Joseph Louis Gay-Lussac

How to use this course

Joseph Louis Gay-Lussac gave his name to a gas law, a law of volumes, a scale of alcoholic strength and a tower in a sulphuric acid works. Behind the names stands a single method: measure carefully, look for the simple ratio, and trust it. His law of combining volumes was the clue that led Amedeo Avogadro to molecules, and his analytical methods trained a generation of chemists, Justus von Liebig among them.

Each technical lesson opens with a paragraph for the general reader, then states the laws precisely, derives them in modern language, and ends with exercises whose solutions are folded. Gay-Lussac worked before the modern atomic weights were settled, so the lessons point out where his data were sound and where the interpretation had to wait for others.

Timeline

Saint-Léonard and the Revolution, 1778–1797

Joseph Louis Gay was born on 6 December 1778 in Saint-Léonard-de-Noblat, a small town on the Vienne east of Limoges. His father, Antoine Gay, was a lawyer and procurator who served as a judge at Pont-de-Noblat. To distinguish their branch from other families named Gay in the district, they added the name Lussac; father and son settled on Gay-Lussac around 1803.

He learned Latin from a local priest and then from lay teachers in the town. The Revolution reached the family directly. In late 1793, under the Law of Suspects, Antoine Gay was arrested as a former royal official and held until the fall of Robespierre in July 1794. The episode left the son with a lasting distaste for political violence and a respect for order that later shaped his politics.

At about sixteen he was sent to Paris to prepare for the new engineering schools. He studied with the abbé Dumonteil and then at private boarding schools, the last at Nanterre, where he took mathematics, English and drawing. The disruption of the period made schooling irregular, and the family’s resources were stretched. The entrance examination of the École Polytechnique, founded in 1794 and free to those who passed, was his route forward.

Polytechnique and Berthollet, 1797–1802

Gay-Lussac entered the École Polytechnique at nineteen. Its chemistry teaching was the best in Europe. In his first year he heard Antoine François Fourcroy and Nicolas Vauquelin; in the second, Jean-Antoine Chaptal; in the third, Louis-Bernard Guyton de Morveau and Claude-Louis Berthollet, all of them collaborators or heirs of Antoine Lavoisier. Mathematics came from teachers in the circle of Gaspard Monge and Joseph-Louis Lagrange, and the habit of quantitative argument stayed with him.

In his third year he worked with Berthollet on bleaching linen with chlorine. Berthollet, back from Egypt with Napoleon, was looking for an assistant. Gay-Lussac passed on to the École des Ponts et Chaussées, the normal next step for a polytechnicien, but attended irregularly and was soon working full time in Berthollet’s private laboratory at Arcueil, south of Paris.

Berthollet was the most important influence on his career. He gave the young man apparatus, problems and, above all, the expectation of exact measurement. Berthollet’s neighbour at Arcueil was Pierre-Simon Laplace, whose programme of explaining heat, light and chemistry by short-range forces between particles set many of the questions Gay-Lussac would attack experimentally.

Arcueil, balloons and Humboldt, 1802–1809

His first major paper, read to the Institut in 1802, showed that all gases and vapours expand by the same fraction when heated through the same range (Lesson 04). It made his reputation at 23. In 1804 the Institut, at Laplace’s urging, organized balloon ascents to test whether the Earth’s magnetism weakens with height. On 24 August Gay-Lussac and Jean-Baptiste Biot rose from the garden of the Conservatoire des Arts et Métiers to about 4000 m. On 16 September Gay-Lussac went up alone and reached about 7000 m, a height record for its time (Lesson 05). The same year he became répétiteur, an assistant teacher, at Polytechnique.

In 1805 the Prussian naturalist Alexander von Humboldt, just back from the Americas, joined him in a study of air analysis by the eudiometer. Their joint paper established that hydrogen and oxygen combine in the ratio of 2 volumes to 1, to within a fraction of a percent. The two men then travelled together for a year through France, Italy, Switzerland and Germany, measuring magnetism and air composition, visiting Vesuvius and meeting Alessandro Volta. They remained friends for life.

