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August Kekulé

Friedrich August Kekulé, from 1895 August Kekule von Stradonitz

A course in two strands: the life of the would-be architect who taught chemists to draw molecules, and the structural theory he built, from the four valences of carbon to the six-membered ring of benzene.

Born 7 September 1829, Darmstadt Died 13 July 1896, Bonn Benzene ring published January 1865 Level advanced undergraduate
Benzene, C₆H₆. Kekulé’s two alternating structures (1865, with the 1872 oscillation between them) and the modern picture of six equal bonds.
Lesson 00

How to use this course

Every organic chemist draws a molecule as letters joined by lines, with each carbon carrying four bonds and benzene as a hexagon. That habit comes largely from August Kekulé. Between 1857 and 1865 he argued that carbon is tetravalent, that carbon atoms bond to one another in chains, and that benzene is a closed ring of six carbons. Together these ideas turned organic chemistry from a catalogue of formulas into a science of structure that could predict how many isomers a compound should have.

Prerequisites for Part II
  • A first course in general chemistry: moles, empirical and molecular formulas, balancing equations.
  • Lewis structures and the idea of a covalent bond.
  • For Lesson 08, elementary counting with symmetry (the Burnside lemma is introduced as needed).
  • For Lesson 09, the basics of quantum mechanics and molecular orbitals help but are not essential.

Each technical lesson opens with a paragraph for the general reader, then gives the key ideas in boxes, the reasoning behind them, and exercises with folded solutions. The lessons follow the history: the type theory Kekulé inherited (Lesson 04), his structural theory of 1857–58 (Lessons 05–06), the benzene theory of 1865 and its testing (Lessons 07–08), and the twentieth-century explanation of why benzene behaves as it does (Lesson 09).

Reference

Timeline

1829Born 7 September in Darmstadt, Grand Duchy of Hesse, into a family of civil servants.
1847Enters the University of Giessen to study architecture; after hearing Justus von Liebig lecture, turns to chemistry.
1851–52Studies in Paris; hears Jean-Baptiste Dumas and meets Charles Gerhardt and Adolphe Wurtz.
1852Doctorate at Giessen, on amyloxide sulfuric acid and its salts.
1852–53Assistant to Adolph von Planta at Reichenau, near Chur, Switzerland.
1853–55London. Assistant to John Stenhouse at St Bartholomew’s Hospital; friendship with Alexander Williamson.
1856Habilitation and Privatdozent at Heidelberg.
1857Proposes the tetravalence of carbon and adds a marsh-gas type to the theory of types.
1858May: Ueber die Constitution und die Metamorphosen der chemischen Verbindungen in Liebig’s Annalen; carbon chains. June: Archibald Scott Couper’s parallel paper. 8 October: professor of chemistry at Ghent.
1859First part of the Lehrbuch der organischen Chemie.
18603–5 September: co-organizes the Karlsruhe Congress with Wurtz and Karl Weltzien.
1862–63Marries Stephanie Drory in Ghent. In 1863 their son Stephan is born and she dies days later.
1864Elected associate of the Royal Academy of Belgium.
1865January: Sur la constitution des substances aromatiques, the benzene ring.
1866German account in the Annalen: Untersuchungen über aromatische Verbindungen.
1867Called to Bonn to succeed August Wilhelm Hofmann.
186811 May: the new Bonn chemical institute at Poppelsdorf opens.
1872Oscillation hypothesis for benzene. J. H. van ’t Hoff works in his Bonn laboratory.
1876Marries Luise Högel.
1877–78Rector of the University of Bonn.
1885Copley Medal of the Royal Society.
189011 March: the Benzolfest in Berlin; his speech tells of two reveries.
1893Order Pour le Mérite for Sciences and Arts.
1895Ennobled as Kekule von Stradonitz.
1896Dies 13 July in Bonn; buried in the Poppelsdorf cemetery.
Part I · Formation
Lesson 01

Darmstadt and Giessen, 1829–1852

Friedrich August Kekulé was born in Darmstadt on 7 September 1829. His family were upper-middle-class civil servants of the Grand Duchy of Hesse. The acute accent on the final e had been added by his father during the French occupation of Hesse in the Napoleonic period. August, who never used his first given name, was a gifted schoolboy at the Grand Ducal Gymnasium, good at languages and at drawing, and he planned to become an architect.

In the autumn of 1847 he entered the University of Giessen to study architecture. Giessen was then the most famous chemistry school in the world. Justus von Liebig had built there a teaching laboratory where students learned analysis by doing it, and he lectured with great force. Kekulé heard him in his first semester and changed subjects.

Chemists of his generation knew the composition of compounds, but few asked how their atoms might be arranged. Kekulé came to the subject with a draughtsman’s habit of thinking in drawings and spatial arrangements. Biographers have often connected this training with his later structural theory, though the connection is a matter of interpretation.

The doctorate

After four years at Giessen he completed a short compulsory military service and, on Liebig’s advice, went to Paris in 1851 to widen his chemical education. He returned to take his doctorate at Giessen in the summer of 1852 with a thesis on amyloxide sulfuric acid and some of its salts, a compound of amyl alcohol and sulfuric acid. The work was competent analytical chemistry in the Giessen style and gave no hint of the theorist to come.

Lesson 02

Paris, Reichenau, London, 1851–1855

The year in Paris in 1851–52 shaped Kekulé’s chemistry more than the doctorate did. He attended the lectures of Jean-Baptiste Dumas and came to know Charles Gerhardt and Adolphe Wurtz. Gerhardt was then completing his theory of types, which classified organic compounds by analogy with a few simple inorganic molecules (Lesson 04). Gerhardt was a difficult man and an outsider in French chemistry, but Kekulé found his ideas congenial, and they became the starting point for his own.

After the doctorate, Kekulé spent about a year as private assistant to Adolph von Planta, a wealthy Swiss chemist who worked in a laboratory at the castle of Reichenau, near Chur in the canton of Graubünden. The work was routine analysis. He then moved to London, where from 1853 to 1855 he worked as assistant to John Stenhouse at the medical school of St Bartholomew’s Hospital.

