Reactions that stop halfway

Start with the picture of chemistry that this lesson takes apart, because it is a good one and it was built out of real work. A reaction goes, or it does not. Torbern Bergman published the great affinity tables in 1775: for every substance, a ranked list of the others that would drive it out of a compound. Silver above copper, copper above lead, and so on down. Look up your two reagents, find which sits higher, and you know what will happen. And the tables worked. They were assembled from thousands of real displacements, they predicted new ones correctly, and every assayer and apothecary in Europe could use them. This is not a superstition being cleared away. It is a working instrument with an assumption buried inside it. The assumption is completeness. If A drives B out, it drives all of B out. Affinity is a fixed property of a pair of substances, like a rank in an army, and the outcome of putting them together does not depend on how much of each you brought. That last clause is the one that fails, and the evidence for its failing turned up in a place nobody was looking.

Claude-Louis Berthollet went to Egypt with Bonaparte in 1798, as one of the scientists attached to the expedition, and on the shores of the salt lakes west of the Nile delta he saw something the affinity tables forbade. Sodium carbonate — natron — crusting out of the ground. The lakes sat on limestone, calcium carbonate, and the water was thick with common salt. The tables said the reaction ran the other way: sodium carbonate plus calcium chloride gives limestone plus salt, reliably, in any laboratory in Europe. Here was the reverse happening on a scale you could shovel. Berthollet drew the right conclusion. Affinity is not the only thing that decides. The quantity present decides too — enough salt standing over enough limestone, with the products removed as they form, will run a reaction backwards against its own affinity. He published it in the Essai de statique chimique in 1803. It is worth saying plainly that Berthollet is remembered mainly for being wrong. He argued that compounds did not have fixed compositions, lost that argument to Proust over eight years, and lost it decisively. He was right about this, and being right about this is the more useful of the two.

Take a moment on why two thirds is such a hard number to explain away. It is not exhaustion. A third of the acid is still in the tube. If the reaction were a one-way process running to completion, it has no reason to be sitting next to a reagent it could still consume. It is not slowness. The tubes reached this point and then held it for a year. A reaction that is merely slow gets further given a year. It is not the apparatus. Change the size of the tube and nothing moves: this particular reaction has two molecules on each side, so the concentrations cancel and dilution does not touch the answer. Change the proportions you start with and the endpoint moves in a way you can calculate. And it is not one-directional. That is the sealed tubes of ester and water. They arrive at the same mixture with no acid or alcohol anywhere in sight at the start. One explanation covers all four at once.

Cato Maximilian Guldberg and Peter Waage — a mathematician and a chemist, brothers-in-law, working in Christiania, the city now called Oslo — wrote the rule down in 1864. Their claim, the law of mass action: the rate at which a reaction proceeds is proportional to the "active masses" of the substances reacting, meaning their concentrations. Equilibrium is where the forward expression and the backward expression are equal. And the ratio that falls out of setting them equal is a constant for that reaction at that temperature. They published it in Norwegian, in the proceedings of the academy in Christiania. Nobody read it. They published a French edition in 1867. Nobody read that either. It took a German edition — Ueber die chemische Affinität, in the Journal für praktische Chemie — in 1879, fifteen years after the original, and even then it landed only because Jacobus Henricus van ’t Hoff had reached the same law independently in the meantime and the subject had become fashionable. Guldberg and Waage were not obscure figures pushing a crank idea. They were correct, in print, and in the wrong language. This site keeps running into that shape, and it is worth naming: being right and being read are different achievements, and the second one is mostly about where you are standing.

Henry Louis Le Chatelier stated the general rule in 1884, in a note to the Comptes Rendus; Karl Ferdinand Braun arrived at it independently in 1887, which is why it is sometimes the Le Chatelier–Braun principle. What everyone learns is the short version: disturb a system at equilibrium and it shifts to oppose the disturbance. What Le Chatelier wrote is longer, uglier, and full of conditions — and the conditions are the part doing the work. His statement restricts itself to a change in temperature or in "condensation", says the change must be applied from outside, and, crucially, describes the response as the internal change that would if it occurred alone push back on that same variable. Every one of those clauses is load-bearing. The short version drops all of them, and once they are gone it will happily give you the wrong sign. The honest replacement is not harder. Work out the reaction quotient Q from whatever amounts you now have, and compare it with K. If Q is less than K the reaction runs forward; if Q is greater, it runs back; if they are equal, nothing happens. That rule tells you the direction and how far, and it has no exceptions to memorise.

Every system in stable chemical equilibrium, submitted to the influence of an exterior force which tends to cause variation either in its temperature or its condensation — pressure, concentration, number of molecules in unit volume — either as a whole or in some of its parts, can undergo only those interior modifications which, if they occurred alone, would produce a change of temperature, or of condensation, of a sign contrary to that resulting from the exterior force.

1. 1775Bergman’s affinity tables: for every substance, a ranked list of what displaces it. Reactions go, or they do not.
2. 1799Berthollet, on the Egyptian expedition, finds sodium carbonate forming where the tables say it cannot.
3. 1803Essai de statique chimique: quantity matters as much as affinity, and a reaction can be pushed backwards.
4. 1862Berthelot and Péan de Saint-Gilles reach the same ester mixture from both ends, in sealed tubes held for a year.
5. 1864Guldberg and Waage state the law of mass action. In Norwegian.
6. 1867A French edition. Still nobody reads it.
7. 1877Van ’t Hoff reaches the same law independently, and is heard.
8. 1879A German edition of Guldberg and Waage, fifteen years late, and the law finally acquires their names.
9. 1884Le Chatelier states the principle, hedged with conditions that will be dropped from every later retelling.
10. 1887Braun states it independently.
11. 1913Hevesy and Paneth invent the radioactive tracer, which will finally make a dynamic equilibrium visible.