Berthollet, C.L. (1803). Essai de statique chimique [Essay on chemical statics] (in French). Paris, France: Firmin Didot. On pp. 404–407, Berthellot mentions that when he accompanied Napoleon on his expedition to Egypt, he (Berthellot) visited Lake Natron and found sodium carbonate along its shores. He realized that this was a product of the reverse of the usual reaction Na2CO3 + CaCl2 → 2NaCl + CaCO3↓ and therefore that the final state of a reaction was a state of equilibrium between two opposing processes. From p. 405: " ... la décomposition du muriate de soude continue donc jusqu'à ce qu'il se soit formé assez de muriate de chaux, parce que l'acide muriatique devant se partager entre les deux bases en raison de leur action, il arrive un terme où leurs forces se balancent." ( ... the decomposition of the sodium chloride thus continues until enough calcium chloride is formed, because the hydrochloric acid must be shared between the two bases in the ratio of their action [i.e., capacity to react]; it reaches an end [point] at which their forces are balanced.)
The notation ⇌ was proposed in 1884 by the Dutch chemist Jacobus Henricus van 't Hoff. See: van 't Hoff, J.H. (1884). Études de Dynamique Chemique [Studies of chemical dynamics] (in French). Amsterdam, Netherlands: Frederik Muller & Co. pp. 4–5. Van 't Hoff called reactions that didn't proceed to completion "limited reactions". From pp. 4–5: "Or M. Pfaundler a relié ces deux phénomênes ... s'accomplit en même temps dans deux sens opposés." (Now Mr. Pfaundler has joined these two phenomena in a single concept by considering the observed limit as the result of two opposing reactions, driving the one in the example cited to the formation of sea salt [i.e., NaCl] and nitric acid, [and] the other to hydrochloric acid and sodium nitrate. This consideration, which experiment validates, justifies the expression "chemical equilibrium", which is used to characterize the final state of limited reactions. I would propose to translate this expression by the following symbol:
HCl + NO3 Na ⇌ NO3 H + Cl Na .
I thus replace, in this case, the = sign in the chemical equation by the sign ⇌, which in reality doesn't express just equality but shows also the direction of the reaction. This clearly expresses that a chemical action occurs simultaneously in two opposing directions.)
Clugston, Michael J. (1990). "A mathematical verification of the second law of thermodynamics from the entropy of mixing". Journal of Chemical Education. 67 (3): 203. Bibcode:1990JChEd..67Q.203C. doi:10.1021/ed067p203.
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Eigen, Manfred (December 11, 1967). "Immeasurably fast reactions"(PDF). Nobel Prize. Archived(PDF) from the original on 2022-10-09. Retrieved November 2, 2019.
Clugston, Michael J. (1990). "A mathematical verification of the second law of thermodynamics from the entropy of mixing". Journal of Chemical Education. 67 (3): 203. Bibcode:1990JChEd..67Q.203C. doi:10.1021/ed067p203.
Eigen, Manfred (December 11, 1967). "Immeasurably fast reactions"(PDF). Nobel Prize. Archived(PDF) from the original on 2022-10-09. Retrieved November 2, 2019.