Charles de Marignac (1817-1894)

Chemical Equivalents and Atomic Weights considered as bases of a system of Notation

Moniteur Scientifique 19, 920-6 (1877), translated by P. Casamajor, American Journal of Science 115, 89-98 (1878) [facsimile published in Mary Jo Nye, The Question of the Atom (Los Angeles: Tomash, 1984)]

The Academy of Sciences in Paris has witnessed lately, at several of its sittings, an interesting discussion, in which several eminent chemists, among its members, have taken part.[1] This discussion related to two questions which have often been brought before it, and which will probably be brought before it again many times.

One subject of discussion was a principle, stated in 1811 by an Italian philosopher, Avogadro, on the equality of the molecules of all bodies in a gaseous state. This principle is often placed in opposition to the law of Gay Lussac, on the simple relations which exist between volumes of gases, capable of combining with one another, which law was established a few years before, and which, to tell the truth, is not in contradiction with the hypothesis of Avogadro. From this question arose another, on the relative merits of the chemical notations, expressed in equivalents or atoms.

For the present, I will not discuss the first of these questions. The truth of the principle of Avogadro can only be admitted on the condition of supposing that the atoms of simple gases cannot exist in a free state, but are welded together in pairs, forming molecules occupying two volumes, like the molecules of compound bodies. Exceptions should be made for mercury and cadmium, whose molecules are formed of only one atom, and for phosphorus and arsenic, whose molecules must contain four atoms.

This hypothesis is not absurd in itself. It may account for certain chemical facts, such, for instance, as the greater energy of action that bodies possess in a nascent state, or before their atoms have combined two by two to form molecules; also for the ease with which certain reactions take place, as pointed out by M. Würtz. It also explains several physical facts, such as the equality of specific heat for the same volume of simple or compound gases, whose molecule is formed of two atoms, as carbonic oxide, hydrochloric acid. It found lately an important confirmation in the researches of Messrs. Kundt and Warburg[2] on the specific heat of vapor of mercury, which show that this heat agrees with the mechanical theory of heat for monatomic gases, and that this agreement does not exist for other simple gases. We must acknowledge, however, that these considerations do not constitute sufficient proofs.

On the other hand, there are some compound bodies whose vapor densities are in contradiction with the principle of Avogadro. We should be forced to admit that all these compounds suffer decomposition when they seem to be reduced to vapor, so that, instead of measuring their volume, we measure that of their elements, or of the products of their decomposition. Although this decomposition has been ascertained in some cases, it has not in all.

As may be seen, the principle of Avogadro gives rise to many serious objections, and, without being convinced of its worthlessness, like my eminent friend, M. Deville, I acknowledge that it is as yet but an hypothesis, in contradiction with facts, which have not been satisfactorily explained. But, I repeat it, I have no wish to enter into this discussion at present, as it would require to be extensively developed, and it can only be definitely settled by long and difficult experiments. I have recalled this discussion because its solution must exert a certain influence on chemical notations, although the connection between the two questions is not necessarily very close.

As to the best system of notations, it may be necessary to explain why such a question is raised and can only be raised in France. In every other country the question has solved itself gradually, as chemists have, one after another, accepted the atomic notations, and given up the formulas by equivalents in their writings and in their teachings.[3] In this gradual manner, in almost every country, by the successive assent of the great majority of chemists, atomic formulas have been substituted for the others without any formal struggle. In France, however, it has been very different. I am not aware whether the regulations of the University[4] forbid a professor from adopting the method of instruction which he thinks best, or whether teachers adopt a uniform system from the belief that otherwise their pupils would be placed in a relatively inferior position, if they did not adopt the system most in favor with examiners; at any rate, such an important change, as the introduction of a system of chemical notation, can only be generally introduced when it has been judged necessary, not only by the majority of teachers, but also by the Superior Councils, which govern the University, and, in these, chemists are not the only persons who have influence. It is easily understood that, under these conditions, the partisans of both systems wish to have them discussed in the presence of the scientific body which has the greatest authority, with the object of maintaining the established system, or of introducing the other.