On 8 December 1806, aged 28, he was elected to the physics section of the First Class of the Institut. In 1807 Berthollet and Laplace formed the Société d’Arcueil, a small private academy that met at their houses and published three volumes of Mémoires; Gay-Lussac was a founding member and one of its most productive authors. In 1808 he began a long partnership with Louis Jacques Thénard, the son of a peasant from Champagne who had risen through Vauquelin’s laboratory. Their work on the alkali metals made both famous (Lesson 08). He married Geneviève Rojot, whom he had met while she was working in a Paris linen shop; they had five children.

The expansion of gases

For the general reader. Heat a gas at constant pressure and it swells. Gay-Lussac showed in 1802 that every gas swells by the same fraction for the same rise in temperature, whatever its chemical nature, and that steam above the boiling point behaves the same way. The rule is so uniform that it defines a thermometer and points to an absolute zero.

The experiment

Earlier workers had found different expansions for different gases, because their gases were moist. Water vapour evaporating into a warming sample adds volume of its own. Gay-Lussac dried his gases carefully and filled a dry glass flask with a long calibrated neck, closed by a short index of mercury that moved as the gas expanded. He heated the flask in a water bath from melting ice to boiling water and read the volume change. He tested air, oxygen, hydrogen, nitrogen and several gases that dissolve readily in water, as well as the vapour of ether above its boiling point.

Gay-Lussac credited unpublished experiments made by Jacques Charles in the 1780s, which is why the law is often called Charles’s law. John Dalton reached a similar result independently in 1801, with less exact data. The modern coefficient is \(1/273.15\) per kelvin.

Absolute temperature

Write the law as \(V(\theta)=V_0(1+\alpha\theta)\), with \(\theta\) in degrees Celsius and \(\alpha\) the same for all gases. Then \(V\) vanishes at \(\theta=-1/\alpha\). Define \(T=\theta+1/\alpha\). The law becomes

With \(\alpha=1/266.67\) the zero lies at −266.7 °C; with the modern value it lies at −273.15 °C. Neither Gay-Lussac nor Dalton drew this conclusion. It became the basis of the absolute scale in the hands of William Thomson in 1848, by a thermodynamic argument that does not depend on any substance.

The companion law

At constant volume the same reasoning gives \(p\propto T\). Textbooks in many countries call this pressure–temperature form Gay-Lussac’s law. He did not publish it as a separate law, but it follows at once from his result combined with Robert Boyle’s law.

The atmosphere at 7000 metres

For the general reader. In 1804 Gay-Lussac carried barometers, thermometers, hygrometers, magnetic needles and empty glass flasks into the sky. He wanted to know whether the Earth’s magnetism weakens with height and whether high air differs from low air. He found that magnetism changed little and that the air at 7000 metres had the same proportion of oxygen as at the ground.

Two ascents

The first ascent, with Biot on 24 August 1804, reached about 4000 m. The oscillation period of a horizontal magnetic needle was unchanged within error, contradicting a claim by Horace-Bénédict de Saussure from Alpine measurements. On 16 September Gay-Lussac went up alone with lighter instruments and more ballast. At the top his barometer stood at less than half its ground reading and the thermometer well below freezing. He opened evacuated flasks to collect air, sealed them, and analysed the samples in Paris. The oxygen fraction matched that of ground air to within the precision of his eudiometer, close to 21%.

Altitude from pressure

For an atmosphere in hydrostatic equilibrium, \(dp=-\rho g\,dz\), and for an ideal gas of molar mass \(M\), \(\rho=pM/RT\). Then

where \(\bar T\) is a suitable mean temperature of the layer (exactly the harmonic mean over height). The scale height \(H=R\bar T/(Mg)\) is about 8 km near the ground. Laplace had given a refined version of this formula, with corrections for humidity and the variation of gravity, in the Mécanique céleste; Gay-Lussac used it to reduce his barometer readings to heights.

