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«by Bernard Fernandez, PhD, Honorary research fellow at the Commissariat à l’Énergie atomique ABSTRACT This analysis of a text by Avogadro from ...»

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Two Hypotheses of Avogadro (1811)

by Bernard Fernandez, PhD,

Honorary research fellow at the Commissariat à

l’Énergie atomique


This analysis of a text by Avogadro from 1811 recounts an episode

on the long road towards the characterisation o f atoms and the ascertainment

of their reality. This road saw notable advances between 1790 and 1820, before

slowing down until the turn of the 20th century, and the pace was set during

this period by the formulation of Dalton's atomic theory (between 1803 and 1806) and by Gay-Lussac 's experimental observations on the volumes of gases (in 1808). Avogadro took the apparently contradictory works of these two chemists as his basis, and reconciled them by venturing two hypotheses.

The first, known as Avogadro's hypothesis, lead to the present notion of the mole, and is characterised by the Avogadro number (N). The second allowed for a distinction to be made between O and O 2, namely, the atom and its molecule, and is the basis for the notion of a molecule and present chemical notation.


Avogadro's text is difficult for today's minds to follow, being as they are totally accustomed to the notion of atoms and molecules: it is convenient to read these terms bearing in mind that the notions were quasi-unknown in 1811. They could only be inferred from some experimental facts, which made them evidently rather distant. Let us also remark that the term 'molecule' is used for what we now call 'atom'.

Furthermore, it is important to signal that Avogadro's text, apart from his luminous hypotheses, contains a certain number of considerations and suppositions that have since been rejected.


Amedeo Avogadro, Count of Quaregna and Ceretto (born in Turin on 9th August 1776, died in the same city on 9th July 1856), is an exceptional figure in the particularly fertile history of physics of the beginning of the 19th century.

Piedmont was part of the Kingdom of Sardinia then, administered in a very autocratic way by king Victor Amadeus III. Due to punctilious censorship

numerous scientists emigrated, among them two famous savants:

the mathematician Giuseppe Ludovico Lagrangia (1736-1813), known under frenchified name Joseph-Louis Lagrange, and the chemist Claude Louis Berthollet (1748-1822), a medical doctor educated in Turin.

Fig1 : Portrait of Amedeo Avogadro The issue of an ancient Piedmontese magistrate family, Avogadro at first followed the family route by undertaking studies in law and theology, entering l'Avvocatura dei Poveri in 1896, then l'Avvocatura Generale. When in 1801 France annexed Piedmont, Avogadro became Secrétaire du Département d'Eridanus.2 From this point he took an interest in natural sciences and mathematics. He attended a university course in physics and read a lot in his free time. In 1804, aged 28, he sent two essays on electricity to the Academy of Sciences of Turin, of which he became a corresponding member. Two years later he addressed two memoirs on electricity, this time in French, to the Journal

1. See the well-documented biography by Mario Morselli, Amedeo Avogadro, A Scientific Biography, Dordrecht Publishing C o, Dordrecht 1984.

2. Le département d’Eridanus, from the Greek name of the Po river, was one of the six French departments that constituted Piedmont.

de Physique, de Chimie, d'Histoire Naturelle et des Arts, a magazine run by Jean-Claude de la Méthérie. In 1809, Avogadro was nominated professor of mathematics and physics at the ancient Collège Royal in Vercelli, a town located some 50 kilometres east of Turin. In 1820, he became professor of physics at the University of Turin, a post he held for the rest of his life (with a break from 1823 to 1833, seemingly due to his occupation of political posts).

Avogadro led a withdrawn life we know little about. He never sought honours nor travelled beyond Piedmont. Aged 38, he married Felicita Mazzia, with whom he had seven children.

The text in focus here is a memoir submitted to Journal de Physique in spring 1811, and published in July of that year. The title, ‘Essay on Determining the Relative Masses of the Elementary Molecules of Bodies and the Proportions by Which They Enter These Combinations’, announces an ambitious programme. It formulated what is now known as Avogadro's hypothesis.

