Dmitri Mendeleev

How to use this course

Every chemistry classroom has Mendeleev’s table on the wall, usually in a form he would not recognize. This course explains what he actually did in 1869–1871, why it convinced the chemical world, which parts of it were wrong, and how twentieth-century physics explained the pattern he found. It also covers his work on gases and solutions, and the long public career of a scientist who advised the Russian state on oil, gunpowder, tariffs and measures.

Russia used the Julian calendar until 1918. Dates are given in the Gregorian (New Style, N.S.) calendar unless marked O.S.; in the nineteenth century O.S. dates run 12 days behind. Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions.

Timeline

Tobolsk, 1834–1849

Dmitri Ivanovich Mendeleev was born on 8 February 1834 (27 January O.S.) in Verkhnie Aremzyani, a village near Tobolsk in western Siberia. He was the youngest child of a large family; sources disagree on how many, with figures between fourteen and seventeen. His father, Ivan Pavlovich Mendeleev, was director of the Tobolsk gymnasium until he lost his sight. His mother, Maria Dmitrievna Kornilieva, ran a small glass factory to support the household.

Ivan Pavlovich died in 1847, when Dmitri was thirteen, and the glass works burned soon afterwards. The boy attended the Tobolsk gymnasium, where his father had taught.

In 1849 he finished school. His mother, determined that her last son should have a university education, took him and a sister to Moscow, a journey of more than two thousand kilometres. Moscow University would not admit him, and the family moved on to St Petersburg.

St Petersburg, Crimea, Odessa, 1850–1859

In 1850 Mendeleev entered the Main Pedagogical Institute in St Petersburg, which trained gymnasium teachers and offered a solid course in mathematics and natural science. His mother died the same year, and a sister soon after, both of tuberculosis. He himself fell ill with the disease. He nevertheless graduated in 1855 at the top of his class, with a gold medal.

For the sake of his health he went south. He taught at the gymnasium in Simferopol in the Crimea, where the Crimean War was then being fought, and moved after a short time to the lyceum in Odessa for the school year 1855–56. The warm climate helped. In the autumn of 1856 he returned to St Petersburg, defended a master’s thesis, and obtained the right to lecture at the university as a privatdocent.

His early research concerned the volumes occupied by substances, isomorphism (the tendency of chemically similar compounds to form similar crystals) and the relation between composition and physical properties. The common thread, which runs through his whole career, is the search for numerical regularities that link a substance’s physical behaviour to its chemical nature.

Heidelberg, Karlsruhe and the textbook, 1859–1868

In 1859 the government sent Mendeleev abroad for two years. He settled in Heidelberg, where Robert Bunsen and Gustav Kirchhoff had just founded spectral analysis. Rather than work in Bunsen’s crowded laboratory, he set up a small private one in his lodgings and studied capillarity and the cohesion of liquids. From this work came his idea of an “absolute boiling point”, the temperature at which cohesion vanishes and a liquid can no longer exist (Lesson 09).

In September 1860 he attended the first international congress of chemists at Karlsruhe, called to settle the confusion over atomic weights. There Stanislao Cannizzaro argued that Avogadro’s hypothesis, applied consistently, fixed a single set of atomic weights. Mendeleev later said that this was the decisive moment for his own thinking about the elements. Lesson 04 explains why.

Back in St Petersburg in 1861, short of money, he wrote Organic Chemistry, the first Russian textbook on the subject, in a few months. It won the Demidov Prize. In 1862 he married Feozva Nikitichna Leshcheva; they had a son, Vladimir, and a daughter, Olga. He became professor at the Technological Institute in 1864, and in 1865 he defended his doctoral dissertation on the combinations of alcohol with water (Lesson 10) and was appointed professor of chemistry at St Petersburg University. In 1868 he helped found the Russian Chemical Society.

The same year he began a new textbook for his inorganic chemistry course, Principles of Chemistry, published in parts in 1868–1871. He needed an order in which to present the elements. Searching for that order led him to the periodic law.