The constant composition matters. If gases were stratified by weight, each would follow its own exponential with scale height \(RT/(M_ig)\), and oxygen (\(M=32\)) would thin faster than nitrogen (\(M=28\)). Gay-Lussac’s samples showed that turbulent mixing dominates in the lower atmosphere, a conclusion consistent with Dalton’s view that each gas in a mixture acts independently but is stirred together by winds.

Free expansion and the heat of gases

For the general reader. When a gas rushes into an empty vessel, does it cool? In 1807 Gay-Lussac let air flow from one globe into another and measured both. One cooled, the other warmed, and the two changes cancelled. Forty years later the same experiment, repeated by James Prescott Joule, became evidence that the energy of an ideal gas depends only on its temperature.

The experiment

Gay-Lussac connected two equal glass globes by a tube with a stopcock, filled one with dry air and evacuated the other. Sensitive thermometers sat inside both. When the stopcock opened, the full globe cooled and the empty one warmed by nearly the same number of degrees. He repeated the test at several initial pressures and with other gases, and always found the cooling and warming nearly equal.

His motive was the caloric theory. Many supposed that a gas’s capacity for heat depends on its volume, so that a gas allowed to expand would absorb heat. If that were so, the combined system should cool on balance. It did not. Gay-Lussac recorded the result without drawing a firm theoretical conclusion; the experiment was largely forgotten until Joule repeated it in 1845.

Derivation. The two globes form an isolated system: no heat enters (\(Q=0\)) and the rigid walls do no work (\(W=0\)), so \(\Delta U=0\). If the final temperature equals the initial temperature while the volume has doubled, then \(U(T,2V)=U(T,V)\). The local cooling and warming arise because the gas left behind in the first globe expands and pushes the escaping gas, which is compressed in the second; work is transferred inside the system, not across its boundary.

Specific heats and sound

For an ideal gas, Joule’s law implies \(C_p-C_V=R\) per mole. The ratio \(\gamma=C_p/C_V\) governs adiabatic compression, \(pV^\gamma=\) constant. In 1816 Laplace showed that sound waves are adiabatic, so their speed is \(c=\sqrt{\gamma p/\rho}\) and not Isaac Newton’s \(\sqrt{p/\rho}\). Laplace used a measurement of \(\gamma\) made by Gay-Lussac with Jean-Joseph Welter in the early 1820s, by the sudden-expansion method of Clément and Desormes, to bring theory and the measured speed of sound into agreement.

The law of combining volumes

For the general reader. Weigh the substances in a reaction and the ratios are untidy: 8 grams of oxygen for each gram of hydrogen in water. Measure the gases by volume and the ratios become small whole numbers: exactly two volumes of hydrogen to one of oxygen. Gay-Lussac found that this simplicity holds for every reaction between gases. It was the strongest early hint that gases are made of countable particles.

He announced the law to the Société philomathique on 31 December 1808 and published it in 1809 in the second volume of the Mémoires d’Arcueil. His starting point was the 2 : 1 ratio for water he had measured with Humboldt. He then noticed the same simplicity in reactions of the acid gases with ammonia, which form solid salts and so leave no gaseous product to confuse the count.

His examples

From his own measurements and those of others (100 volumes of the first gas in each case):

• muriatic gas (HCl) with 100 of ammonia; carbonic gas with 200 of ammonia;
• nitrogen with 300 of hydrogen (in ammonia);
• nitrogen with 50, 100 and 200 of oxygen (nitrous oxide, nitrous gas and nitrogen dioxide, then called nitric acid);
• carbonic oxide with 50 of oxygen, giving 100 of carbonic acid gas;
• hydrogen with 50 of oxygen, giving 100 of steam.

