Jacobus Henricus van ’t Hoff

How to use this course

Jacobus Henricus van ’t Hoff founded two sciences. In 1874, as a student, he proposed that the four bonds of carbon point to the corners of a tetrahedron, which explained why some compounds rotate polarized light and began stereochemistry. Ten years later he turned to the rates and equilibria of reactions and to dilute solutions, and helped create physical chemistry. He received the first Nobel Prize in Chemistry in 1901.

Each technical lesson opens with a paragraph for the general reader, then gives the key results in boxes, derivations, and exercises with folded solutions. Lessons 04–05 cover stereochemistry (1874–75), Lessons 06–07 kinetics and equilibrium (1884), Lessons 08–09 dilute solutions (1885–87), and Lesson 10 the salt-deposit studies of his Berlin years.

Timeline

Rotterdam and Delft, 1852–1871

Jacobus Henricus van ’t Hoff was born in Rotterdam on 30 August 1852, the third of seven children. His father, also named Jacobus Henricus, was a physician with literary interests; his mother was Alida Kolff. As a schoolboy at the Rotterdam Hogere Burgerschool, a modern secondary school with a science curriculum, he carried out chemical experiments of his own and read widely, especially poetry. Lord Byron was his idol, and he wrote verse throughout his life.

His parents doubted that pure science offered a living and steered him toward a practical career. In September 1869 he entered the Polytechnic School at Delft to train as a chemical technologist. Delft gave him a solid grounding in chemistry and physics. He passed the final examination on 8 July 1871 with a diploma as a chemical technologist, but he had already decided that he wanted a life in research, not in industry.

Van ’t Hoff combined a taste for mathematics with a poet’s imagination. He hoped that chemistry could one day be made as exact as mechanics. That ambition, unusual among chemists of his time, links his early stereochemistry to his later physical chemistry, and it explains why he went to Leiden next to study mathematics.

Leiden, Bonn, Paris, 1871–1874

From Delft he went to the University of Leiden in 1871, where he studied mainly mathematics and passed the candidate examination in 1872. He then spent 1872–73 in Bonn in the laboratory of August Kekulé, the founder of structural organic chemistry. Kekulé used lecture models with carbon’s four valences pointing toward the corners of a tetrahedron, though he regarded the geometry as a teaching convenience.

In 1873 he moved to Paris to work with Adolphe Wurtz, whose laboratory was the centre of the atomic theory in France. He followed much of Wurtz’s teaching programme for 1873–74. Another young man in the same laboratory was the Alsatian Joseph Achille Le Bel. There is no evidence that the two discussed the problem that both were about to solve.

The problem of optical activity

Since the work of Jean-Baptiste Biot early in the century, chemists had known that some organic compounds, in solution, rotate the plane of polarized light. In 1848 Louis Pasteur separated crystals of sodium ammonium racemate into two mirror-image forms whose solutions rotated light in opposite directions, and he suggested that the molecules themselves were mirror images. In 1873 Johannes Wislicenus showed that the lactic acid of muscle and the lactic acid of fermentation have the same structural formula but different optical properties, and he concluded that the difference must lie in the arrangement of atoms in space. Structural formulas, which recorded only which atom was bonded to which, could not express this.

Utrecht and the pamphlet, 1874–1877

Returning to the Netherlands in 1874, van ’t Hoff published on 3 September a short pamphlet in Dutch, a proposal to extend the structural formulas now used in chemistry into space. It argued that the four valences of carbon point to the corners of a regular tetrahedron with the carbon atom at its centre. A carbon bearing four different groups, which he called an asymmetric carbon atom, then exists in two mirror-image forms, and every compound known to be optically active in solution contains such an atom (Lesson 04).

Later in 1874 he received his doctorate at Utrecht under Eduard Mulder, with a conventional thesis on cyanoacetic and malonic acids. The same year Le Bel, in Paris, published in the Bulletin de la Société Chimique an independent paper reaching the same conclusion about optical activity by an argument from molecular symmetry. Van ’t Hoff’s version was more concrete, with a definite tetrahedral geometry; Le Bel’s was more general and did not require the tetrahedron to be rigid.

The Dutch pamphlet attracted little notice. In May 1875 van ’t Hoff published an expanded French version, La chimie dans l’espace, and in 1877 a German translation appeared with a foreword by Wislicenus, who welcomed it. Finding no academic post at first, in 1876 he became lecturer in physics at the Veterinary School in Utrecht.