Atomic weights after Karlsruhe

For the general reader. To arrange the elements by weight you must first know their weights. Before 1860 chemists could not agree: some wrote water as HO and gave oxygen the weight 8, others wrote H₂O and gave it 16. The same doubt affected half the elements. Cannizzaro showed at Karlsruhe how to settle it, and Mendeleev’s table would have been impossible without his method.

The problem

Chemical analysis gives the equivalent weight \(E\) of an element: the mass that combines with 8 g of oxygen (or 1 g of hydrogen). The atomic weight is \(A=vE\), where \(v\) is the valence, and analysis alone cannot tell you \(v\). Indium, for example, has \(E\approx37.8\). Before 1870 it was taken to be divalent with \(A\approx75.6\).

The method needs volatile compounds. For metals, which rarely have them, chemists used a second rule.

Dulong–Petit gives only a rough value of \(A\), but that is enough to choose the right multiple of the exact equivalent weight. Light, hard elements such as beryllium, boron, carbon and silicon fall well below \(3R\) at room temperature, a quantum effect explained by Albert Einstein in 1907, so the rule must be used with care.

The periodic law, 1869–1871

For the general reader. List the elements in order of atomic weight and their properties come back at regular intervals: a reactive metal, then a less reactive one, and so on until a reactive non-metal, and then the cycle starts again. Several chemists had noticed fragments of this pattern. Mendeleev stated it as a law of nature, applied it to every element, and trusted it enough to say where the data were wrong.

Before Mendeleev

Johann Wolfgang Döbereiner noticed in 1829 that some elements come in triads, such as chlorine, bromine and iodine, where the middle weight is close to the mean of the outer two. In 1862 Alexandre-Émile Béguyer de Chancourtois wound the elements around a cylinder, his “telluric helix”, so that similar elements lined up vertically. In 1864–65 John Newlands arranged the known elements in order and compared the recurrence at every eighth element to the musical octave; the Chemical Society declined to publish his paper. Lothar Meyer in 1864 grouped 28 elements by valence, and in a paper published early in 1870 gave a table of 55 elements with a curve of atomic volumes.

The 1869 table

Mendeleev completed his first table on 1 March 1869 (17 February O.S.). It placed 63 elements in order of atomic weight, in columns, so that similar elements fell in rows. Mendeleev was absent from the Russian Chemical Society meeting of 18 March (6 March O.S.); Nikolai Menshutkin read the paper for him. A short German abstract carried it to western Europe. The well-known story that the arrangement came to him in a dream rests on a single later anecdote. The careful drafts he left show steady work with lists of elements and their properties.

In 1871 he published the full theory in the Journal of the Russian Chemical Society, and soon after in a long German paper, with the elements in eight groups. The group number fixes the highest valence toward oxygen, and for groups IV–VII also the valence toward hydrogen:

The oxygen valence in group \(g\) is \(g\), the hydrogen valence is \(8-g\), and their sum is 8. Each long period was written in two series, so that copper sits under the alkali metals in group I and zinc under magnesium in group II, with group VIII holding the triads Fe–Co–Ni, Ru–Rh–Pd and Os–Ir–Pt.

What made it a law

Three features set Mendeleev’s work apart. He included all known elements, not a selection. He placed elements by their chemistry when this disagreed with the accepted weight, and said the weight must be wrong. And he left gaps, describing in detail the elements that should fill them. Lessons 06 and 07 show how these choices were tested.

Correcting the data: interpolation in the table

For the general reader. A table of patterns lets you read across and down. If an element’s neighbours on all four sides are known, its properties should lie between theirs. Mendeleev used this idea in both directions: to correct bad atomic weights of known elements, and to describe unknown ones.

This is a discrete form of the statement that \(P\) is approximately harmonic on the grid of the table: its value at a point is the mean of its four neighbours. It works well where properties change gradually and fails at the ends of periods, where they jump.

Corrections

Beryllium. Its equivalent weight is about 4.7. Many chemists took it to be trivalent, like aluminium, so that \(A\approx14\), which would place it near nitrogen where no room existed. Mendeleev argued for valence 2 and \(A\approx9.4\), between lithium and boron, with an oxide BeO resembling magnesia. Later vapour-density measurements of beryllium chloride confirmed him.

