Jöns Jacob Berzelius (1779-1848)

Essay on the Cause of Chemical Proportions, and on Some Circumstances Relating to Them: Together with a Short and Easy Method of Expressing Them.

Annals of Philosophy 2, 443-454 (1813), 3, 51-2, 93-106, 244-255, 353-364 (1814) [from David M. Knight, ed., Classical Scientific Papers (New York: American Elsevier, 1968)][1]

II. On the Cause of Chemical Proportions.

The fact that bodies combine in definite proportions when other forces do not oppose their re-union, added to the observation that when two bodies, A and B, combine in different proportions, the additional portions of the one are always multiples by whole numbers, 1, 2, 3, 4, &c. lead us to conclude the existence of a cause in consequence of which all other combinations become impossible. Now what is that cause? It is obvious that the answer to this question must constitute the principal basis of chemical theory.

When we reflect on this cause it appears at first evident that it must be of a mechanical nature; and what presents itself as the most probable idea, and most conformable to our experience, is, that bodies are composed of atoms, or of molecules, which combine 1 with 1, 1 with 2, or 3, 4, &c.; and the laws of chemical proportions seem to result from this with such clearness and evidence, that it seems very singular that an idea so simple and so probable has not only not been adopted, but not even proposed before our own days. As far as I know, the English philosopher, Mr. John Dalton, guided by the experiments of Bergman, Richter, Wenzel, Berthollet, Proust, and others, was the first person who endeavoured to establish that hypothesis. Sir H. Davy has lately assured us that Mr. Higgins, in a book published in 1789, established the same hypothesis. I have not seen the work of Mr. Higgins, and can only notice the circumstance on the authority of Davy.[2]

Notwithstanding the great clearness and simplicity which characterize this hypothesis, it is connected with great difficulties, which make their appearance when we apply it to a number of chemical phenomena. These difficulties naturally excite doubts as to the truth of the hypothesis. Among the numerous experiments which I have made in order to discover the chemical proportions in which bodies unite, I have met with cases when, notwithstanding the completest agreement with the laws which I conceived myself to have discovered, the composition of a body could not be explained according to the hypothesis which we are considering. I shall state some of these cases, without, however, considering them as absolute proofs against the hypothesis, but rather as difficulties which we must endeavour to surmount, in order to obtain a clear and well established theory of chemical proportions.

I shall begin with a short explanation of the corpuscular theory, such as I conceive it. I shall employ the word atoms to signify the corpuscles, or smallest parts of which bodies are composed. When I say the smallest parts, I mean that they cannot be divided into other parts still smaller. I do not enter into any discussion whether matter be infinitely divisible or not, but take it for granted that an atom is mechanically indivisible; and of course that a fraction of an atom cannot exist. I suppose likewise that atoms are all spherical, and that they have all the same size. (This last circumstance is not necessarily attached to the idea of atoms, but it is absolutely necessary if regular figures are to result from their union, and if they unite in definite proportions, even in the most complicated combinations). It appears likewise necessary that when an atom of the body, A, combines with one or more atoms of the body B, to form a new compound atom, the atom of A touches each of the atoms of B. Hence a compound atom is formed by the juxtaposition of several elementary atoms; just as an aggregate is formed by the juxtaposition of different homogeneous atoms. But the difference consists in this, that in the first case an electric discharge takes place of the specific polarity of the heterogeneous atoms, which cannot take place between homogeneous atoms. (See my conjectures on this subject in Nicholson's Journal for March 1813, p. 154.)

A compound atom, for very obvious reasons, cannot be considered as spherical; but as it is composed of atoms mechanically indivisible, or which cannot be separated by mechanical means, the compound atom is justly as completely mechanically indivisible as the elementary atom. It is likewise evident that an atom composed of A + 3B ought to be greater, and to have a different figure from an atom composed of A + B. The former ought to have the form of a triangular and equilateral pyramid, while the latter must have a linear form.

We may divide the atoms into two classes: 1. Elementary atoms: 2. Compound atoms. The compound atoms are of three different species; namely, 1. Atoms formed of two elementary substances united. We shall call them compound atoms of the first order. 2. Atoms composed of more than two elementary substances: and as these are only found in organic bodies, or bodies obtained by the destruction of organic matter, we shall call them organic atoms. 3. Atoms formed by the union of two or more compound atoms, as, for example, the salts. We shall call them compound atoms of the second order.