–  –  –

In order to explain the combustion of bodies, German chemist Johann Joachim Becher (1635-1682) created the theory of phlogiston, which was further developed by Georg Ernst Stahl (1660-1734). Phlogiston (from the Greek phlogistos, meaning flammable) was a fluid contained in all flammable bodies, given off during combustion or oxidation. These bodies were hence being

3. A. Avogadro, 'Considérations sur l'état dans lequel doit se trouver une couche d'un corps non-conducteur de l'électricité, lorsqu'elle est interposée entre deux surfaces douées d'électricités de différente espèce', Journal de physique, de chimie, d'histoire naturelle et des arts, Issue 63, p.450-462, December 1806; 'Second mémoire sur l'électricité', ibid. 65, p.130-145, August 1807.

4. Amedeo Avogadro, 'Essai de déterminer les masses relatives des molécules élémentaires des corps, et les proportions dans lesquelles elles entrent dans ces combinaisons ', Journal de Physique, de Chimie, d'Histoire naturelle et des arts, Issue 73, p.58-76, 1811. This article is a part of the book (unfortunately run out) Les atomes, une anthologie historique; texts selected, presented and annotated by Bernadette BensaudeVincent & C atherine Kounelis, Paris, Presses-Pocket, 1991. One may also consult Histoire de l’atome, a collection of texts selected and presented by Pierre Radvanyi, Belin, 2007.

dephlogistated - deprived of phlogiston. However, measurements

showed that the mass of metals increases during combustion:

but this made some scientists even suppose that phlogiston had negative mass. Lavoisier showed that combustion is a combination of body and oxygen, namely oxidation.

He also showed that air was a mixture of oxygen, nitrogen, etc.

Most importantly, he established the notion of a 'simple body' or an 'element' a non-decomposable chemical substance, as opposed to a 'compound body':

We m ust adm it, as elem ents, all the substances into which we are capable, by any m eans, to reduce bodies by decom position. [...] we ought never to suppose them com pounded until experim ent and observation has proved them to be so.5 In 1794 Joseph-Louis Proust (1754-1826) stated in a general way the law of constant composition as a result of experimental studies on iron oxides and oxides of other metals. His article "Recherches sur le bleu de Prusse" was not published until 1799, though a considerable extract appeared in Journal

de Physique (1794):

[...] these experim ents [prove] the principle which I established at the beginning of this m em oir; nam ely, that iron is, like several other m etals, subject by that law of nature which presides over all true com binations, to two constant proportions of oxygen. It does not at all differ in this regard from tin, m ercury, lead etc. and finally from virtually all of the known combustibles…I will m ake known the kind of oxide that results from the combination of oxygen with carbon, in a lower proportion to that corresponding to carbon dioxide (carbon m onoxide).

What Proust designates as the ‘true combination’, is what we now call a ‘chemical combination’, in opposition to ‘mixture’ (for example table salt, NaCl, is a chemical combination of chlorine and sodium in a fixed proportion, one atom of one substance for one atom of the other. Salt has no physical or chemical property of one or the other. This is different from a simple mixture, without combination, which can be made in whatever proportion). In the same time, German chemist Jeremias Benjamin Richter (1762-1807) also stated this law of

5. Antoine Laurent Lavoisier, Elements of Chemistry, Edinburgh, 1790, transl. R. Kerr, Preface, p. xxiv.

6. Joseph-Louis Proust, ‘Recherches sur le bleu de Prusse‘, Journal de Physique, de Chimie, d’Histoire naturelle et des Arts, vol.VI, issue 50, p. 241–251, 1799.

7. Joseph-Louis Proust, ‘Extrait d’un Mémoire intitulé: Recherches sur le Bleu de Prusse ’, Journal de Physique, de Chimie, d’Histoire naturelle et des Arts, vol.II, issue 45, p. 334–341, November 1794.

constant composition, formulated in a work of three volumes published between 1792 and 1794, in which he introduced the term stoichiometry to designate the way of measuring the relative proportions of elements in a chemical compound.

Unfortunately his work, in German and in a style difficult to follow, was little disseminated and remained rare. It was through the relation by Berthollet in his book Essai de statique chimique, published in 1803, that Richter became known.