Williamson and London

The decisive contact in London was Alexander Williamson of University College. Williamson had shown in 1850 that ethers are formed by replacing both hydrogens of water with organic groups, and he had made water the model for a whole family of compounds. Kekulé extended the idea in 1854 by preparing thioacetic acid, replacing oxygen by sulfur with phosphorus pentasulfide, and arguing that hydrogen sulfide could serve as a type just as water did. In this paper he began to speak of atoms of different “basicity”, that is, of different combining capacity.

Kekulé later told how, riding on the top of a London omnibus one summer evening, he fell into a reverie in which atoms danced before his eyes, the larger ones taking the smaller ones in their grip and dragging chains of atoms behind them. Historians date the episode, if it happened, to the late summer of 1855. He said that he spent part of that night sketching what he had seen, and that this was the origin of the structure theory. The story was told 35 years later (Lesson 11), and it should be read as a recollection, not a record.

Lesson 03

Heidelberg, 1856–1858

Returning to Germany, Kekulé habilitated at Heidelberg in 1856 and became a Privatdozent, an unsalaried lecturer paid by student fees. Heidelberg’s chemistry was dominated by Robert Bunsen, a great experimentalist with little interest in theory. Kekulé fitted out a small private laboratory of his own and taught organic chemistry to a handful of students. Among those who worked with him was the young Adolf von Baeyer, with whom he argued long and hard about chemical theory.

In these two years he wrote his most important theoretical papers. A paper of 1857 in Liebig’s Annalen, on so-called conjugated compounds and the theory of polyatomic radicals, proposed that carbon is tetravalent and added a fourth type, marsh gas \(\mathrm{CH_4}\), to Gerhardt’s three. A second paper on the constitution of mercury fulminate showed the new ideas at work. In May 1858 the Annalen published his paper on the constitution and metamorphoses of chemical compounds and the chemical nature of carbon. It added the second essential step: carbon atoms bond to one another, forming chains (Lesson 05).

A month later Archibald Scott Couper, a Scot working in Wurtz’s laboratory in Paris, published the same idea independently in the Comptes rendus and the Annales de chimie et de physique, with diagrams in which lines joined atoms. Couper had asked Wurtz to present his paper to the Academy of Sciences, and Wurtz delayed. Kekulé’s paper appeared first, and the priority went to him. That autumn, on 8 October 1858, Kekulé was appointed professor of chemistry at the University of Ghent in Belgium, at 29.

Part II · The chemistry
Lesson 04

Types, radicals and formulas

For the general reader. In the 1850s chemists could measure what a compound was made of, but they disagreed even on how to write its formula. One school grouped organic compounds into families, each modelled on a simple molecule such as water or ammonia. Kekulé learned this “theory of types” in Paris and London. His structural theory grew directly out of it.

Goals
  • Convert between equivalent-weight formulas of the 1850s and modern formulas.
  • Read a compound as a derivative of Gerhardt’s types.
  • See how the types already contained the idea of valence.

Two systems of weights

Many chemists of the 1840s and 1850s used equivalent weights with \(\mathrm H=1\), \(\mathrm C=6\), \(\mathrm O=8\). In that system water was HO and acetic acid \(\mathrm{C_4H_4O_4}\). Gerhardt and Auguste Laurent argued for \(\mathrm C=12\), \(\mathrm O=16\), which gave water as \(\mathrm{H_2O}\) and made the formulas of organic compounds consistent with their vapour densities. Kekulé adopted the Gerhardt values, but chemists did not settle the question until after the Karlsruhe Congress of 1860 (Lesson 06).

Gerhardt’s types

The theory of types (Gerhardt, 1853; Kekulé, 1857)

Organic compounds are derived from a small number of type molecules by replacing hydrogen with radicals (groups of atoms that pass unchanged through reactions). Gerhardt used the types hydrogen \(\mathrm{H{-}H}\), hydrogen chloride \(\mathrm{H{-}Cl}\), water \(\mathrm{H_2O}\) and ammonia \(\mathrm{NH_3}\). Kekulé added the marsh-gas type \(\mathrm{CH_4}\).

\[ \text{water type: } \begin{matrix}\mathrm{H}\\ \mathrm{H}\end{matrix}\Big\}\mathrm{O} \ \longrightarrow\ \begin{matrix}\mathrm{C_2H_5}\\ \mathrm{H}\end{matrix}\Big\}\mathrm{O}\ \text{(ethanol)},\quad \begin{matrix}\mathrm{C_2H_5}\\ \mathrm{C_2H_5}\end{matrix}\Big\}\mathrm{O}\ \text{(ether)},\quad \begin{matrix}\mathrm{C_2H_3O}\\ \mathrm{H}\end{matrix}\Big\}\mathrm{O}\ \text{(acetic acid)} \]

Williamson’s ether synthesis of 1850 was the key evidence for the water type. Potassium ethoxide and ethyl iodide give diethyl ether, and potassium ethoxide with methyl iodide gives the mixed ether ethyl methyl ether. A single oxygen holds two groups, so the oxygen atom must be “dibasic”, as Williamson and Kekulé put it.

\[ \mathrm{C_2H_5OK} + \mathrm{CH_3I} \longrightarrow \mathrm{C_2H_5{-}O{-}CH_3} + \mathrm{KI} \]

From types to valence

Read the types as a list of atomic capacities: hydrogen and chlorine combine with one partner, oxygen with two, nitrogen with three. Kekulé’s thioacetic acid of 1854 showed sulfur behaving like oxygen. The marsh-gas type assigned carbon four partners. Once each atom has a fixed combining capacity, the types become unnecessary, because any molecule can be built by satisfying the capacities of its atoms. This is the step Kekulé took in 1858.