The greatest number of spherical atoms of the same diameter, capable of touching a single atom of the same diameter, is 12. Hence it follows that A + 12B contains the greatest number of atoms which a compound atom of the first order can contain. If, on the other hand, we pay attention to the electric polarity of the atoms, an atom of A cannot combine with more than 9 atoms of B, if the atom A + 9B preserve any part of the electric polarity originally belonging to A: for example, oxymuriatic acid, which is a compound of 1 atom of muriatic radicle and 8 atoms of oxygen, still preserves a part of the original polarity of the radicle, by means of which it re-acts; while the supersulphuret of arsenic, of which I shall give an account in the sequel, and which is composed of 1 atom of arsenic and 12 atoms of sulphur, has no other electrochemical re-action than that of sulphur.

It is contrary to sound logic to represent a single compound atom of the first order as composed of 2 or more atoms of A combined with 2 or more atoms of B; as, for example, 2A + 2B, 2A + 3B, 7A + 7B, &c.: for in such a case there is no obstacle, either mechanical or chemical, to prevent such an atom from being divided, by means purely mechanical, into 2 or more atoms of more simple composition. Besides, such a composition would almost totally destroy chemical proportion. Hence it follows, that in stating the result of an analysis conformably to the views of the corpuscular theory, we must always consider one of the constituents as unity, that is to say, as a single atom. What I have stated here appears to me to be necessary consequences, or reflections inseparable from the theory of atoms, not one of which can be rejected without committing what is called contradictio in adjecto.

I shall now give an account of the difficulties to which I conceive the corpuscular theory is liable.

1. The first of these difficulties is, the circumstance that there are combustible bodies, iron, for example, which unite only with two doses of oxygen, the second of which is only 11/2 times greater than the first. This difficulty, however, is only apparent: for I have already, in my former memoirs on this subject, shown that, in all probability, it is owing to our being still unacquainted with all the degrees of oxidation of which the body in question is capable. The multiple of 11/2 implies the existence of an inferior degree of oxidation to that which we consider as the minimum. I hope in this essay to prove the truth of this opinion in a still more satisfactory manner.

2. I think I have proved that when two oxides combine they always unite in such proportions that each contains either an equal quantity of oxygen, or the one contains a quantity which is a multiple by a whole number of the oxygen in the other. This law, though in itself conformable to the corpuscular theory, admits, on the one side, of combinations inconsistent with that theory; and, on the other hand, it excludes combinations perfectly conformable with that theory. I shall explain this by an example. Let O be oxygen, A and B two combustible bodies. The law which we are considering admits of a combination of A + 3O with 11/2 BO, because 11/2 x 2 = 3: and we shall see immediately that such combinations exist, though, according to the corpuscular theory, they appear absurd. On the other hand, the law does not admit the combination of A + 3O with B + 2O, though such a combination be conformable to the theory of atoms. The black oxide of copper is composed, according to our present knowledge, of 1 atom of metal and 2 atoms of oxygen, and sulphuric acid of 1 atom of sulphur and 3 atoms of oxygen. We know that there is a subsulphate of copper in which the acid and the oxide contain each equal quantities of oxygen. Of course, this subsulphate must contain for every atom of sulphuric acid an atom and a half of oxide of copper. It is true that we may object to this, that there is some appearance that sulphuric acid is composed of 6 atoms of oxygen to 1 of sulphur. But I shall have occasion to discuss this opinion when I come to speak particularly of sulphur. Arsenic acid, from new experiments of which I shall give an account in the sequel, is composed of 1 atom of arsenic and 6 atoms of oxygen. The yellow oxide of lead is composed of 1 atom of metal and 2 atoms of oxygen. The arseniate of lead is composed in such a manner that the acid contains three times as much oxygen as the oxide, that is to say, of an atom of acid and an atom of oxide. The subarseniate of lead is composed in such a manner that the acid contains twice as much oxygen as the oxide; that is to say, of an atom of acid and an atom and a half of oxide.

If we suppose that the yellow oxide of lead contains but one atom of oxygen, this subsalt ceases to be an objection to the atomic theory; but in that case we meet with an equally formidable objection in the composition of the red oxide of lead.