Kolbe’s attack

In 1877 Hermann Kolbe of Leipzig, editor of the Journal für praktische Chemie, published an essay titled “Signs of the times” deploring speculative chemistry. He singled out the young lecturer at the Utrecht veterinary school, who in his view had no taste for exact research and preferred to mount Pegasus and fly to the chemical Parnassus. The attack backfired. It made the theory widely known, and within a year van ’t Hoff had a post at the new University of Amsterdam. His inaugural lecture there in 1878 was a defence of imagination in science.

The tetrahedral carbon atom

For the general reader. Your left and right hands are mirror images, but you cannot turn one into the other by rotating it. Van ’t Hoff saw that a carbon atom with four different neighbours at the corners of a tetrahedron is “handed” in the same way. Its two forms have identical connections and almost identical properties, but they rotate polarized light in opposite directions and can behave differently in living systems.

Why a tetrahedron?

The tetrahedron was not the only geometry available. Van ’t Hoff argued against a planar square carbon, with the four groups at the corners of a square, by counting isomers. A square predicts two isomers of \(\mathrm{CH_2X_2}\) (adjacent and opposite) and no optical activity for \(\mathrm{CHXYZ}\), since the plane of the square is a mirror plane. Only one \(\mathrm{CH_2Cl_2}\) is known, and \(\mathrm{CHXYZ}\) compounds can be optically active. The regular tetrahedron gives one \(\mathrm{CH_2X_2}\), one \(\mathrm{CH_3X}\), and two forms of \(\mathrm{CXYZW}\), exactly as observed.

Chirality and symmetry

In modern language, a molecule is chiral if and only if it has no improper rotation axis \(S_n\), that is, no mirror plane (\(S_1\)), no inversion centre (\(S_2\)) and no higher \(S_{2k}\). Chirality, not the presence of an asymmetric carbon, is the real criterion. Van ’t Hoff already saw this: in 1875 he predicted that allenes \(\mathrm{abC{=}C{=}Cab}\), which contain no asymmetric carbon, should exist as mirror-image pairs because the two terminal planes are perpendicular. The prediction was confirmed in 1935.

Geometry

Place carbon at the origin and the four bonds along \((1,1,1)\), \((1,-1,-1)\), \((-1,1,-1)\), \((-1,-1,1)\), alternate corners of a cube. The angle \(\theta\) between any two satisfies

Counting stereoisomers

For the general reader. Once carbon has a shape, the number of possible molecules for a given formula goes up. Van ’t Hoff gave rules for counting them. A molecule with several handed carbon atoms has many forms, some of which cancel their own handedness. Double bonds, which hold their neighbours rigidly, create a different kind of isomer, explaining a long-standing puzzle about two acids with the same formula.

For tartaric acid, \(\mathrm{HOOC{-}CH(OH){-}CH(OH){-}COOH}\), \(n=2\) but the two halves are identical. The configurations \((R,R)\) and \((S,S)\) are enantiomers, the dextro- and laevo-tartaric acids. The configurations \((R,S)\) and \((S,R)\) are the same molecule, which has an internal mirror plane: this is meso-tartaric acid, optically inactive. Racemic acid, Pasteur’s substance, is a 1:1 mixture of the two active forms. Three stereoisomers in all, as the model predicts.

Double bonds

In van ’t Hoff’s model two carbons joined by a double bond share an edge of their tetrahedra. The four remaining bonds then lie in one plane and rotation is blocked. A compound \(\mathrm{abC{=}Cab}\) exists as two isomers, with like groups on the same side or on opposite sides, now called cis and trans (or Z and E). Van ’t Hoff applied this to maleic and fumaric acids, both \(\mathrm{HOOC{-}CH{=}CH{-}COOH}\). Maleic acid, which readily loses water to form a cyclic anhydride, must be the cis isomer, with its two carboxyl groups close together.

Chemical kinetics: the Études of 1884

For the general reader. Some reactions are over in a flash, others take years. In his Études de dynamique chimique of 1884 van ’t Hoff set out how to measure and describe reaction speed. He classified reactions by how their rates depend on concentrations, gave methods to find that dependence from experiment, and studied how warming speeds reactions up.