Exercise 4.1In the equivalent system \(\mathrm H=1,\ \mathrm C=6,\ \mathrm O=8\), a chemist writes acetic acid as \(\mathrm{C_4H_4O_4}\) and alcohol as \(\mathrm{C_4H_6O_2}\). Convert both to modern formulas and check that the masses agree.

Show solution
Each old C is half a modern C, and each old O half a modern O. So \(\mathrm{C_4H_4O_4}\to\mathrm{C_2H_4O_2}\) and \(\mathrm{C_4H_6O_2}\to\mathrm{C_2H_6O}\). Masses: \(4\cdot6+4+4\cdot8=60=2\cdot12+4+2\cdot16\), and \(4\cdot6+6+2\cdot8=46=2\cdot12+6+16\).

Exercise 4.2Balance Kekulé’s 1854 preparation of thioacetic acid, \(\mathrm{CH_3COSH}\), from acetic acid and phosphorus pentasulfide \(\mathrm{P_2S_5}\), assuming the other product is \(\mathrm{P_2O_5}\). In type notation, what has changed?

Show solution
\(5\,\mathrm{CH_3COOH}+\mathrm{P_2S_5}\to5\,\mathrm{CH_3COSH}+\mathrm{P_2O_5}\). Check: C 10, H 20, O 10, P 2, S 5 on both sides. In type notation the hydroxyl oxygen of the water type, \(\mathrm{(C_2H_3O)(H)O}\), is replaced by sulfur, \(\mathrm{(C_2H_3O)(H)S}\): the compound belongs to the hydrogen sulfide type, and sulfur is dibasic like oxygen.

Exercise 4.3Write methylamine, dimethylamine and trimethylamine as derivatives of the ammonia type. Why did these compounds, discovered by Wurtz and Hofmann around 1849–50, support the type theory?

Show solution
\(\mathrm{(CH_3)H_2N}\), \(\mathrm{(CH_3)_2HN}\), \(\mathrm{(CH_3)_3N}\): one, two or three hydrogens of \(\mathrm{NH_3}\) replaced by methyl. They are basic like ammonia and form salts with acids, so a graded series of replacements on one type preserved chemical character, as the theory claimed.
Lesson 05

Tetravalence and the carbon chain

For the general reader. Carbon is special because its atoms can join one another to form long chains and rings, which is why there are millions of organic compounds. Kekulé’s 1858 paper made two claims: each carbon atom has four bonds to give, and carbon atoms can use some of those bonds on each other. From these two rules alone he could explain the formulas of whole families of compounds.

Goals
  • State Kekulé’s two postulates and derive the general formula of the alkanes.
  • Compute the degree of unsaturation of a formula.
  • Compare Kekulé’s and Couper’s 1858 theories.
Kekulé’s postulates (1857–1858)

(1) The carbon atom is tetratomic (tetravalent): it combines with four atoms of hydrogen or chlorine, two of oxygen, and so on. (2) Carbon atoms can combine with one another, each such link using one unit of affinity from each atom. In a chain of \(n\) carbons joined by single links, the number of remaining affinities is

\[ 4n - 2(n-1) = 2n+2. \]

Hence the saturated hydrocarbons have the formula \(\mathrm{C}_n\mathrm{H}_{2n+2}\), as observed for methane, ethane, propane and the paraffins. Kekulé used the same count to explain series in which successive members differ by \(\mathrm{CH_2}\), a regularity Gerhardt had called homology. Each added carbon brings four affinities and uses two to join the chain, leaving two for hydrogen.

Degree of unsaturation

Any ring or multiple bond lowers the hydrogen count by two compared with the open saturated chain. Allowing for nitrogen (valence 3) and halogens (valence 1), the number of rings plus π bonds in a formula \(\mathrm{C}_c\mathrm{H}_h\mathrm{N}_n\mathrm{O}_o\mathrm{X}_x\) is

\[ U = \frac{2c+2+n-h-x}{2}. \]

Oxygen and other divalent atoms do not change \(U\), because a divalent atom inserted into a chain uses both of its bonds. Kekulé did not write this formula, but it is a direct consequence of his counting, and he used the equivalent reasoning for ethylene, \(\mathrm{C_2H_4}\), and for benzene.

Kekulé and Couper

Couper’s paper of June 1858 reached the same two postulates and went further in notation. He wrote formulas with dotted or straight lines between atoms, the ancestor of the modern structural formula. He also allowed carbon a combining power of two as well as four. Kekulé gave no diagrams in 1858, and his first graphical formulas, in the Lehrbuch of 1859, used elongated “sausage” shapes for atoms. Couper published nothing further after a breakdown; his work was rescued from obscurity in the early twentieth century by Kekulé’s former student and biographer Richard Anschütz. Aleksandr Butlerov introduced the phrase “chemical structure” in 1861 and argued, more firmly than Kekulé, that a compound has one structure that determines its properties.

Exercise 5.1Show from the postulates that a cyclic saturated hydrocarbon of \(n\) carbons has the formula \(\mathrm{C}_n\mathrm{H}_{2n}\), and that an open chain with one C=C double bond has the same formula.

Show solution
A ring of \(n\) carbons has \(n\) C–C links, using \(2n\) affinities, so \(4n-2n=2n\) remain for H. An open chain with one double bond has \(n-2\) single links and one double link, using \(2(n-2)+4=2n\) affinities, again leaving \(2n\). Formula alone cannot distinguish cyclohexane from hexene; both have \(U=1\).

Exercise 5.2Compute \(U\) for \(\mathrm{C_6H_6}\), \(\mathrm{C_2H_2}\), \(\mathrm{C_5H_5N}\) (pyridine), and \(\mathrm{C_7H_5ClO}\) (benzoyl chloride).

Show solution
Benzene: \((12+2-6)/2=4\) (three C=C and one ring). Acetylene: \((4+2-2)/2=2\) (a triple bond). Pyridine: \((10+2+1-5)/2=4\). Benzoyl chloride: \((14+2-5-1)/2=5\) (benzene ring 4, C=O 1).