Indium and uranium. Indium went from 75.6 to 113 and uranium from about 120 to 240 (Exercise 4.2). In each case the table forced a new valence and the heat capacity confirmed it. Mendeleev measured the specific heats of indium, cerium and uranium himself.

Tellurium. The accepted weights put tellurium (about 128) above iodine (127). Mendeleev placed tellurium in group VI with sulfur and selenium regardless, and predicted that its true weight would turn out to be lower, around 125. Here he was wrong about the weight and right about the place. Lesson 08 explains the paradox.

Gallium, scandium, germanium

For the general reader. A theory that only arranges known facts can always be adjusted to fit them. Mendeleev did something riskier. He described three missing elements in enough detail that anyone who found one could check him. All three were found within fifteen years, and the measured properties matched.

The predictions of 1871

In the 1871 paper Mendeleev named the gaps with the Sanskrit numeral eka (“one”): eka-boron below boron, eka-aluminium below aluminium, eka-silicon below silicon. He gave each an atomic weight, density, oxide and chloride.

Lecoq’s first density was 4.7. Mendeleev wrote that the sample was probably impure and the value should be near 6. After purifying the metal, Lecoq found 5.9. The episode impressed chemists more than any agreement could have, since the theory had corrected a measurement.

Mendeleev also left places for elements below manganese (found as technetium in 1937 and rhenium in the 1920s), below caesium (francium) and between thorium and uranium. Not every prediction succeeded. He expected several elements lighter than hydrogen, including a candidate for the luminiferous ether, and none exists.

Inversions, atomic number and the shell structure

For the general reader. Mendeleev ordered the elements by weight, and in a few places chemistry forced him to break that order. He thought the weights were wrong. The real explanation came after his death: the true ordering number is the electric charge of the nucleus, and the pattern of periods comes from the quantum mechanics of electrons.

Inversions

Modern atomic weights give three pairs out of order relative to chemistry: argon (39.95) before potassium (39.10), cobalt (58.93) before nickel (58.69), and tellurium (127.60) before iodine (126.90). Atomic weight is an average over isotopes. A slightly larger nuclear charge can go with a lighter average mass if the element’s abundant isotopes have fewer neutrons.

Moseley’s law

In 1913 Antonius van den Broek proposed that an element’s position equals its nuclear charge \(Z\). The same year Henry Moseley measured characteristic X-ray lines across the table and found that the square root of the frequency is linear in position.

Derivation. In the Bohr model an electron in shell \(n\) of a nucleus of charge \(Z\) has energy \(-hR_\infty c\,Z^2/n^2\). A K\(\alpha\) photon is emitted when an electron drops from \(n=2\) to a vacancy in \(n=1\). The remaining \(1s\) electron screens one unit of charge, so the effective charge is about \(Z-1\), and \(h\nu=hR_\infty c(Z-1)^2(1-\tfrac14)\). Moseley’s data placed cobalt (27) before nickel (28), and tellurium (52) before iodine (53), as Mendeleev’s chemistry had demanded, and showed exactly which gaps remained.

Why the periods have the lengths they do

An orbital is labelled by \(n\ge1\) and \(0\le l\le n-1\), and holds \(2(2l+1)\) electrons. In many-electron atoms, subshells fill approximately in order of increasing \(n+l\), and for equal \(n+l\) in order of increasing \(n\) (the Madelung rule). A new period begins with each new \(s\) subshell.

Mendeleev’s groups correspond to the number of electrons outside the last closed shell. His splitting of the long periods into two series, with copper and zinc under the alkali and alkaline-earth metals, reflects the filled \(d\) subshell of Cu (\(3d^{10}4s^1\)) and Zn (\(3d^{10}4s^2\)).