The differential method

If rates \(r_1,r_2\) are measured at concentrations \(c_1,c_2\), then \(r_1/r_2=(c_1/c_2)^n\), so

Van ’t Hoff applied this to his own measurements and to older data, such as the decomposition of arsine and the reaction of chloroacetic acid with water. He also noticed that the order found in experiment often differs from the number of molecules in the overall equation, a sign that many reactions proceed in steps.

Temperature

Van ’t Hoff observed that, near room temperature, many reaction rates roughly double or triple for every 10 °C rise. By analogy with his equation for the temperature dependence of equilibrium constants (Lesson 07), he proposed that \(\dfrac{d\ln k}{dT}=\dfrac{A}{T^2}\) for a constant \(A\). In 1889 Svante Arrhenius interpreted \(A\) as \(E_a/R\), with \(E_a\) an activation energy, giving the Arrhenius equation \(k=A_0\,e^{-E_a/RT}\).

Equilibrium and temperature

For the general reader. Many reactions do not go to completion. They stop at an equilibrium where forward and reverse reactions balance. Van ’t Hoff showed how the position of that balance shifts when the temperature changes, with a formula that uses only the heat given out or absorbed by the reaction. It explains, for example, why heat favours reactions that absorb heat.

Dynamic equilibrium

For \(\mathrm{A}+\mathrm{B}\rightleftharpoons\mathrm{C}+\mathrm{D}\), with forward rate \(k_1[\mathrm A][\mathrm B]\) and reverse rate \(k_{-1}[\mathrm C][\mathrm D]\), equilibrium means equal rates, so \(K=\dfrac{[\mathrm C][\mathrm D]}{[\mathrm A][\mathrm B]}=\dfrac{k_1}{k_{-1}}\). This is the law of mass action of Cato Guldberg and Peter Waage (1864), which van ’t Hoff rederived and used in the Études.

Derivation. In modern form, \(\Delta_rG^\circ=-RT\ln K\), so \(\ln K=-\Delta_rG^\circ/RT\). The Gibbs–Helmholtz equation gives \(\dfrac{d}{dT}\left(\dfrac{\Delta_rG^\circ}{T}\right)=-\dfrac{\Delta_rH^\circ}{T^2}\). Dividing by \(-R\) yields the result. Van ’t Hoff obtained it by applying the second law of thermodynamics to a reversible cycle, before the Gibbs energy was in common use among chemists.

Van ’t Hoff also identified the affinity of a reaction with the maximum work obtainable from it, which for ideal systems is \(RT\ln(K/Q)\), where \(Q\) is the reaction quotient. This is the quantity now written \(-\Delta_rG\), and it settled a long confusion between affinity and heat of reaction.

Osmotic pressure and the gas analogy

For the general reader. If a sugar solution is separated from pure water by a membrane that lets water through but not sugar, water flows into the solution until a pressure builds up to stop it. This is osmotic pressure. Van ’t Hoff found that it follows the same law as the pressure of a gas: dissolved molecules in a dilute solution push like gas molecules in a container of the same volume.

The data

In 1877 the plant physiologist Wilhelm Pfeffer measured osmotic pressures using porous porcelain cells lined with a precipitated membrane of copper ferrocyanide, which passes water but holds back sugar. He found that the pressure was proportional to concentration at fixed temperature and rose with temperature. The Dutch botanist Hugo de Vries, who studied osmosis in plant cells, drew van ’t Hoff’s attention to these results, and van ’t Hoff saw in them the laws of Boyle and Gay-Lussac.

Derivation

Let the solvent A have mole fraction \(x_A=1-x_B\). In an ideal dilute solution its chemical potential is \(\mu_A=\mu_A^*(p)+RT\ln x_A\). At equilibrium across the membrane the solvent’s chemical potential must be the same on both sides, so the solution side needs an extra pressure \(\Pi\):

using \(\partial\mu^*/\partial p=V_A\) (the molar volume of solvent) and \(\ln(1-x_B)\approx-x_B\). Hence \(\Pi V_A=RT\,x_B\approx RT\,n_B/n_A\), and since \(n_AV_A\approx V\), \(\Pi=n_BRT/V\). Van ’t Hoff’s own argument, published in the first volume of the Zeitschrift für physikalische Chemie in 1887, used reversible cycles with semipermeable pistons in the same spirit.