Exercise 5.3Draw all structural isomers of \(\mathrm{C_5H_{12}}\). How many are there, and how does this show that the formula does not determine the compound?

Show solution
Three: pentane \(\mathrm{CH_3(CH_2)_3CH_3}\), 2-methylbutane \(\mathrm{(CH_3)_2CHCH_2CH_3}\), and 2,2-dimethylpropane \(\mathrm{C(CH_3)_4}\). All satisfy the postulates with the same atoms; they differ in how the carbons are connected. The structural theory predicts the number of isomers, which can then be checked by isolating them.
Lesson 06

Structural formulas, isomers, atomic weights

For the general reader. A structural theory is only as good as the formulas it starts from, and in 1860 chemists still disagreed about the relative weights of atoms. Kekulé helped call the first international chemistry conference at Karlsruhe to settle the matter. There a paper by Stanislao Cannizzaro showed how to fix atomic weights reliably. With correct weights, structural formulas could predict which isomers exist.

Goals
  • Apply Cannizzaro’s method to determine an atomic weight.
  • Count constitutional isomers by building structures.
  • See what the structure theory predicted and what it left open.

The Karlsruhe Congress

Kekulé, Wurtz and Karl Weltzien sent out invitations, and about 140 chemists met in Karlsruhe on 3–5 September 1860. Kekulé gave an opening address. The debates on the meaning of atom, molecule and equivalent ended without a vote, but on the last day copies of Cannizzaro’s 1858 Sunto were handed out. Lothar Meyer later wrote that reading it cleared his doubts. Within a decade most chemists used \(\mathrm C=12\), \(\mathrm O=16\).

Cannizzaro’s method (1858)

By Avogadro’s hypothesis, equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, so the molecular weight of a volatile compound is twice its vapour density relative to hydrogen gas \(\mathrm{H_2}\). For a given element, take many of its volatile compounds and find the mass of the element in one molecular weight of each. The atomic weight is the largest number of which all these masses are whole multiples.

Structural isomers

With tetravalent carbon and correct weights, chemists could enumerate the possible structures for a formula. The theory predicted, for example, that there should be two propyl alcohols, one with OH on an end carbon and one on the middle carbon. Hermann Kolbe predicted the secondary alcohols on a similar basis, and Charles Friedel made isopropyl alcohol in 1862. Each success strengthened the theory. What the theory did not yet address was the arrangement of atoms in space: two compounds with the same connections but mirror-image arrangements remained unexplained until van ’t Hoff and Joseph Le Bel in 1874.

Exercise 6.1Molecular weights (from vapour densities) and carbon mass fractions are: methane 16, 0.750; carbon dioxide 44, 0.273; ethylene 28, 0.857; ether 74, 0.649; benzene 78, 0.923. Use Cannizzaro’s method to find the atomic weight of carbon.

Show solution
Mass of carbon per molecule: \(16\times0.750=12\); \(44\times0.273=12\); \(28\times0.857=24\); \(74\times0.649=48\); \(78\times0.923=72\). These are 12, 12, 24, 48, 72, all multiples of 12 and with 12 itself occurring. The atomic weight of carbon is 12, so methane has one carbon and benzene six.

Exercise 6.2How many isomeric alcohols \(\mathrm{C_4H_9OH}\) does the structure theory predict? Name them.

Show solution
Four. On butane: butan-1-ol and butan-2-ol. On isobutane: 2-methylpropan-1-ol and 2-methylpropan-2-ol (tert-butyl alcohol). Butan-2-ol has a carbon with four different groups and exists as two mirror-image forms, which the 1858 theory could not distinguish.
Lesson 07

The benzene ring, 1865

For the general reader. A large family of compounds, from coal-tar dyes to oil of bitter almonds, contain at least six carbon atoms and behave differently from ordinary chains. They were called aromatic. In January 1865 Kekulé proposed that they all share a core of six carbon atoms closed into a ring, benzene, with alternating single and double bonds. The idea organized the chemistry of the dye industry for the next century.

Goals
  • State Kekulé’s benzene hypothesis and its experimental basis.
  • Predict the number of substitution isomers of benzene.
  • Distinguish the closed chain from the open-chain alternatives.

The puzzle

Benzene, \(\mathrm{C_6H_6}\), had been isolated by Michael Faraday in 1825. Its formula gives \(U=4\), so it should be highly unsaturated. Yet benzene resists addition reactions and undergoes substitution, keeping its six carbons intact through reaction after reaction. Every aromatic compound had at least six carbons. Its substitution products were remarkably few: there was only one bromobenzene, one phenol, one nitrobenzene.

Kekulé’s benzene hypothesis (1865)

All aromatic compounds contain a nucleus of six carbon atoms forming a closed chain. Each carbon uses one affinity to bind one atom or group outside the ring, and the carbons are joined alternately by one and two affinities. In modern notation, benzene is a hexagon with alternating single and double bonds and one hydrogen on each carbon. The six hydrogen positions are equivalent.

Count the affinities: each carbon has 4, uses 1 for H, and 3 within the ring (one single and one double link, shared with its two neighbours). The six carbons thus use \(6\cdot3/2=9\) bonds in the ring: 6 sigma links and 3 double-bond second links, consistent with \(U=4\) (one ring plus three double bonds).

Kekulé first published the idea in French in the Bulletin de la Société Chimique de Paris in January 1865, and at length in German in the Annalen in 1866. His early figures drew the ring with his sausage-shaped atoms; the regular hexagon soon became the standard symbol. Johann Josef Loschmidt, in his privately printed Chemische Studien of 1861, had drawn benzene as a circle, and Couper had proposed other cyclic structures for aromatic compounds in 1858. Neither developed the idea into a theory of isomers.

Predictions

Equivalence of the six positions implies one monosubstituted derivative \(\mathrm{C_6H_5X}\), and three disubstituted derivatives \(\mathrm{C_6H_4X_2}\), with substituents at positions 1,2 (ortho), 1,3 (meta) and 1,4 (para). These counts matched what chemists found, and Kekulé made them the test of his theory.

