Always the same recipe

Copper carbonate dug out of a mine and copper carbonate made on a bench turn out to have identical composition, to the limit of anyone’s ability to measure. Establishing that took eight years of argument against the best chemist in France — who was not being obtuse, and who was right about half of it.

1794 – 180615 min

By the end you should be able to

State the law of definite proportions, and what has to count as a compound for it to be true
Explain why Berthollet’s objection was a serious scientific position rather than an error
Tell a compound from a solution, an alloy or a glass by what its composition does
Recognise a berthollide, and say why non-stoichiometric solids do not overturn the law

Lavoisier left chemistry with a conserved quantity, and a conserved quantity turns a description into an account. You can now write down what went in and what came out and insist that the two sides match. Which immediately raises the next question: how much of each? It sounds minor. It is the question that ends in atoms, and answering it took twelve years and a long public argument between two chemists who were both very good at their job. The state of the art in 1794 was better than you might expect. Analysis meant burning a known mass and weighing the products, or precipitating a metal out of solution and weighing the precipitate — slow, but reproducible to a fraction of a per cent in careful hands. The instruments were not the obstacle. The obstacle was that nobody agreed on what the numbers were supposed to be.

Start with the answer that turned out to be wrong, and take it seriously, because it was held by the most influential chemist in France. Claude Louis Berthollet thought composition was continuous. Offer a metal more oxygen and it takes up more; the proportions in the product depend on the quantities you began with, on the temperature, on how long you left it. Chemical affinity, on his account, was a force like gravitation — and like gravitation, its effect depended on how much mass was present. Look around a laboratory in 1800 and that is plainly what most things do. Salt in water goes on dissolving until it stops, at whatever proportion you like along the way. Alloys can be made to any composition a founder wants. Glass has no formula at all. If those are your examples, continuous composition is not a hypothesis, it is a description. And he had one observation nobody could wave away. Berthollet went with Napoleon to Egypt in 1798, and at the margins of the salt lakes he found deposits of natron — sodium carbonate — where the accepted chemistry said none should form. In a beaker, sodium carbonate and calcium chloride give chalk and common salt. In Egypt the reaction was running the other way, because there was a vast excess of salt sitting in the water. He drew the right conclusion from it: the quantity of a substance present changes what a reaction does. That is the law of mass action, arrived at fifty years early, and it is correct. It was also, unfortunately, the argument he then used against fixed composition.

An engraved portrait of Joseph Louis Proust in high collar and coat, facing slightly left. — Proust ran the royal laboratory in Madrid; Berthollet was the senior figure of French chemistry, a member of the commission that gave chemistry its modern names and the founder of the Society of Arcueil. The argument between them ran in the journals from 1797 to 1807, and it is one of the better-tempered disputes in the history of science: neither man ever accused the other of incompetence, and both kept publishing analyses.

A painted portrait of Claude Louis Berthollet seated, in dark coat and white cravat. — Proust ran the royal laboratory in Madrid; Berthollet was the senior figure of French chemistry, a member of the commission that gave chemistry its modern names and the founder of the Society of Arcueil. The argument between them ran in the journals from 1797 to 1807, and it is one of the better-tempered disputes in the history of science: neither man ever accused the other of incompetence, and both kept publishing analyses.

The experiment

Carbonate of copper, from a mine and from a bench

Joseph Louis Proust · 1799, with the argument running to 1807 · The Royal Laboratory, Madrid

The question: If composition is continuous, then a compound assembled under one set of conditions should differ from the same compound assembled under another. Does it?
The apparatus: Two specimens of carbonate of copper. One dug out of the ground and picked clean; the other precipitated on the bench from a solution of a copper salt. Each analysed by decomposing a weighed sample, driving off the carbon dioxide, reducing the residue and weighing the metal.

Theory predicted

On Berthollet’s view the two should differ, and differ systematically — the mineral formed slowly under whatever quantities the ground supplied, the precipitate formed quickly under quantities Proust chose. On Proust’s view they must be identical.

They measured

Identical, within the error of the analysis, which was a few parts in a thousand. The same held for the oxides of copper, of tin, of iron, and of antimony, and for the sulphides of iron — a decade of analyses, all giving the same answer.