Colligative properties and electrolytes

For the general reader. Dissolving anything in water lowers its freezing point, raises its boiling point and produces osmotic pressure. These effects depend on how many particles are dissolved, not on what they are. Salts gave effects that were too large, sometimes nearly double. Van ’t Hoff recorded the excess as a factor \(i\). Arrhenius explained it: salts split into ions in water.

Derivation. At the freezing point the pure solid and the solvent in solution have equal chemical potentials: \(\mu_A^{s}(T)=\mu_A^{*,l}(T)+RT\ln x_A\). So \(\ln x_A=-\Delta_{\mathrm{fus}}G(T)/RT\). Differentiating with Gibbs–Helmholtz and integrating from the pure freezing point gives \(\ln x_A=-\dfrac{\Delta_{\mathrm{fus}}H}{R}\left(\dfrac1T-\dfrac1{T_f}\right)\). For small \(x_B\), \(-\ln x_A\approx x_B\approx bM_A\). With \(T=T_f-\Delta T_f\), \(\dfrac1T-\dfrac1{T_f}\approx\dfrac{\Delta T_f}{T_f^2}\), which gives \(x_B=\dfrac{\Delta_{\mathrm{fus}}H\,\Delta T_f}{RT_f^2}\), which rearranges to the boxed formula. François-Marie Raoult had found the law experimentally; van ’t Hoff gave its thermodynamic basis.

The factor \(i\)

For salts, acids and bases in water, van ’t Hoff found that osmotic pressure, freezing-point depression and vapour-pressure lowering were all larger than predicted, by the same factor in each case. He wrote \(\Pi=icRT\), with \(i\) close to 2 for dilute sodium chloride. In 1887 Arrhenius proposed that electrolytes dissociate partly into ions. If a fraction \(\alpha\) of the solute splits into \(\nu\) ions, the number of particles per formula unit is

Arrhenius compared \(\alpha\) found this way with \(\alpha\) from electrical conductivity and found agreement for many electrolytes. Van ’t Hoff’s law and Arrhenius’s theory supported each other; together with Wilhelm Ostwald’s work on affinity and conductivity, they formed the programme of the “ionists” (Lesson 11).

Salt deposits and phase equilibria

For the general reader. Thick layers of salts lie under northern Germany, left by evaporating ancient seas. The mine at Stassfurt supplied potassium salts to much of the world. In Berlin van ’t Hoff spent his last fifteen years working out, with many collaborators, the order in which these salts crystallize as seawater dries out and at what temperatures one salt turns into another. It was a large application of equilibrium thermodynamics to geology.

Josiah Willard Gibbs stated the rule in 1876; Hendrik Willem Bakhuis Roozeboom, van ’t Hoff’s colleague and successor at Amsterdam, made it the basis of experimental work on heterogeneous equilibria. Van ’t Hoff’s salt work was an exploration of multi-component phase diagrams: the oceanic system contains water and the chlorides and sulfates of sodium, potassium and magnesium, and gives minerals such as carnallite \(\mathrm{KMgCl_3\cdot6H_2O}\), kainite and polyhalite.

Transition points

Glauber’s salt, \(\mathrm{Na_2SO_4\cdot10H_2O}\), is stable in contact with its saturated solution only below about 32.4 °C. Above that temperature it converts to anhydrous \(\mathrm{Na_2SO_4}\) and solution. At the transition point three condensed phases and vapour coexist in a two-component system, so at fixed pressure \(F=2-3+1=0\): the temperature is fixed. Van ’t Hoff and his collaborators measured many such transition points. In the Stassfurt work, measured transition temperatures told him the range of temperatures under which the observed mineral layers could have formed.

Amsterdam and the ionists

Van ’t Hoff became lecturer at the University of Amsterdam in 1877 and in 1878 professor of chemistry, mineralogy and geology, a chair he held for eighteen years. In 1878 he married Johanna Francina Mees; they had two daughters and two sons. In his first years he published Ansichten über die organische Chemie (1878–81), an attempt to correlate properties of organic compounds with structure. His nomination to the Royal Netherlands Academy was rejected in 1880, then accepted in 1885.

From about 1880 his interests moved to physical problems: the rates and equilibria of reactions and the behaviour of dilute solutions. The Études de dynamique chimique (1884) and the papers on dilute solutions of 1885–87 established his reputation. In 1887 Leipzig offered him a chair; he declined after the city of Amsterdam agreed to build him a new laboratory.