Densities from volumes

The law lets one predict the density of a gaseous compound from those of its components. If \(a\) volumes of gas A and \(b\) of B give \(c\) volumes of product, conservation of mass gives

with all densities relative to air at the same temperature and pressure. Gay-Lussac used this to check the law against measured densities: for ammonia from 1 volume of nitrogen and 3 of hydrogen contracting to 2, he computed 0.594 against a measured 0.596.

Interpretation

Gay-Lussac remarked that his law fitted Dalton’s atomic theory and suggested that combining volumes might give relative numbers of atoms. Dalton disagreed. If equal volumes held equal numbers of atoms, then 1 volume of nitrogen and 1 of oxygen could make only 1 volume of nitrous gas, not the 2 observed, unless atoms split. In 1811 Avogadro resolved the paradox: equal volumes contain equal numbers of molecules, and the molecules of the elementary gases can contain two atoms. The modern equations make the volume ratios immediate:

Potassium, boron, chlorine and iodine

For the general reader. In 1807 Humphry Davy used a giant battery to tear potassium out of potash. Napoleon’s savants answered with chemistry. Gay-Lussac and Thénard made potassium by heating potash with iron, in quantities large enough to use as a reagent, and with it they isolated boron. Over the next six years Gay-Lussac also helped show that chlorine and iodine are elements, and that acids need not contain oxygen.

Potassium and boron (1808)

Davy’s electrolysis yielded tiny amounts of metal. Gay-Lussac and Thénard passed molten potash over red-hot iron filings in a gun barrel and collected potassium by the gram. An explosion in this work seriously injured Gay-Lussac’s eyes. They then heated boric acid with potassium in a copper tube and obtained an olive-brown powder, a new element they called bore. They announced it in 1808, at nearly the same time as Davy, who isolated boron by a similar route that year.

For this work the pair received the prize Napoleon had founded for advances in galvanism, in 1809. Their two-volume Recherches physico-chimiques (1811) collected these and many other experiments.

Chlorine and the hydracids

Following Lavoisier, chemists held that every acid contains oxygen. Chlorine was therefore “oxygenated muriatic acid”, an oxide of an unknown radical. In 1809 Gay-Lussac and Thénard found that no means could extract oxygen from it; even charcoal heated in it gave no carbonic acid. They noted that it could be treated as an element but did not insist. Davy argued firmly in 1810 that it is an element and named it chlorine. Muriatic acid is then simply HCl, an acid with no oxygen.

Iodine (1813–1814)

In 1811 the saltpetre maker Bernard Courtois noticed violet vapour rising from seaweed ash treated with sulphuric acid. Samples went to several chemists. Gay-Lussac and Davy, who was visiting Paris in 1813 with special permission despite the war, worked on it at the same time. Gay-Lussac named it iode, from the Greek for violet, and in his memoir of 1814 described it as an element analogous to chlorine. He prepared hydriodic acid HI and iodic acid, and concluded that acidity does not require oxygen. He introduced the term hydracide for acids of hydrogen with a non-metal, extending the class later to hydrofluoric acid.

Cyanogen, radicals and organic analysis

For the general reader. Plants and animals are made of a few elements: carbon, hydrogen, oxygen and nitrogen. To find their proportions you must burn the substance completely and weigh or measure what comes out. Gay-Lussac and Thénard built the first reliable method in 1810. In 1815 Gay-Lussac found that a group of atoms, carbon with nitrogen, can pass unchanged through reactions like a single element. He had discovered the first compound radical.

Combustion analysis (1810)

Gay-Lussac and Thénard mixed a weighed organic sample with potassium chlorate, pressed it into pellets, and dropped them one by one into a heated vertical tube. The gases were collected over mercury. They measured the oxygen consumed and the carbonic acid formed, and inferred hydrogen from the balance. Later Gay-Lussac replaced chlorate with copper oxide, which is safer. Liebig, who learned the method in Paris, turned it into the standard five-bulb apparatus of the 1830s.