To enter into this discussion, it is doubtless advisable, in the first instance, to define what is understood by these equivalents and these atomic weights, which are placed in opposition to one another.

As to equivalents, I see that M. Berthelot tells us that "their definition is a clear conception." Unfortunately he did not give this definition, and I confess that I do not know of any, at least of any that is precise and general. Doubtless when we compare, with one another, elements, such as chlorine, bromine and iodine, the definition of their relative equivalents is perfectly clear, as the term equivalent is its own definition. But when we deal with bodies which have not a similar analogy, and particularly if they do not perform the same functions, the idea of equivalence has no meaning. I defy anybody to give a general definition of equivalents which justifies the weight 14, adopted for nitrogen. In volume, it corresponds to the equivalents of hydrogen and of chlorine, but it has not the same chemical value. It has the same chemical value as the equivalents of phosphorus and arsenic, but it does not occupy the same volume. Moreover, it corresponds neither in volume nor in chemical value to the equivalents of oxygen, of sulphur and of most metals. Why then should this number exist?

If, instead of starting from a general definition, which does not exist, we try to find the meaning of equivalents in the methods employed in determining them, we are led to the following conclusion:

It is proved by experience that we may assign to a body, be it simple or compound, various weights, multiples of the same number, and that these weights express the proportions according to which all bodies combine with one another. We may choose one of these weights to express the equivalent of the body. All combinations may then be represented by formulas which are not generally complicated. This is, after all, the only condition required of equivalents, and hence the only general definition, although not very precise, which can be given is that the equivalent represents for every element or compound body one of the weights which may combine with other equivalents. Theoretically it matters little which of the weights is chosen. Practically, however, one of the weights is preferred, taking as a guide one of the following rules, which cannot be considered as very rigid, as they do not all lead, in all cases, to the same result:

1. When bodies are analogous, and have the same chemical character, their equivalents are represented by the weights which replace each other in analogous combinations. Let us note, however, that this rule is not followed for compound bodies, such as bases and acids, whose so-called equivalents are weights which often have very different values of combination, and we are thereby led to very singular anomalies of statement, such as these: two equivalents of alumina corresponds to three equivalents of magnesia; one equivalent of phosphoric acid to three of nitric acid, &c. In reality the fundamental principle of equivalents has been entirely abandoned for compound bodies, and, in its stead, a method has been adopted, which has been borrowed from the atomic theory, by taking for their weights the sum of the equivalents of the elements which they contain.

I believe I am not in error when I affirm this, as M. Berthelot[5] says: "One equivalent of phosphoric acid corresponds to three equivalents of nitric acid, when it forms a tribasic phosphate."

2. Equivalents are chosen in such a way that compounds, which offer the greatest analogies, are represented by similar formulas. This principle served as a guide in determining the equivalents of aluminum and of copper. It is often in contradiction with the preceding. For instance, aluminum and magnesium, which are both powerful deoxidizing agents, do not replace each other in the proportions indicated by the equivalents adopted for these two metals.

3d. When neither of these rules is applicable, or when they lead to complicated formulas, the equivalent of a body is chosen in such a way as to give the simplest possible formulas for its most important combinations. This rule justifies the adoption of the equivalents of nitrogen, phosphorus, arsenic and of some other elements.

We may see by the above that the equivalents constitute a purely conventional and arbitrary system, without any scientific value.

The explanation I have given of equivalents is somewhat different from that which my illustrious teacher, M. Dumas, gave in his lessons of chemical philosophy. This eminent chemist took as his starting point the equivalents of bases, as determined by their true chemical equivalence, founded on the same quantity of oxygen contained in the base. The equivalents of acids are rigorously deducted from the weights necessary to neutralize an equivalent of base. Afterwards, he seeks to establish the equivalents of the elements by considerations which, he acknowledges, are often arbitrary. This method of determining equivalents however, has been either never adopted, or entirely abandoned, doubtless because it led to formulas which are inadmissible. I have given the meaning of equivalents, such as they have been adopted, and not such as they might have been.

