** The meso form is a different compound, not part of the [racemic mixture](#def-g12-stereochemistry-enantiomer) of L and D.

**18.** By dissolving each pile: the solutions turn polarised light by the same amount in opposite directions (and the crystals are mirror images).

**19.** Four: its two [asymmetric carbons](#def-g12-stereochemistry-chiral) carry different groups ($\ce{Cl}$ on one, $\ce{OH}$ on the other), so no combination has a mirror plane, and no two combinations are the same [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule).

**20.** Three: L, D and meso.