From their analyses Gay-Lussac also gave the overall equation of alcoholic fermentation, in modern form

Prussic acid and cyanogen (1815)

Carl Wilhelm Scheele had made prussic acid (HCN) from Prussian blue in 1782. Gay-Lussac prepared the pure anhydrous acid and showed that it contains no oxygen. Heating mercuric cyanide, he obtained a colourless, poisonous gas that burns with a peach-coloured flame. He analysed it by combustion: 1 volume gave 2 volumes of carbonic acid and 1 volume of nitrogen, so its formula is C\(_2\)N\(_2\). He named it cyanogène, generator of blue.

This was the first clear example of a compound radical. Liebig and Friedrich Wöhler’s benzoyl radical (1832) and the radical theory of organic chemistry built on it. In 1824 Liebig, working in Gay-Lussac’s laboratory, analysed silver fulminate; Wöhler at the same time analysed silver cyanate. The two salts had the same composition and different properties, an early case of isomerism, which Jöns Jacob Berzelius named in 1830.

Volumetric analysis and industrial chemistry

For the general reader. To find how much silver is in a coin, you can dissolve it and add salt water drop by drop until no more silver chloride forms. The volume of salt solution used tells you the silver. Gay-Lussac turned this idea into a precise method for the Paris Mint and gave chemistry the burette and the pipette. He also measured the strength of spirits for the tax office and cut the pollution of sulphuric acid works.

Burette and pipette

Titration was older; François-Antoine Descroizilles had used a graduated tube in the 1790s to test bleach. Gay-Lussac made it exact. In his 1824 paper on standardizing indigo solutions for bleach assay he introduced the words burette and pipette, and described an improved burette with a side arm.

The silver assay

As assayer to the Mint from 1829, Gay-Lussac replaced the old fire assay (cupellation), which lost silver and gave errors of several parts per thousand, by a wet method published in 1832. A sample is dissolved in nitric acid and titrated with a standard sodium chloride solution:

Near the end point he added the salt in small decimal portions, shaking until the precipitate settled and the liquid cleared, and watched whether a further drop still gave a cloud. The method was far more precise than cupellation and was adopted by mints across Europe.

Alcoholometry

In 1824 a French law based the tax on spirits on his measurements. Gay-Lussac determined the densities of water–ethanol mixtures as a function of composition and temperature and built a hydrometer graduated directly in percentage of alcohol by volume at 15 °C. The “degree Gay-Lussac” (°GL) is still used for the strength of wines and spirits.

The Gay-Lussac tower

In the lead-chamber process for sulphuric acid, nitrogen oxides catalyse the oxidation of sulphur dioxide and then escape with the exhaust. Gay-Lussac proposed in 1827 to absorb them in a tower packed with coke, down which concentrated sulphuric acid trickles, forming nitrosylsulphuric acid. John Glover’s tower (1859) later released the oxides at the front of the plant. The Gay-Lussac tower was first installed at the Chauny works of the Saint-Gobain company, which Gay-Lussac served as director and, from 1843, as chairman.

Professor, editor, deputy, 1809–1840

From 1809 Gay-Lussac held a chair of chemistry at the École Polytechnique, becoming its chief chemistry professor after Fourcroy’s death in 1810, and the first chair of physics at the new Faculty of Sciences of Paris. He held the Sorbonne chair until 1832, when he moved to the chair of chemistry at the Muséum d’histoire naturelle, and left Polytechnique in 1840, succeeded by his former assistant Théophile-Jules Pelouze. Students remembered a clear, careful lecturer who described his own discoveries with conspicuous modesty.

His laboratory drew foreign students. Justus von Liebig arrived in Paris in 1822, was introduced by Humboldt, and in 1824 worked with Gay-Lussac on the fulminates. Liebig later described those months as decisive, and modelled his famous teaching laboratory at Giessen partly on what he had seen. Gay-Lussac’s eldest son Jules later studied under Liebig at Giessen.