I have endeavoured to prove that two different oxides of the same radicle sometimes combine in such a manner that each contains an equal quantity of oxygen, or that the one contains two, three, &c. times as much as the other. Among these combinations there are some which do not agree with the hypothesis of atoms: for example, the red oxide of iron contains 3 volumes of oxygen, and the black oxide 2 volumes. Gay-Lussac has lately found that the oxide of iron formed at a high temperature by the action of the vapour of water is composed of 100 iron + 37.8 oxygen. But this combination of the two oxides is composed in such a manner that the red oxide in the compound contains exactly twice as much oxygen as the black: that is to say, that it is composed of 11/2 atom of the first and 1 atom of the second. One method of refuting this objection would be to consider the black oxide of iron as containing 4 atoms of oxygen, the red as containing 6, and the intermediate oxide as containing 5: but in this case he analysis of Gay-Lussac is incorrect. He should have obtained 36.8 of oxygen instead of 37.8. But we are not at present acquainted with any example of a body containing 5 atoms of oxygen; and I shall prove in the sequel that the oxide in question cannot be considered as a particular oxide, since it possesses all the characters of a compound of the red and black oxides of iron.

3. We have seen that an elementary atom cannot combine with more than 12 elementary atoms. Inorganic nature has not yet presented us with any body which is inconsistent with this supposition: but among organic bodies such examples are very frequent. It is in the study of the composition of organic bodies that our knowledge of the laws of chemical proportions, and of the electrochemical theory, will one day reach that degree of perfection which the human mind is capable of giving it. I shall give the composition of oxalic acid as an example of the constitution of an organic atom. I analysed this acid by decomposing it, by distilling oxalate of lead mixed with a quantity of brown oxide of lead, and making the gaseous products pass through muriate of lime, and then through limewater. I repeated this analysis with so little variation, that I consider my results as a close approximation to the truth. In neither of these analyses did I obtain as much water as amounted to a quantity of hydrogen equivalent to 1 per cent. of the acid: but we cannot conceive an atom of oxygen to be united with a fraction of an atom of hydrogen. We must therefore consider the small quantity of hydrogen which we obtain as an entire atom. If we admit water to be a compound of 2 atoms of hydrogen and 1 atom of oxygen, and carbonic acid of 1 atom of carbon and 2 atoms of oxygen, it follows from my analysis, that the atom of oxalic acid is composed of 1 atom of hydrogen, 27 atoms of carbon, and 18 atoms of oxygen; that is to say, that it consists of an atom of hydrogen combined with 45 other atoms.

If, on the other hand, we chuse to consider the organic atoms as consisting of an atom of compound radicle combined with 1 or more atoms of oxygen, and of course oxalic acid as composed of an atom of radicle and 3 atoms of oxygen: the radicle in that case will be a compound of 1 atom hydrogen + 27 atoms carbon, and will remain equally inapplicable to the hypothesis of atoms. It follows, likewise, that an atom of oxalic acid is eleven times greater than an atom of sulphuric acid, and fifteen times greater than an atom of potash: yet in the superoxalate of potash discovered by Dr. Wollaston an atom of potash should be combined with 11/2 atom of oxalic acid.

I have already, in preceding memoirs, made mention of another method of viewing chemical proportions--a method founded on a fact discovered by Gay-Lussac; namely, that bodies when in the state of gases unite either in equal volumes, or 1 volume of one combines with 2, 3, &c. volumes of the other. This fact has been already verified by several distinguished chemists. From what we know respecting definite proportions, it follows, that it would hold with all bodies in the temperature and pressure at which they would assume the gaseous form. Hence there is no other difference between the theory of atoms and that of volumes, than that the one represents bodies in a solid form, the other in a gaseous form. It is clear, that what in the one theory is called an atom, is in the other theory a volume. In the present state of our knowledge the theory of volumes has the advantage of being founded upon a well constituted fact, while the other has only a supposition for its foundation. In the theory of volumes we can figure to ourselves a demi-volume, while in the theory of atoms a demi-atom is an absurdity. On the other hand, the theory of volumes has a disadvantage from which the atomic theory is free; namely, the existence of compound bodies, especially of an organic nature, which we cannot suppose ever to have existed in the form of gas.

I ought to observe, that we have here, as well as in the theory of atoms, elementary volumes and compound volumes of the first and second order . It follows from the laws of chemical proportions, that two compound volumes, containing a common constituent, ought to combine in such a manner that they contain either equal volumes of this common constituent, or that the one contains two, three, &c. times the number of volumes of the other. It is almost demonstrated that an elementary volume never combines with 11/2 volume of another elementary substance: but at present we are obliged to admit that this sometimes happens with compound volumes.