We may now consider the definition of atomic weights. If the precise definition of equivalents is impossible, while their determination is comparatively easy, for they are adopted by arbitrary rules, it is the reverse with atomic weights.

If we refer to the fundamental hypothesis of the atomic theory, which supposes that the divisibility of bodies is not indefinite, but that they are formed by the agglomeration of excessively small but indivisible particles, or atoms, the theoretical definition of atomic weights is of the simplest, as they are the relative weights of these ultimate particles. But, however simple the definition may be, the determination of the weights is surrounded with great difficulties.

The hypothesis of the existence of atoms accounts in such a simple manner for that of chemically equivalent proportions for elements which play the same part, that we are naturally led, at first sight, to consider these proportions as representing their relative atomic weights, although this consequence is not rigorously necessary. It is evident, however, that as neither this consideration of chemical equivalence, nor any other consideration drawn from chemistry alone, has led to a complete and logical system of chemical equivalents, we cannot by such considerations be guided in the choice of all the atomic weights, and as these, on account of the hypothesis that is made on their nature, cannot be arbitrary, like equivalents, it has become necessary to study the physical properties of the elements and of compound bodies to find motives for this determination of the atomic weights. Among the properties which can be appealed to, the most important are the densities of gases and vapors, the specific heats and isomorphism.

I acknowledge that in some very rare cases these three orders of physical properties do not lead to the same result, and I agree with M. Berthelot that between these three data we must make a choice. I am, however, in complete disagreement from him in the conclusion that I draw from this. If he does not say so expressly, his whole argument proves that, in his opinion, no account is to be taken of these physical properties, when they disturb the usage established for weights that have been adopted for a long time in chemical notations. On the contrary, I think that great account should be taken of these physical properties, and that when they all agree we must have no fear of modifying a few formulas which have only long usage in their favor, particularly if the necessary modification is unimportant. If, moreover, the physical properties do not agree, it is necessary to study the facts with the greatest care, and see if, in some cases, a disagreement can be explained and then choose the weight which agrees the best with the general properties of the elements and its combinations.

Is it impossible to do this? The best proof that it is not, and that there is even no serious difficulty in determining the atomic weights which agrees the best with the physical properties, is to be found in this circumstance that there is no disagreement among chemists, who accept this system of notation, as to the atomic weights, except for a few bodies that are not, as yet, sufficiently known; whose physical properties have not been sufficiently studied, and for which, besides, the idea of equivalents is quite as uncertain as that of atomic weights.

I am perfectly aware that the majority of chemists, who have adopted atomic formulas, believe that they are now able to give a rigorous definition of atomic weights. Starting from molecules, which they define as the smallest quantity of a body, simple or compound, which can exist in the state of liberty; admitting as an axiom the principle of Avogadro, which states the equality of volume of all molecules in a gaseous state, from which may be deducted their relative weights, they define the atom as the smallest quantity of a body which may enter into the composition of a molecule. This definition allows them to determine the atomic weights with certainty, at least for those bodies that enter into volatile combinations. I have not given great weight to this consideration because, not more than Messrs. Deville and Berthelot, do I regard the principle of Avogadro as absolutely demonstrated. But I wish it to be specially noticed that there is not so far as I know, a single case in which the application of the above definition of atomic weight has been used to change an atomic weight previously obtained by considerations based on the physical properties. Perhaps I should except boron and silicon; but the atomic weights of these elements had never been considered as firmly established, nor indeed had their equivalents. This observation might be appealed to as the strongest proof of the accuracy of the definition of atomic weights, but I have no wish to admit it, as constituting a sufficiently sure base for the determination of atomic weights.