The ionists

In 1887 Wilhelm Ostwald founded the Zeitschrift für physikalische Chemie with van ’t Hoff as co-editor. Its first volume contained van ’t Hoff’s paper on osmotic pressure and Svante Arrhenius’s paper on electrolytic dissociation. The three men, who promoted the new physical chemistry together against considerable scepticism, were nicknamed the ionists. Among van ’t Hoff’s students at Amsterdam was Ernst Cohen, his assistant from 1893 and later his biographer.

Van ’t Hoff disliked routine teaching, especially elementary courses for medical students, and by 1895 he wanted more time for research.

Berlin, the Nobel Prize, legacy

In 1896 the Prussian Academy of Sciences offered van ’t Hoff a research professorship, with an honorary chair at the University of Berlin and only light lecturing duties. He moved to Berlin in April 1896 and stayed until his death. There he led the long study of the Stassfurt salt deposits, published in two volumes as Zur Bildung der ozeanischen Salzablagerungen (1905–09), and lectured on physical chemistry and its applications. Frederick Donnan, later known for membrane equilibria, worked with him in Berlin.

On 10 December 1901 he received the first Nobel Prize in Chemistry, for the discovery of “the laws of chemical dynamics and osmotic pressure in solutions”. The same year he lectured at the University of Chicago and received honorary doctorates from Harvard and Yale. Other honours included the Davy Medal of the Royal Society (1893, shared with Le Bel), Foreign Membership of the Royal Society (1897), the Paris Académie des Sciences (1905) and the Helmholtz Medal of the Prussian Academy (1911).

He died of tuberculosis in Steglitz, near Berlin, on 1 March 1911, aged 58.

Legacy

• Stereochemistry: the tetrahedral carbon underlies the configuration of sugars, amino acids and drugs, and the chemistry of chirality in biology and pharmacology.
• Kinetics and equilibrium: reaction orders, the van ’t Hoff equation and the link between affinity and maximum work are standard in every physical chemistry course.
• Solutions: the osmotic law and the factor \(i\) are used daily in biology, medicine and membrane technology, and they prepared the ground for the ionic theory.
• Physical chemistry as a discipline: with Ostwald and Arrhenius he gave the field a journal, a programme and a generation of students.

Sources and further reading

Biography

1. Nobel Prize, Jacobus H. van ’t Hoff, Biographical.
2. Jacobus Henricus van ’t Hoff, Wikipedia.
3. Neue Deutsche Biographie, Hoff, Jacobus Henricus van ’t.
4. Science History Institute, Jacobus Henricus van ’t Hoff.
5. E. Cohen, Jacobus Henricus van ’t Hoff: sein Leben und Wirken, Akademische Verlagsgesellschaft, Leipzig, 1912.
6. H. A. M. Snelders, Van ’t Hoff, Jacobus Henricus, Dictionary of Scientific Biography, vol. 13, Scribner, 1976.

Chemistry

1. J. H. van ’t Hoff, Voorstel tot uitbreiding der tegenwoordig in de scheikunde gebruikte structuur-formules in de ruimte, Utrecht, 1874.
2. J. A. Le Bel, Sur les relations qui existent entre les formules atomiques des corps organiques et le pouvoir rotatoire de leurs dissolutions, Bull. Soc. Chim. Paris 22 (1874) 337–347.
3. J. H. van ’t Hoff, La chimie dans l’espace, Bazendijk, Rotterdam, 1875.
4. H. Kolbe, Zeichen der Zeit, J. prakt. Chem. 15 (1877) 473.
5. J. H. van ’t Hoff, Études de dynamique chimique, Muller, Amsterdam, 1884.
6. J. H. van ’t Hoff, Die Rolle des osmotischen Druckes in der Analogie zwischen Lösungen und Gasen, Z. phys. Chem. 1 (1887) 481–508. English translation.
7. P. J. Ramberg, Pragmatism, belief, and reduction: stereoformulas and atomic models in early stereochemistry, HYLE 6 (2000).
8. Van ’t Hoff equation, Wikipedia.
9. J. H. van ’t Hoff, Zur Bildung der ozeanischen Salzablagerungen, 2 vols., Vieweg, Braunschweig, 1905–1909.