In the theory of volumes we cannot suppose the combination of 2 volumes with 3, &c.: for on such a supposition there can be no reason assigned why 4 volumes should not combine with 5, 7 with 9, 999 with 1000, &c.: so that in such a case no reason could be assigned for the existence of chemical proportions. Here, as well as in the theory of atoms, it is absolutely necessary that in each compound one of the constituents should be considered as a single volume.

It is evident that if the weight of the volumes of the elementary bodies be known, and expressed in numbers, we have nothing more to do in every case of analysis but to count the relative number of volumes of the constituent parts, whatever the form of their aggregation may be: but in order to obtain the relative weights of the elementary volumes expressed in numbers, that is to say, to obtain their specific gravity in the form of gas, we must have a general measure with which we may compare them. We may chuse among the elementary bodies one, the weight of a volume of which must be denoted by unity; just as water has been chosen for unity in determining the specific gravity of liquids and solids.

There are only two elementary bodies possessed of the requisite qualities to serve as our unit. These are oxygen and hydrogen. But hydrogen has disadvantages from which oxygen is free. The weight of a volume of hydrogen is so small, that if we employ it as our unit, the number representing a volume of some of the metals becomes inconveniently great. Besides, hydrogen enters much less frequently into compounds than oxygen; and of course the number 100, when applied to hydrogen, does not nearly so much facilitate calculation as when it is applied to oxygen. Add that oxygen constitutes among elementary bodies a particular class, and, as it were, the centre round which chemistry turns. It exists in the greater number of unorganic bodies, and without exception in all the products of organic nature. I think, then, that it is at once most convenient, and most agreeable to the scientific views of chemistry, to take oxygen as our unit. I shall represent its volume by the number 100.

The question which we have now to resolve is this, What is the specific gravity of all other elementary bodies in the form of gas, compared with that of the oxygen? This question is not easily answered: for at present there are no other bodies except oxygen and hydrogen which we are capable of weighing in the state of gas. All other bodies are converted into gas at such high temperatures that it is not in our power to ascertain their weight. We must therefore endeavour to discover the weight of their volumes by other means. Our results will be, doubtless, very uncertain; but not altogether unsuccessful; as I hope to be able to show in the sequel.

In the first place, it appears reasonable to suppose that bodies ought to combine most generally in equal volumes: but in examining the greatest number of the combination of elementary bodies, we find that those which are distinguished by a strong affinity between their constituent parts, and by the force of their chemical affinity for other bodies, contain evidently more than one volume of one of their elements. This is the case with water, carbonic acid, nitrous gas, &c., and, with very few exceptions, it is always the electro-negative element the volume of which is multiplied. On the other hand, in bodies composed distinctly of equal volumes, such as the nitric suboxide (azote), and carbonic suboxide (carbonic oxide), we find all the negative properties which characterize the suboxides. This leads me to suppose that all the suboxides are composed of equal volumes of their elements. It follows from these observations that the most part of the salifiable oxides and acids ought to be composed of more than one volume of oxygen for each volume of radicle.

Experiment seems to prove that if a combustible radicle combine in preference with 2 or 3 volumes of oxygen, it combines likewise in preference with 2 of 3 volumes of sulphur. If a salifiable oxide be composed of 1 volume of radicle and 2 or 3 volumes of oxygen; and if we neutralize this oxide by any acid whatever, it is to be supposed that the neutral combination which results ought to contain for 1 volume of the radicle of the oxide as many volumes of the radicle of the acid as the oxide contains volumes of oxygen; and consequently, that the number of times which the acid contains the oxygen of the oxide will be the number of volumes of oxygen combined with 1 volume of the radicle of the acid: for example, we consider sulphuric acid as composed of 1 volume of radicle and 3 volumes of oxygen; because it is very probable that the quantity of sulphur and of oxygen capable of combining at an elevated temperature with a given portion of lead constitute equal volumes. But if we want to know by another method how many volumes of oxygen exist in sulphuric acid, we have only to examine the composition of some sulphate; for example, sulphate of iron (sulphas ferrosus). The black oxide of iron contains 1 volume of metal and 2 volumes of oxygen. It follows, from what has been said, that the black oxide of iron ought to be neutralized by a quantity of acid containing 2 volumes of sulphur for every volume of iron: so that the number of volumes of sulphur of the acid and of the oxygen of the base shall be equal. But the acid contains three times as much oxygen as the base; consequently, it is composed of 3 volumes of oxygen and 1 volume of sulphur. If, instead of the sulphate of iron, we were to make choice of the persulphate of iron (sulphas ferricus), it is evident that in such a case the iron is combined with 3 volumes of sulphur so that the result is just the same.