Exercise 7.1Use the hexagon to count the isomers of \(\mathrm{C_6H_3X_3}\) and of \(\mathrm{C_6H_4XY}\) (two different substituents).

Show solution
\(\mathrm{C_6H_3X_3}\): 1,2,3 (vicinal), 1,2,4 (unsymmetrical), 1,3,5 (symmetrical), so 3. \(\mathrm{C_6H_4XY}\): ortho, meta, para, so 3; since X and Y differ, one might expect more, but the reflection of the hexagon maps 1-X,2-Y onto 1-Y,2-X.

Exercise 7.2An open-chain structure for \(\mathrm{C_6H_6}\) such as \(\mathrm{CH_2{=}C{=}CH{-}CH{=}C{=}CH_2}\) fits the formula. How many monobromo derivatives would it give? Why did Kekulé reject such chains?

Show solution
Hydrogens sit on C1 and C6 (the \(\mathrm{CH_2}\) ends, equivalent by symmetry) and on C3 and C4 (the inner CH groups, also equivalent). Substituting at an end or at an inner carbon gives two different monobromides. Only one bromobenzene exists, so all six hydrogens must be equivalent, which a ring achieves.
Lesson 08

Counting isomers and the oscillation hypothesis

For the general reader. Kekulé’s ring could be tested by counting. If it was right, chemists should find exactly three forms of every disubstituted benzene. Albert Ladenburg, who had worked in his Ghent laboratory, pointed out a flaw: a ring with fixed alternating bonds should give two different ortho compounds, depending on whether the substituents straddle a single or a double bond. Only one was ever found. In 1872 Kekulé answered that the bonds do not stay fixed.

Goals
  • Count substitution patterns on the hexagon with the Burnside lemma.
  • Apply Körner’s method to assign ortho, meta, para.
  • Understand Ladenburg’s objection and Kekulé’s reply.

Counting with symmetry

If all six positions are equivalent, the symmetry group of the regular hexagon, the dihedral group \(D_6\) of order 12, acts on substitution patterns. Two patterns describe the same compound if a symmetry carries one to the other.

Burnside’s lemma

If a finite group \(G\) acts on a finite set \(\Omega\), the number of orbits is \(\displaystyle\frac{1}{|G|}\sum_{g\in G}|\mathrm{Fix}(g)|\), where \(\mathrm{Fix}(g)\) is the set of elements fixed by \(g\).

Colour each of the six positions H or X. A symmetry with cycles of lengths \(\ell_1,\dots,\ell_k\) on the vertices fixes \(2^k\) colourings. For \(D_6\): the identity has 6 cycles; rotations by \(\pm60^\circ\) have 1, by \(\pm120^\circ\) have 2, by \(180^\circ\) has 3; three reflections through opposite vertices have 4 cycles each, and three through opposite edge midpoints have 3. So

\[ \frac{1}{12}\big(2^6 + 2\cdot2^1 + 2\cdot2^2 + 2^3 + 3\cdot2^4 + 3\cdot2^3\big) = \frac{156}{12} = 13. \]

The 13 patterns split by number of X as \(1,1,3,3,3,1,1\), matching one parent, one mono-, three di-, three tri-, three tetra-, one penta- and one hexa-substituted benzene.

Körner’s absolute method (1874)

Knowing that three disubstituted isomers exist does not say which is which. Wilhelm Körner, who had worked with Kekulé in Ghent, gave a method: introduce a third substituent and count products. From 1,2-dibromobenzene one gets two tribromo (or bromo-nitro) derivatives, from 1,3 three, from 1,4 only one.

Ladenburg’s objection and the oscillation hypothesis

In 1869 Ladenburg observed that in a ring with fixed alternating bonds, 1,2-disubstitution across a double bond differs from 1,2-disubstitution across a single bond (sometimes labelled 1,2 and 1,6). Only one ortho isomer of each kind was known. Ladenburg himself proposed a triangular prism structure with six equivalent carbons and only single bonds. James Dewar, who had also worked in Kekulé’s Ghent laboratory, had described several other \(\mathrm{C_6H_6}\) structures in 1867, including the bicyclic one now called Dewar benzene.

Oscillation hypothesis (Kekulé, 1872)

Atoms in a molecule are in constant motion and collide with their neighbours. In benzene each carbon collides alternately with its two neighbours, so that over time each pair of adjacent carbons is linked as often by a double as by a single bond. The two alternating structures are not distinct compounds but phases of one motion, and the 1,2 and 1,6 positions are equivalent.

The hypothesis appeared in a paper on condensation products of aldehyde in the Annalen of 1872. It is not the modern theory, but it captured the essential point: no single valence-bond drawing describes benzene, and the real molecule has six equivalent bonds.

Exercise 8.1Verify Körner’s counts. For each of 1,2-, 1,3- and 1,4-dibromobenzene, list the free positions and group them into classes equivalent under the symmetry that fixes the two bromines.

Show solution
1,2: free 3,4,5,6; the reflection exchanging 1 and 2 gives \(3\leftrightarrow6\), \(4\leftrightarrow5\): two classes. 1,3: free 2,4,5,6; the reflection through 2 and 5 gives \(4\leftrightarrow6\): classes {2}, {4,6}, {5}, three. 1,4: free 2,3,5,6, all equivalent under the symmetries fixing {1,4}: one class. So 2, 3, 1 products.

Exercise 8.2Use Burnside to count disubstituted benzenes \(\mathrm{C_6H_4X_2}\) directly: let \(D_6\) act on the 15 two-element subsets of the six positions.

Show solution
Fixed pairs: identity 15; rotations by \(\pm60^\circ,\pm120^\circ\) fix none; rotation by \(180^\circ\) fixes the 3 opposite pairs; each vertex reflection fixes 3 pairs (the two fixed vertices as a pair, and two swapped pairs); each edge reflection fixes 3 swapped pairs. Total \(15+3+3\cdot3+3\cdot3=36\), and \(36/12=3\).