In 1816 he and François Arago, his closest friend, took over the Annales de chimie as the Annales de chimie et de physique, which they edited for decades and which became one of the leading journals of physical science. He was president of the Académie des sciences in 1822 and 1834. He served on government committees for gunpowder and saltpetre, for arts and manufactures, and as assayer to the Mint, posts that brought both income and influence over French industry.

After the July Revolution he entered politics. He was elected deputy for the Haute-Vienne in 1831 and re-elected in 1834 and 1837, sitting with the moderate supporters of the July Monarchy, while Arago sat on the left. In 1839 Louis-Philippe made him a peer of France. In the Chamber of Peers he spoke on industrial and technical questions; he opposed a bill to limit child labour in factories, and lost.

Last years, death and legacy, 1840–1850

In his last decade Gay-Lussac gave more time to Saint-Gobain and to his duties at the Mint, while still experimenting; an explosion during work on hydrocarbon gases in 1844 injured him again. The Revolution of 1848 ended the Chamber of Peers, and he resigned his post at the Mint, which passed to his son Jules. He died after a short illness on 9 May 1850 at his residence in the Jardin des Plantes, aged 71, and was buried in the Père Lachaise cemetery.

Legacy

• Gas laws: the uniform expansion of gases is a foundation of the ideal-gas law and of absolute temperature; in many countries the pressure–temperature law carries his name.
• Atoms and molecules: the law of combining volumes led directly to Avogadro’s hypothesis (1811) and, through Stanislao Cannizzaro in 1858–60, to consistent atomic weights.
• Elements and radicals: boron, the elementary status of chlorine and iodine, the idea of oxygen-free acids, and the cyanogen radical.
• Analytical chemistry: combustion analysis, volumetric titration with burette and pipette, the silver assay and alcoholometry.
• Honours: foreign member of the Royal Society (1815) and of the Royal Swedish Academy of Sciences (1821); grand officer of the Legion of Honour; the Prussian Pour le Mérite (1842). His name is among the 72 engraved on the Eiffel Tower, and a lunar crater bears it.

Sources and further reading

Biography

1. M. Crosland, Gay-Lussac: Scientist and Bourgeois, Cambridge University Press, 1978. The standard biography.
2. M. Crosland, The Society of Arcueil: A View of French Science at the Time of Napoleon I, Heinemann, 1967.
3. Joseph Louis Gay-Lussac, Wikipedia; Louis Joseph Gay-Lussac, Wikipédia (French).
4. P. Jolibois, Notice on Gay-Lussac, Académie des sciences, 1950.
5. Gay-Lussac, Louis Joseph, Encyclopædia Universalis.

Science

1. J. L. Gay-Lussac, Recherches sur la dilatation des gaz et des vapeurs, Annales de chimie 43 (1802), 137–175.
2. J. L. Gay-Lussac and A. von Humboldt, Expériences sur les moyens eudiométriques et sur la proportion des principes constituants de l’atmosphère, Journal de physique 60 (1805).
3. J. L. Gay-Lussac, Memoir on the combination of gaseous substances with each other, Mémoires de la Société d’Arcueil 2 (1809), 207; English translation in the Classic Chemistry collection, Le Moyne College.
4. J. L. Gay-Lussac and L. J. Thénard, Recherches physico-chimiques, 2 vols., Paris, 1811.
5. J. L. Gay-Lussac, Mémoire sur l’iode, Annales de chimie 91 (1814).
6. J. L. Gay-Lussac, Recherches sur l’acide prussique, Annales de chimie 95 (1815).
7. J. L. Gay-Lussac, Instruction sur l’essai des matières d’argent par la voie humide, Paris, 1832.
8. A. J. Ihde, The Development of Modern Chemistry, Harper & Row, 1964; Dover reprint 1984.