This observation would be sufficient to determine the volume of a substance whose oxide possesses the character of an acid, or of an electro-negative body, were it not for the numerous exceptions which exist to the rule, some very remarkable instances of which I shall have occasion to notice in the sequel. Hence it is always necessary, in order to discover those exceptions, and to verify the weight of the volume sought to compare the result of the preceding calculation with the known degrees of oxidation of the substance whose volume is wanted. If, for example, we find that an acid or electronegative-oxide is neutralized by a quantity of base or electro-positive oxide which contains 1/3 of the oxygen in the acid, this acid will appear to contain 3 volumes of oxygen. But if among the oxides of the radicle of this we find one which contains half the oxygen of the acid, it is clear that the saline combination in question is an exception, and that the acid must contain 6 instead of 3 volumes of oxygen. I refer, for a farther explanation of this, to what I shall say in the sequel concerning arsenic and chromium.

The preceding observations explain why, when a salifiable base has combined with more oxygen, it requires always an additional volume of acid for every volume of oxygen which it has absorbed. It is for the same reason that oxygen appears to determine exclusively the composition of bodies; though there can be no doubt that every element contributes equally to that composition.

While treating in the sequel of each particular substance, I shall explain the way in which I determine the weight of a volume of it, and likewise state the experiments on which the calculation is founded. As none of our experiments, except from accident, can be perfectly correct, and as a small error in the result often increases in the calculation, it is not possible that my determinations can be perfectly exact: but I hope to approach within very near limits, at least, of the truth. The difference in the analytical results will point out to us the limits of error, and show us degrees beyond which our determinations cannot be incorrect. I shall give an account of these minima and maxima indicated by experiment, as well as of the experiments themselves, which point them out. We have, for example, every reason to believe that a volume of sulphur weighs 201: but some experiments raise it as high as 210, while others sink it as low as 200. As we cannot determine at present which of these numbers is most exact, it is good to know within what limits our knowledge is uncertain.

As far as I know, the English chemists Dalton, Davy, and Young, are the only persons who have yet attempted to make these determinations; and they have proceeded in a manner somewhat different. Mr. Dalton, to whom the honour of the first attempt is due, has endeavoured to determine the relative weights both of simple and compound atoms. (New System of Chemical Philosophy.) Davy, though he has not adopted the atomic theory of Dalton, has embraced the doctrine of definite proportions; and what Dalton calls an atom, he calls a proportion. (Elements of Chemical Philosophy.) Dr. Young, in his Introduction to Medical Literature, has made similar determinations; but what Davy calls proportion, Young calls combining weight. But none of these philosophers have attempted to give any great degree of exactness to their determinations. They have frequently even omitted stating the experiments from which these determinations are derived. The method which they have adopted of giving round numbers, though it facilitates the recollection and calculation, is scarcely consistent with the object of scientific researches, and ought to be rejected: for even supposing that perfect exactness could never be obtained, it is nevertheless the object towards which all our efforts should be directed.

[1][The excerpt includes all of section II from this long paper. Section III and a table of elements from this paper are posted separately. --CJG]

[2]The work of Higgins on Phlogiston is certainly possessed of much merit, and anticipated some of the most striking subsequent discoveries. But, when he wrote, metallic oxides were so little known, and so few exact analyses existed, that it was not possible to be acquainted with the grand fact that oxygen, &c. always unite in determinate proportions which are multiples of the minimum proportion. The atomic theory was taught by Bergman, Cullen, Black, &c., just as far as it was by Higgins. The latter, indeed, states some striking facts respecting the gases, and anticipated Gay-Lussac's theory of volumes; but Mr. Dalton first generalized the doctrine, and thought of determining the weight of the atoms of bodies. He showed me his table of symbols, and the weights of the atoms of six or eight bodies in 1804; and I believe the same year explained the subject in London in a course of lectures delivered in the Royal Institution. The subject could scarcely have been broached sooner. But about the same time several other persons had been struck with the numbers in my table of metallic oxides published in my Chemistry; and the doctrine would have certainly been started by others if Dalton had missed it. --T. [T. is Thomas Thomson, editor of Annals of Philosophy and an early advocate of Dalton's atomic theory. --CJG]

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