Exercise 8.3With fixed double bonds, the symmetry group of a Kekulé structure is only \(D_3\) (order 6). Count \(\mathrm{C_6H_4X_2}\) isomers under \(D_3\) and explain Ladenburg’s objection.

Show solution
\(D_3\) contains the identity (15 fixed pairs), rotations by \(\pm120^\circ\) (0), and three reflections. A reflection through two opposite vertices would swap a single and a double bond, so it is lost. The three surviving reflections pass through the midpoints of two opposite bonds; each swaps three pairs of vertices and so fixes 3 two-element subsets. Total \((15+0+3\cdot3)/6=4\). The extra isomer is the second ortho compound: X,X across a double bond versus across a single bond. Experiment shows three, which favours full \(D_6\) symmetry.
Lesson 09

Benzene after Kekulé

For the general reader. Kekulé’s two alternating structures were a brilliant guess, but chemistry needed physics to explain them. In the twentieth century, X-rays showed benzene to be a flat regular hexagon, and quantum mechanics showed that its six bonding electrons are shared around the whole ring. That sharing lowers the energy and explains why benzene resists the addition reactions typical of double bonds.

Goals
  • Estimate the stabilization of benzene from heats of hydrogenation.
  • Derive the Hückel π energies of benzene.
  • State the 4n+2 rule and apply it.

Evidence

In 1929 Kathleen Lonsdale’s X-ray study of hexamethylbenzene showed the ring to be a planar regular hexagon. All six C–C bonds in benzene have length about 139–140 pm, between a typical single bond (154 pm) and double bond (134 pm). Thermochemistry gives the energetic signature. Hydrogenating cyclohexene releases about 120 kJ/mol; three isolated double bonds would release about 360 kJ/mol; benzene releases only about 208 kJ/mol. The difference, about 150 kJ/mol, is the aromatic stabilization.

Resonance

In 1933 Linus Pauling and George Wheland described benzene as a quantum-mechanical superposition dominated by the two Kekulé structures. The molecule does not oscillate between them, as Kekulé had suggested; its single ground state is a combination of both, lower in energy than either.

Hückel theory

Hückel π energies of a ring (Hückel, 1931)

For a planar ring of \(N\) identical \(sp^2\) atoms, with Coulomb integral \(\alpha\) and nearest-neighbour resonance integral \(\beta<0\), the π orbital energies are

\[ E_k = \alpha + 2\beta\cos\frac{2\pi k}{N},\qquad k=0,1,\dots,N-1. \]

A closed shell with all bonding levels filled arises when the ring holds \(4n+2\) π electrons (Hückel’s rule). Such rings are aromatic.

Derivation. The Hückel matrix is \(H=\alpha I+\beta A\), where \(A\) is the adjacency matrix of the \(N\)-cycle. \(A\) is circulant, so its eigenvectors are \(c_j=e^{2\pi ijk/N}\) with eigenvalues \(e^{2\pi ik/N}+e^{-2\pi ik/N}=2\cos(2\pi k/N)\). The lowest level (\(k=0\)) is single; the others pair up as \(k\) and \(N-k\). Filling one single level and \(n\) degenerate pairs takes \(2+4n\) electrons.

For benzene (\(N=6\)) the levels are \(\alpha+2\beta\), \(\alpha+\beta\) (twice), \(\alpha-\beta\) (twice), \(\alpha-2\beta\). Six electrons fill the three bonding orbitals: \(E_\pi=2(\alpha+2\beta)+4(\alpha+\beta)=6\alpha+8\beta\). Three isolated ethylene π bonds give \(3\cdot2(\alpha+\beta)=6\alpha+6\beta\). The delocalization energy is \(2\beta\), a negative number, so delocalization stabilizes the molecule.

Exercise 9.1Hydrogenation of 1,3-cyclohexadiene releases about 232 kJ/mol. Compare with two cyclohexene units and with benzene. What do the numbers say about conjugation and aromaticity?

Show solution
Two isolated double bonds: \(2\times120=240\) kJ/mol. The diene releases 232, so conjugation gives only about 8 kJ/mol of stabilization. Benzene releases 208 instead of 360, about 150 kJ/mol. Aromatic stabilization is far larger than ordinary conjugation; indeed adding \(\mathrm{H_2}\) to benzene to give the diene is slightly uphill (\(232-208=24\) kJ/mol endothermic).

Exercise 9.2Apply the Hückel formula to cyclobutadiene (\(N=4\), 4 π electrons). Compute its delocalization energy and say why it is not aromatic.

Show solution
Levels: \(\alpha+2\beta\), \(\alpha\) (twice), \(\alpha-2\beta\). Two electrons go into \(\alpha+2\beta\); the remaining two must occupy the degenerate nonbonding pair, one each (a diradical). \(E_\pi=2(\alpha+2\beta)+2\alpha=4\alpha+4\beta\), equal to two ethylenes: zero delocalization energy, and an open shell. With \(4n\) electrons the ring is antiaromatic in this simple sense.

Exercise 9.3Which of these are aromatic by Hückel’s rule: the cyclopentadienyl anion \(\mathrm{C_5H_5^-}\), the tropylium cation \(\mathrm{C_7H_7^+}\), cyclooctatetraene \(\mathrm{C_8H_8}\)?

Show solution
\(\mathrm{C_5H_5^-}\): 6 π electrons, aromatic. \(\mathrm{C_7H_7^+}\): 6 π electrons, aromatic. Planar \(\mathrm{C_8H_8}\) would have 8, a \(4n\) count; the real molecule avoids this by adopting a nonplanar tub shape with localized double bonds, and it reacts like an ordinary polyene.
Lesson 10

Constant valence, multiple bonds, models

For the general reader. Kekulé’s theory rested on a simple rule: each element has a fixed number of bonds. The rule worked beautifully for carbon, but other elements, such as phosphorus and nitrogen, seemed to change their combining power from compound to compound. Kekulé defended the fixed rule all his life. He also built some of the first molecular models, with carbon’s four bonds pointing to the corners of a tetrahedron, though he gave that geometry no physical meaning.