I have here to answer an objection, which I acknowledge to be serious, and which I believe is at the bottom of the opposition of M. Berthelot. The atomic weights rest on an hypothesis which has never been, and, in fact, can never be demonstrated, which many scientific men do not consider as verisimilar, that of the existence of atoms.

I am nearly ready to agree with M. Berthelot in his opposition, and I have certainly no idea of defending the atomic theory, but merely the chemical notations founded on the atomic weights. My answer to the objection stated above is that the existence of atoms is only useful in justifying the name of atomic weights,which, for my part, I would very willingly have replaced by any other. I know of no case in which an atomic weight has been determined by a method founded on the indivisibility of atoms; consequently we may consider atomic weights as entirely independent of this indivisibility. In reality, I consider atomic weights, and I believe that many chemists agree in this, as being only equivalents, in the determination of which arbitrary conventions have been replaced by scientific considerations, based on the study of physical properties.

Let us now sum up the advantages that atomic notations present from this point of view.

For the elements, in the first place, the atomic weights represent equal volumes of all simple gases, so that their ratios of combination in volumes are directly expressed by atomic formulas, while the formulas in equivalents do not offer this advantage. This law presents some exceptions for vapors, in the cases of phosphorus, arsenic, mercury and cadmium, but the same divergence exists for equivalents.

Atomic weights are exactly proportional to the specific heats of simple gases, that are not liquifiable, which agreement does not exist for equivalents. According to the law of Dulong and Petit, the specific heats of the atoms of all simple bodies, either solid or liquid, are nearly the same, except for three bodies, carbon, boron and silicon, whose physical properties offer numerous irregularities, and in which the specific heat varies with the temperature in a manner unknown in other bodies. Equivalents do not offer this concordance. I will not insist on the objection raised by M. Berthelot, and founded on this, that the equality of specific heats of atoms is far from being absolute, as he was sufficiently answered by MM. Würtz and Fizeau. I will merely add that if we only admitted physical laws that are absolute, we should have to reject them all. Even the law of volumes of Gay Lussac would have to be dropped, as it has been ascertained that all gases have not the same coefficient of expansion, so that the existence of simple ratios in combinations by volume are not strictly accurate.

As to compound bodies, the molecular formulas, based on the use of atomic weights, present the same advantages, perhaps to a higher degree, when we compare them to the formulas in equivalents.

The use of atomic weights allows us to simplify the formulas of a great number of compounds by dividing them by two. Particularly is this the case with organic compounds. Not only does the formula become simpler, but there is an important advantage gained, that the formulas of almost all compounds correspond to the same volume, which is double the volume of the simple atom. The only exceptions are for a very limited number of bodies, generally belonging to types of complex composition, such as salts of ammonia and of bases derived from ammonia; even for these it has not been proved that they are not regulated by any law, even if M. Deville is right in thinking that the irregularities they present are not due to the decomposition of the vapors. On the other hand, the formulas by equivalents teach us nothing on the vapor densities of compound bodies, as their equivalents may correspond to two, four or eight volumes of vapor, perhaps even of six, if the old equivalent of silicon is kept, as is done by many of those who prefer the notations by equivalents. Molecular formulas also agree with the specific heats of compound bodies in the solid state. According to the law of Woestyn, molecular heats are proportional to the number of the atoms contained in the molecule, which law has the same degree of approximation as that of Dulong and Petit. Formulas by equivalents do not show these properties.

Finally, the system of notation, based on atomic weights, gives the explanation of several cases of isomorphism which are incomprehensible with the notation based on equivalents. For instance, in the case of perchlorates and permanganates, and in the case of chloride and sulphide of silver when compared to protochloride and protosulphide of copper. I may also recall that it was by considerations of the same kind that I was led to discover oxygen in fluorine compounds of niobium, where its presence had not been suspected, and that the formulas of these compounds, expressed in equivalents, would never have suggested this idea.