Gases: the absolute boiling point and the gas law

For the general reader. Heat a liquid in a closed vessel and it never quite boils away: the vapour above it grows denser while the liquid grows thinner, until at one temperature the two become the same. Mendeleev reached this idea in 1861, studying the cohesion of liquids, and called it the absolute boiling point. Thomas Andrews found it experimentally for carbon dioxide in 1869, and we now call it the critical point.

The absolute boiling point (1861)

In Heidelberg Mendeleev measured how the capillary rise of liquids decreases with temperature. Surface tension and the latent heat of vaporization both fall as the temperature rises. He defined the absolute boiling point as the temperature at which cohesion and the heat of vaporization become zero; above it, no pressure can hold the substance as a liquid.

Derivation. Write \(p=\frac{RT}{V-b}-\frac{a}{V^2}\). The two conditions are \(\frac{RT}{(V-b)^2}=\frac{2a}{V^3}\) and \(\frac{RT}{(V-b)^3}=\frac{3a}{V^4}\). Dividing, \(V-b=\tfrac23V\), so \(V_c=3b\). Substituting back, \(RT_c=\frac{2a(2b)^2}{27b^3}=\frac{8a}{27b}\), and then \(p_c=\frac{RT_c}{2b}-\frac{a}{9b^2}=\frac{4a}{27b^2}-\frac{3a}{27b^2}=\frac{a}{27b^2}\).

The gas law in molar form

Émile Clapeyron combined the laws of Boyle, Charles and Gay-Lussac in 1834 as \(pV=r(T)\) with a constant depending on the amount and kind of gas. In the 1870s Mendeleev, who measured gas compressibility at low and high pressures, wrote the law for a mole with one universal constant, \(pV_m=RT\), or \(pV=\frac mMRT\). Russian textbooks still call it the Clapeyron–Mendeleev equation. His measurements also showed deviations from Boyle’s law of the kind van der Waals’ equation describes.

Solutions: alcohol and water

For the general reader. Mix a litre of alcohol and a litre of water and you get less than two litres. Mendeleev’s doctoral dissertation of 1865 measured this effect with great precision across the whole range of mixtures. He read the results as evidence that alcohol and water form loose chemical compounds in solution, and he defended a chemical view of solutions all his life. (He did not, as a popular story claims, fix the strength of Russian vodka; the 40% standard predates his work.)

Excess volume

For a binary mixture of masses \(m_1,m_2\) with pure densities \(\rho_1,\rho_2\) and mixture density \(\rho\), the volume change on mixing is

For ethanol and water \(\Delta V<0\) at all compositions. The partial molar volume of component \(i\), \(\bar V_i=(\partial V/\partial n_i)_{T,p,n_j}\), satisfies \(V=n_1\bar V_1+n_2\bar V_2\) and the Gibbs–Duhem relation \(x_1\,d\bar V_1+x_2\,d\bar V_2=0\).

Later work showed that the density curve is smooth and that the claimed breaks lie within experimental error. The underlying intuition, that strong specific interactions (in modern terms, hydrogen bonding) between solvent and solute shape the properties of solutions, was sound. In the 1880s and 1890s Mendeleev opposed the ionic dissociation theory of Svante Arrhenius, which explained conductivity and freezing-point depression by free ions. The two views were later partly reconciled in the theory of ion hydration, in which ions are free but surrounded by bound water.

Oil, balloons and weights, 1869–1907

After 1869 Mendeleev’s range widened. He saw science as a means to develop Russia, and the state used him as an expert. From 1863 he advised the young oil industry around Baku, and in 1876 the government sent him to the United States to study the Pennsylvania oil fields. He argued for refining at home instead of exporting crude oil, and for pipelines. He also proposed that petroleum forms deep in the Earth by inorganic reactions, a hypothesis that the geological evidence later rejected in favour of a biological origin.

In 1880 the Imperial Academy of Sciences rejected him as a member. Many saw political motives behind the vote, though the scandal of his private life may also have counted. In 1882 he married Anna Ivanovna Popova, after a divorce whose terms technically forbade him to remarry for several years. Their children included Lyubov, who married the poet Alexander Blok.