Goals
  • Understand Kekulé’s doctrine of constant valence and its difficulties.
  • Describe double and triple bonds in the language of affinities.
  • See how his lecture models led toward stereochemistry.
Constant valence (Kekulé)

The valence (atomicity) of an element is a fixed, fundamental property of its atoms, like the atomic weight. Compounds that seem to violate it, such as \(\mathrm{PCl_5}\) or \(\mathrm{NH_4Cl}\), are “molecular compounds”, loose associations of valence-satisfied molecules, \(\mathrm{PCl_3\cdot Cl_2}\) and \(\mathrm{NH_3\cdot HCl}\), held together by weaker forces.

The doctrine had support: \(\mathrm{PCl_5}\) vapour dissociates into \(\mathrm{PCl_3}\) and \(\mathrm{Cl_2}\) on heating, and ammonium chloride vapour into ammonia and hydrogen chloride. But many chemists, including Edward Frankland and Wurtz, accepted variable valence, and it prevailed. Sulfur shows valence 2 in \(\mathrm{H_2S}\), 4 in \(\mathrm{SO_2}\) and 6 in \(\mathrm{SF_6}\), a stable gas that does not dissociate. Modern theory distinguishes oxidation state, coordination number and the number of electron-pair bonds; none of these is constant across all compounds of an element.

Multiple bonds

If carbon is always tetravalent, ethylene \(\mathrm{C_2H_4}\) leaves each carbon with one unused affinity. Kekulé’s answer, which became standard, was that the two carbons share two affinities with each other, a double bond. Acetylene \(\mathrm{C_2H_2}\) has a triple bond. Unsaturated compounds add two atoms of bromine or hydrogen per double bond, restoring single bonds: the reaction that benzene notably resists (Lesson 09).

\[ \mathrm{H_2C{=}CH_2} + \mathrm{Br_2} \longrightarrow \mathrm{BrH_2C{-}CH_2Br} \]

Models

For lectures Kekulé used ball-and-wire models in which carbon’s four valences point toward the corners of a tetrahedron, an arrangement that allows single, double and triple links between carbons. Like most chemists of the time, he treated the geometry as a teaching device, not a claim about real space. Jacobus Henricus van ’t Hoff, who worked in his Bonn laboratory, took the tetrahedron literally in 1874, and drawings based on Kekulé-style models illustrated the new stereochemistry.

Exercise 10.1Assign the valence of phosphorus in \(\mathrm{PCl_3}\), \(\mathrm{PCl_5}\) and \(\mathrm{POCl_3}\) under variable valence. How would a believer in constant valence write \(\mathrm{POCl_3}\)?

Show solution
Variable valence: 3, 5 and 5 (three Cl plus a double bond to O). Under constant valence phosphorus is trivalent, so one writes \(\mathrm{Cl_2P{-}O{-}Cl}\), with a P–O–Cl chain. The two formulas predict different chemistry: the second implies a hypochlorite-like O–Cl bond, which \(\mathrm{POCl_3}\) does not show, so the chemistry favours the P=O formula.

Exercise 10.2Kekulé’s tetrahedral models make two carbons joined by a double bond share an edge of their tetrahedra. Show that in this model the four remaining bonds lie in one plane, and deduce that \(\mathrm{CHCl{=}CHCl}\) should exist as two isomers.

Show solution
Put the shared edge on the \(z\)-axis from \((0,0,-1)\) to \((0,0,1)\). In a regular tetrahedron the opposite edge is perpendicular to it and bisected by the same perpendicular plane, so one tetrahedron’s free vertices are \((\sqrt2,\pm1,0)\) and the other’s \((-\sqrt2,\pm1,0)\). All four lie in the plane \(z=0\), and the shared edge forbids rotation about the C–C axis. Placing the two Cl atoms on the same or opposite sides gives cis and trans isomers, as van ’t Hoff predicted for maleic and fumaric acids.
Part III · Life and legacy
Lesson 11

Ghent and Bonn: a school of chemists

At Ghent from 1858 Kekulé taught general, inorganic and organic chemistry in French and set up what has been described as the first chemical teaching and research laboratory in Belgium. Jean-Servais Stas had persuaded him to take the chair. Researchers came to him from abroad: Adolf von Baeyer, Wilhelm Körner, Albert Ladenburg and James Dewar all worked in his laboratory, and Théodore Swarts, who succeeded him at Ghent, was among his pupils. He wrote the first volumes of his Lehrbuch der organischen Chemie there, the first textbook built throughout on tetravalent carbon, and there he worked out the benzene theory.

In 1862 he married Stephanie Drory in Ghent. Their son Stephan was born in 1863, and Stephanie died two days later of puerperal fever. He was elected an associate member of the Royal Academy of Belgium on 15 December 1864.

Bonn

In 1867 Kekulé accepted the chair at Bonn left vacant by August Wilhelm Hofmann’s move to Berlin. The Belgian government accepted his resignation on 21 September 1867. The new chemical institute near Poppelsdorf Palace, planned for Hofmann, was occupied on 11 May 1868, and it became one of the great teaching laboratories of Germany. Kekulé declined a call to succeed Liebig at Munich, and the Prussian government extended his building in return. He served as rector of the university in 1877–78. In 1876 he married Luise Högel, with whom he had three more children.

His students and junior colleagues at Bonn included Emil Fischer, who began there before following Baeyer to Strasbourg; Jacobus Henricus van ’t Hoff, who spent 1872–73 in his laboratory; Otto Wallach, Ludwig Claisen, Theodor Zincke and Richard Anschütz, who later succeeded to his chair and wrote his biography. Three of the first five Nobel Prizes in Chemistry went to men who had worked under him: van ’t Hoff (1901), Fischer (1902) and Baeyer (1905). Wallach won in 1910. After an attack of measles weakened his health, Kekulé did less laboratory work and turned his attention to the later volumes of the Lehrbuch.