How sure could they be? This is a measurement whose value is in its repetition rather than its accuracy. Any single analysis at a few tenths of a per cent proves nothing about a law; the same analysis on twenty compounds from twenty sources, always agreeing, is a different kind of evidence — and it is why the dispute took years rather than an afternoon.

Why it mattered

A compound has one recipe. Where you got it, how you made it, and what quantities you used to make it change how much of it you have and change nothing about what it is.

The law of definite proportions

A given compound always contains the same elements in the same proportions by mass. That is the whole of it, and it is worth pulling apart, because each clause is doing work. "A given compound" — not a mixture, not a solution, not an alloy, not a glass. Those vary, everyone knew they varied, and nothing here says otherwise. "The same elements" — the identity of a compound is fixed by what is in it, not by how it was made. There is no such thing as mineral copper carbonate as against laboratory copper carbonate. "The same proportions by mass" — a ratio, not an amount. Twice the sample has twice of everything, and the ratio does not notice. What the law does not say is that you get the compound you wanted. Offer the wrong quantities and you get less of it, or a mixture of two different compounds. What you never get is a compound of intermediate composition.

One gram of copper, and however much oxygen you choose to give it. Drag the slider, heat the mixture, and watch the strip along the bottom rather than the dishes.

Loading the proportions…

The bar at the bottom is the argument. It is the composition of the oxide that forms, and it does not move — not when you starve the copper of oxygen, not when you drown it. What changes is the surplus: too little oxygen leaves copper unreacted, too much leaves oxygen unused. Berthollet expected the oxide itself to get richer. It does not, and the leftovers are where the expectation goes to die.

The surplus is doing more work in that picture than the composition is, and it is worth being explicit about why. A theory in which composition drifts has no reason to leave anything over. If the oxide can be a little richer in oxygen, then the extra oxygen goes in, a little at a time, and the reaction has no natural stopping point short of exhausting one ingredient completely. That is not what happens. The reaction stops at a particular ratio and then simply declines the rest. Something in there is refusing the surplus. Whatever is doing the refusing can count. It is not obvious yet what could count — that is the next four lessons — but a stopping rule this exact is not something a continuous substance has any reason to possess.

The experiment

The two oxides of copper, and everything supposedly between them

Joseph Louis Proust, answering Berthollet directly · 1799 – 1806 · Madrid

The question: Berthollet’s best evidence was that specimens of a metal oxide can be prepared with any composition you like across a range. Are those specimens compounds, or are they something else?
The apparatus: Copper, oxygen, heat, and then the tedious part: taking the intermediate specimens and separating them. Acids that dissolve one oxide and leave the other; differences in colour and in density to follow the separation by.

Theory predicted

If Berthollet is right, an intermediate specimen is a single substance with an intermediate composition, and nothing will separate out of it. If Proust is right, it is a mixture, and the two components can be recovered.

They measured

Copper gives a red oxide and a black one, and nothing in between. Every intermediate specimen came apart into some of each. The oxygen taken up per gram of copper is 0.1259 g for the red and 0.2518 g for the black — and that second number will matter enormously in the next lesson.

Why it mattered

The continuum was an artefact of not separating carefully enough. What looked like a compound of adjustable composition was two compounds of fixed composition in adjustable proportion — which is a different thing, and is testable, and was tested.

The argument was about the word "compound"

Neither man disputed the measurements. What they disputed was which materials the question applied to. Berthollet: composition varies continuously, as you can see in solutions, alloys, glasses and — he believed — the metal oxides. Fixed proportions are a special case, arising when a reaction happens to run to completion. Proust: the things whose composition varies are mixtures and solutions. A compound is by definition the thing that keeps its recipe, and the metal oxides are compounds. Read quickly, Proust looks like he is winning by definition — declaring that anything variable does not count. He is not, and here is why. The line falls in the same place however you draw it. Sort materials by whether their composition is fixed, and you get one grouping. Sort them by whether they have a sharp melting point rather than a softening range; by whether their properties change smoothly with composition or jump; by whether they can be separated by physical means. You get the same grouping every time, from four unrelated properties. A definition that carves the world at a joint four independent measurements agree on is not a definition any more. It is a discovery about the world, and the joint is what needs explaining.