The law of constant composition had an impact on the English physicist John Dalton (1766-1844). For him the sole explanation was that all substances were composed of atoms - elements that combined themselves to form compound bodies. Based on some general hypotheses, he saw there a means to determine the relationships between masses of diverse bodies. In his notebook we may find

on 6th September 1803:

(i) m atter consists of sm all ultim ate particles or atom s (ii) atom s indivisible and cannot be created or destroyed [...] (iii) all atom s of a given elem ent are identical and have the sam e invariable weight (iv) atom s of different elem ents have different weights (v) the particle of a com pound is form ed from a fixed num ber of atoms of its fixed of is com ponent elem ents (law of fixed proportions) Dalton uses the term ‘particle’ for what we now call a ‘molecule’, the smallest part of a substance. He uses the word ‘atom’ to refer to the tiniest part of a simple body or an element. His theory is exposed in a book, the first part of which appeared in 1808, the second in 1810 and the last in 1827.

In the first part, after having stated the principles, he draws up a list of possible

ways in which two or more atoms can combine:

If there are two bodies, A and B, which are disposed to com bine the following is the order in which the com binations m ay take place beginning

with the m ost sim ple, nam ely:

1 atom of A + 1 atom of B = 1 atom of C, binary, Jeremias Benjamin Richter, Anfangsgründe der Stöchyometrie oder Meßkunst chymischer Elemente, (3 vols.) J. F. Korn, Breslau & Hirschberg, 1792-94.

C laude-Louis Berthollet, Essai de statique chimique, Firmin Didot, Paris, 1803.

10 Quote from James Riddick Partington, A History of Chemistry, London, MacMillan, 1931-1964; vol. III,

–  –  –

And he adds what could be called a ‘postulate of simplicity’:

The following general rules m ay be adopted as guides in all our

investigations respecting chem ical synthesis:

1st When only one com bination of two bodies can be obtained, it m ust be presum ed to be a binary one, unless som e cause appear to the contrary.

Figure 2: Table of elements by John Dalton (from his book New System of Chemical Philosophy, 1808). In the middle of each of the two columns we find the name of the element (‘Lime’ represents calcium, ‘Soda’ - sodium, ‘Potash’ - potassium); on the left we have symbols, and on the right are atomic weights as determined by Dalton at that time and later corrected by Avogadro so that they come very close to the values accepted today.

It is notable that Dalton slightly changed his terminology; now he called ‘atom’ the smallest part of a substance, namely of an element or simple body,

12. John Dalton, New System of Chemical Philosophy, op. cit., Vol. I, p. 213.

and of a compound body – a compound of two or more atoms (what we call a ‘molecule’). Hence Dalton speaks of an ‘atom’ of water, according to him constituted by combination of an atom of oxygen and an atom of hydrogen.

The proportion of masses of oxygen and hydrogen had been known since Lavoisier, who estimated it as 7 or 7½ to 1. Yet Dalton maintained it was 6 to 1, and concluded from this that an atom of oxygen is six times heavier than that of hydrogen (though in the second part of his book, published in 1810, he retained 7 to 1). Step by step, a means to determine the relative masses of atoms emerged. The idea that matter is co mposed of atoms was no longer speculation devoid of practical consequences; Dalton in fact threw together the foundations of modern atomism.


On 31st December 1808 Louis-Joseph Gay-Lussac gave a lecture at the Philomatic Society of Paris, soon published in Mémoires de la Société d'Arcueil. At first glance his discovery seems incompatible with Dalton's theory.

Gay-Lussac observed that, during chemical combination between two gases, their volumes are in direct proportionality, and that if the result is a gas,

its volume is also directly proportional to the volumes of the reactants:

Compounds of gaseous substances with each other are always form ed in very sim ple ratios, so that representing one of the term s by unity, the other is 1, 2, or at m ost 3... The apparent contraction of volum e suffered by gas on com bination is also very sim ply related to the volum e of one of them.

For example a litre of oxygen combines with two litres of hydrogen to produce two litres of water (in gaseous form); this is what we now express by the equation O2 (one volume of dioxygen) + 2H2 (two volumes of dihydrogen) → 2H2O (two volumes of water).

There are two very surprising results:

the relations of volumes are in direct proportionality, yet the relation between the volumes of the reactants and the product of the reaction is also in direct proportionality. Moreover, as in the case of water, we start with three litres

13. Thomas Thomson, New System of Chemistry, vol. III, p. 442.

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