DiscussionKekulé’s laboratory produced more Nobel laureates than his own research would suggest. What features of a research school (theory, problems, independence, laboratory resources) make a teacher’s influence outlast his discoveries?

Lesson 12

Dreams, priority and legacy

On 11 March 1890 the German Chemical Society held a celebration in Berlin for the 25th anniversary of the benzene theory, the Benzolfest. In his speech, printed in the Berichte, Kekulé described two reveries. One was the dance of atoms on the London omnibus (Lesson 02). The other came in Ghent, as he dozed by the fire while writing his textbook: chains of atoms twisting like snakes, until one seized its own tail. He woke, he said, and spent the night working out the consequences. He closed with advice to learn to dream, and then to test the dreams before the waking mind.

The snake story has been endlessly retold and sometimes doubted. Historians note that it was first told a quarter of a century after the event, in a speech partly designed to answer rival priority claims. A parody of 1886, in a mock journal of the “Thirsty Chemical Society”, had already drawn benzene as six monkeys holding each other’s tails. Whether or not the dream happened, the ring hypothesis rested on years of work on formulas, isomer counts and the type theory.

Priority

The structure theory had several authors. Couper published the self-linking of carbon a month after Kekulé and drew bonds as lines. Butlerov made structure the organizing principle of a textbook in the 1860s. Loschmidt drew cyclic benzenes in 1861. Kekulé was sensitive about these claims. His lasting contribution was to turn the scattered ideas into a programme: a consistent valence theory, a textbook built on it, and predictions of isomer numbers that experiments confirmed.

Honours and death

The Royal Society awarded him the Copley Medal in 1885. In 1893 he received the Prussian order Pour le Mérite for Sciences and Arts. In 1895 Kaiser Wilhelm II recognized an old Bohemian title in his family, and he took the name Kekule von Stradonitz, dropping the accent. He died in Bonn on 13 July 1896, aged 66, and was buried in an honorary grave in the Poppelsdorf cemetery.

Legacy

  • Structural formulas: the tetravalent carbon and the carbon chain underlie every structure drawn in organic chemistry.
  • Aromatic chemistry: the benzene ring organized the chemistry of dyes, drugs and explosives, and the German chemical industry grew on it.
  • Teaching: his laboratories in Ghent and Bonn trained a generation, including several Nobel laureates.
  • Theory: the problem of benzene’s equivalent bonds led directly to resonance and molecular-orbital theory, and his ball-and-wire lecture models influenced van ’t Hoff’s tetrahedral carbon.

Final projectChoose one prediction of the structure theory (the number of propyl alcohols, the three disubstituted benzenes, or the single ortho isomer). Write a two-page account that states the prediction, shows how it follows from Kekulé’s assumptions, and describes how it was tested.

Reference

Connections

People linked to August Kekulé across this collection. A name without a link has no page here yet. See August Kekulé in the network of all 337 lives →

Teachers and advisors

Students

  • Jacobus Henricus van 't Hoff 1872-1873
  • Adolf von Baeyer 1856-1860
  • Albert Ladenburg
  • Emil Fischer 1871-1872
  • James Dewar
  • Ludwig Claisen
  • Otto Wallach
  • Richard Anschütz
  • Wilhelm Körner

Influenced by

  • Alexander Williamson 1853-1855
  • Charles Gerhardt 1851-1852
  • Jean-Baptiste Dumas 1851-1852

Colleagues and collaborators

Rivals

  • Aleksandr Butlerov
  • Archibald Scott Couper
  • Josef Loschmidt

Family

  • Stephan Kekule von Stradonitz

Also mentioned in this life

Fields

Reference

Sources and further reading

Biography

  1. August Kekulé, Wikipedia; and the German article August Kekulé.
  2. Science History Institute, August Kekulé and Archibald Scott Couper.
  3. Université de Gand, Biographie nationale entry, Kekulé (Friedrich-August).
  4. Kekulé, Friedrich August, Encyclopedia.com.
  5. R. Anschütz, August Kekulé, 2 vols., Verlag Chemie, Berlin, 1929.
  6. A. J. Rocke, Image and Reality: Kekulé, Kopp, and the Scientific Imagination, University of Chicago Press, 2010.
  7. O. T. Benfey, August Kekulé and the birth of the structural theory of organic chemistry in 1858, J. Chem. Educ. 35 (1958) 21.
  8. Karlsruhe Congress, Wikipedia.

Chemistry

  1. A. Kekulé, Ueber die Constitution und die Metamorphosen der chemischen Verbindungen und über die chemische Natur des Kohlenstoffs, Annalen der Chemie und Pharmacie 106 (1858) 129–159.
  2. A. S. Couper, Sur une nouvelle théorie chimique, Annales de chimie et de physique 53 (1858).
  3. A. Kekulé, Sur la constitution des substances aromatiques, Bulletin de la Société Chimique de Paris 3 (1865) 98–110.
  4. A. Kekulé, Untersuchungen über aromatische Verbindungen, Annalen der Chemie und Pharmacie 137 (1866) 129–196.
  5. A. Kekulé, Ueber einige Condensationsproducte des Aldehyds, Annalen der Chemie und Pharmacie 162 (1872) 309–320.
  6. A. Kekulé, Lehrbuch der organischen Chemie, Enke, Erlangen and Stuttgart, 1859–1887.
  7. A. Kekulé, Benzolfest: Rede, Berichte der Deutschen Chemischen Gesellschaft 23 (1890) 1302–1311.
  8. P. J. Ramberg, Pragmatism, belief, and reduction: stereoformulas and atomic models in early stereochemistry, HYLE 6 (2000).
  9. E. Hückel, Quantentheoretische Beiträge zum Benzolproblem, Z. Physik 70 (1931) 204–286.
  10. L. Pauling and G. W. Wheland, The nature of the chemical bond. V, J. Chem. Phys. 1 (1933) 362–374.