In presence of these advantages, we may ask: what are those that are offered by the system of equivalents and its resulting notation? I believe I can indicate two.

In the first place, as the system is conventional, it does not of itself contain any necessary reason for changes, and it may remain invariable. As there was no serious motive for choosing the number fourteen as the equivalent of nitrogen, rather than seven, which would have given it the same volume as oxygen, or 14/3 which would have accounted for its value of combination toward hydrogen and the metals, we may readily believe that there will never be a sufficient motive to replace it by one of these numbers. The determination of equivalents not being governed by any fixed rule, they will not be necessarily modified when we come to have a more accurate knowledge of the properties of bodies.

In the second place, as, in their determination, no account is taken of the physical properties of bodies, greater attention can be given to their chemical equivalence, when it exists. This presents some advantages in practical chemistry.

These considerations are doubtless of some value; but if we examine things a little closer, we may easily see that, in this respect, there is really very little difference between the two systems.

It is true that there was a time when atomic weights had to be changed, and it is doubtless, on this account, that atomic weights were dropped and equivalents adopted. Nevertheless, the history of chemistry shows that for more than thirty years no changes have been judged necessary for well known bodies, and that those which have been admitted for elements, whose properties or whose combinations had previously been imperfectly known, were so thoroughly justified by their chemical properties, that even the equivalents of these bodies have had to be modified. Such was the case for bismuth, uranium, vanadium, tantalum and niobium. In reality, the only important change that atomic weights have had to suffer, since their introduction in chemical science, has been the reduction to half of the weights of silver and of the alkaline metals, a reduction based on their specific heat of their combinations, or on isomorphism as was done in the first instance by M. Regnault.[6] We may see by this that, on the score of invariability, the two systems are on a par.

As to the advantage which results from the fact that equivalents express ratios of real chemical equivalence, in cases where they are not indicated by atomic weights, it would be an important one if chemical equivalence were indicated in all cases; but we know that this is not so. It is really not more difficult to conceive and to remember that an atom of oxygen is worth two of chlorine, and an atom of lead two of silver than to know that an equivalent of nitrogen is worth three of oxygen, and that two equivalents of aluminum are worth three of magnesium. So there is really no advantage, on these two heads, which can counterbalance those which I have shown for atomic notations.

It may be said that the preceding is a contradiction of what I said before. I said that the system of equivalents presents conditions of invariability that are not presented by atomic weights. Further on I have shown that every change of atomic weight had necessitated a corresponding change in equivalents.

If we look for the cause of this apparent contradiction, it seems to me that we shall be led to make an observation which gives the key to the discussion actually going on. It is that, in reality, if we keep out of sight every question as to the origin of the terms equivalents and atomic weights, there is no difference between the two systems, and the partisans of equivalents are willing enough to accept the principles which serve to determine atomic weights, except when the necessity arises of changing the formulas of bodies that are of great importance and occur with great frequency.

[1]Messrs. Sainte Claire Deville, Würtz, Berthelot, Fizeau. [original note]

[2]Berichte der deutschen Chemischen Gesellschaft, 1875, p. 945. [original note]

[3]Fresenius still considers the formulas in equivalents as the best. --Translator

[4]The entire educational system of France is consolidated under one organization, called the University, comprising faculties of letters, medicine, law and theology, lycées for secondary instruction and schools of primary instruction. --Translator.

[5]Meeting of the Académie des Sciences of June 4th, 1877. I cannot in any manner accept what he says, in the same place, that this equivalent of phosphoric acid corresponds to one equivalent of nitric acid in monobasic phosphates, or two equivalents in bibasic phosphates. To admit such expressions, we must deny to water the part that all chemists attribute to it in these salts, since the publication of Graham's researches. [original note]

[6]Annales de Chimie et de Physique, 1841, III, vol. i, p. 191. [original note]

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