The part the story usually rounds off

You will very often see the copper carbonate example quoted with numbers: copper, carbon and oxygen in the mass ratio 5.3 : 1 : 4. It is a real number and it is easy to check — it is the composition of CuCO₃, and it comes out of the atomic weights exactly. The difficulty is that CuCO₃ is almost certainly not what Proust had in either bottle. Precipitate copper carbonate from solution and what comes down is the basic carbonate, Cu₂CO₃(OH)₂ — which is the mineral malachite, and is also what comes out of the mine. The neutral carbonate CuCO₃ does not occur naturally and was not prepared in a pure state until the twentieth century, and then only under pressure of carbon dioxide. So Proust’s two specimens matched because they were the same substance, which is exactly what he claimed. The law is untouched. But the tidy ratio attached to the story is the composition of a compound that neither of his bottles contained, and malachite — 57.5% copper, 5.4% carbon, 36.2% oxygen, 0.9% hydrogen — is a perfectly good definite compound in its own right that simply has a more awkward formula. This is worth knowing not because it changes anything, but because the smoothing is invisible, and you cannot check what you have not been told.

You might think

Berthollet was simply wrong, and the dispute was one man seeing clearly while the other clung to a bad idea.

Actually

He was wrong about the compounds Proust analysed and right about a great deal else, including things that took another century to come back into view. Compounds with genuinely variable composition exist, they are ordinary, and they are called berthollides — a name proposed in his honour by Kurnakov in 1914, once X-ray crystallography had shown what they were. Iron(II) oxide is the standard case: it is never FeO, always short of iron, running from roughly Fe₀.₈₅O to Fe₀.₉₅O, and the exact 1:1 compound is not stable at ordinary pressure at all. Titanium monoxide ranges over about TiO₀.₇ to TiO₁.₃. The high-temperature superconductors are tuned by precisely this mechanism: in YBa₂Cu₃O₇₋ₓ you choose the oxygen content, and the temperature at which the material starts to superconduct follows it. And Berthollet’s Egyptian observation was not merely defensible, it was the germ of the law of mass action, which is Act 7 of this path. What he got wrong was the scope. Fixed proportions are not a special case of a continuum; the continuum is the exception, and it happens in solids whose lattices can carry vacancies.

Problem

Offer it too much

You heat 2.00 g of copper in a stream of oxygen so generous that 1.00 g passes over it — about four times what it could conceivably use. It all converts to the black oxide, CuO. What mass of black oxide do you get? (These are the simulation’s starting quantities, scaled up, so you can check yourself against it.)

Copper taken: 2.00 g
Oxygen offered: 1.00 g
Compound formed: CuO, the black oxide
Molar mass, copper: M(Cu) = 63.546 g/mol
Molar mass, oxygen atoms: M(O) = 15.999 g/mol

Iron, like many other metals, is subject to the law of nature which presides over every true combination — that is to say, that it unites with two constant proportions of oxygen. In this respect it does not differ from tin, mercury, and lead, and, in a word, from almost every known combustible.
Joseph Louis ProustFrom his 1806 memoir on the metallic oxides, in translation. His other well-known line from the same period is worth having beside it: a compound is a being which nature never creates other than balance in hand — pondere et mensura, by weight and measure.

1786Proust leaves France for Spain, to teach at the artillery school at Segovia.
1794Lavoisier is guillotined. Proust begins the analyses that will become the law of definite proportions.
1798Berthollet sails for Egypt with Napoleon, and finds natron where the textbook says it cannot form.
1799Proust moves to the royal laboratory in Madrid, and publishes on the carbonate and the oxides of copper.
1803Berthollet’s Essai de statique chimique: affinity depends on mass, and composition is continuous.
1806Proust’s memoir on the metallic oxides. The two oxides of a metal, and nothing between them.
1808French troops sack Proust’s Madrid laboratory. He returns to France and never really works again.
1811Berzelius begins a decade of analyses far more accurate than either man’s, and they come out on Proust’s side.
1914Kurnakov proposes the names daltonide and berthollide. Berthollet turns out to have been describing something real.