In 1887 he went up alone in a balloon to observe a total solar eclipse, although he had never flown one before. In 1890 he resigned his chair at St Petersburg University after a dispute with the Ministry of Education over the treatment of students. The navy then employed him to develop smokeless powder, and in 1892 he organized the production of a nitrocellulose powder he called pyrocollodion.

In 1892 he became custodian of the Depot of Standard Weights and Measures, and in 1893 he turned it into the Main Chamber of Weights and Measures, which he directed until his death. He worked to renew Russia’s standards of length and mass and pressed for the metric system, whose optional use was permitted in 1899. He also worked on tariff policy and was involved in plans for Arctic navigation with the icebreaker Yermak (1898).

Noble gases, death and legacy

The discovery of argon by Rayleigh and William Ramsay in 1894 posed a problem for the table: an element of atomic weight about 40 with no valence at all. Mendeleev was at first reluctant to accept the inert gases as elements. When helium, neon, krypton and xenon followed, he accepted that they formed a separate family, and in 1902 he placed them as a group 0 between the halogens and the alkali metals. The table absorbed a whole new column without any rearrangement, which strengthened it.

He was suspicious of the new theory of radioactivity, which seemed to threaten the permanence of the elements. In 1904 he published A Chemical Conception of the Ether, arguing that the ether consists of extremely light inert elements placed before hydrogen. Honours came from abroad: the Davy Medal (1882, with Lothar Meyer), Foreign Membership of the Royal Society (1892) and the Copley Medal (1905). In 1906 the Nobel Committee for Chemistry recommended him, but the Royal Swedish Academy of Sciences gave the prize to Henri Moissan by one vote. Svante Arrhenius opposed him again in 1907, and Mendeleev died that year.

He died of influenza in St Petersburg on 2 February 1907 (20 January O.S.), aged 72, and was buried in the Literatorskie Mostki section of the Volkovo Cemetery, near his mother. The Main Chamber of Weights and Measures is now the D. I. Mendeleev Institute for Metrology. In 1955 Albert Ghiorso, Glenn Seaborg and colleagues at Berkeley made element 101 and named it mendelevium.

Legacy

• The periodic system: the organizing framework of chemistry, later explained by nuclear charge and electron shells, and extended by Seaborg’s actinide series and the superheavy elements up to oganesson (118).
• Method: a classification that makes testable predictions, and the willingness to overrule data on the strength of a pattern.
• Physical chemistry: the absolute boiling point, the molar gas law, precision work on solutions.
• Russian science and industry: textbooks, the Russian Chemical Society, metrology, oil refining.

Sources and further reading

Biography

1. Dmitri Mendeleev, Wikipedia (with references).
2. Royal Society of Chemistry, Journey of discovery: Dmitri Mendeleev, 2019.
3. Dmitri Mendeleev, Encyclopaedia Britannica.
4. W. B. Jensen, Flu or cheese? (on the events of February–March 1869).
5. M. D. Gordin, A Well-Ordered Thing: Dmitrii Mendeleev and the Shadow of the Periodic Table, Basic Books, 2004; revised ed. Princeton, 2019.
6. D. I. Mendeleev Institute for Metrology, Wikipedia.

Chemistry and physics

1. D. Mendeleev, The natural system of elements and its application to the indication of the properties of undiscovered elements, Journal of the Russian Chemical Society 3 (1871) 25–56.
2. D. Mendelejeff, Die periodische Gesetzmässigkeit der chemischen Elemente, Annalen der Chemie und Pharmacie, Supplementband 8 (1872).
3. D. Mendeleev, The Principles of Chemistry, English translations from the Russian editions, London, 1891 and later.
4. D. Mendeleev, An Attempt Towards a Chemical Conception of the Ether, London, 1904.
5. History of the periodic table, Wikipedia.
6. Mendeleev’s predicted elements, Wikipedia (property tables).
7. E. R. Scerri, The Periodic Table: Its Story and Its Significance, 2nd ed., Oxford University Press, 2020.
8. H. G. J. Moseley, The high-frequency spectra of the elements, Phil. Mag. 26 (1913) 1024–1034.